variable - Alphabetic character representing a number
-65 times the difference between a number and 79 is equal to the number plus 98-65 times the difference between a number and 79 is equal to the number plus 98
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The first expression, [I]the difference between a number and 79[/I] means we subtract 79 from our arbitrary variable of x:
x - 79
Next, -65 times the difference between a number and 79 means we multiply our result above by -65:
-65(x - 79)
The phrase [I]the number[/I] refers to the arbitrary variable x earlier. The number plus 98 means we add 98 to x:
x + 98
Now, let's bring it all together. The phrase [I]is equal to[/I] means an equation. So we set -65(x - 79) equal to x + [B]98:
-65(x - 79) = x + 98[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=-65%28x-79%29%3Dx%2B98&pl=Solve']type this equation into our search engine[/URL], and you get:
x = [B]76.31818[/B]
1 - n = n - 11 - n = n - 1
Solve for [I]n[/I] in the equation 1 - n = n - 1
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables -n and n. To do that, we subtract n from both sides
-n + 1 - n = n - 1 - n
[SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE]
-2n + 1 = -1
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 1 and -1. To do that, we subtract 1 from both sides
-2n + 1 - 1 = -1 - 1
[SIZE=5][B]Step 4: Cancel 1 on the left side:[/B][/SIZE]
-2n = -2
[SIZE=5][B]Step 5: Divide each side of the equation by -2[/B][/SIZE]
-2n/-2 = -2/-2
n = [B]1
[URL='https://www.mathcelebrity.com/1unk.php?num=1-n%3Dn-1&pl=Solve']Source[/URL][/B]
1/2 of a number decreased by twice a number1/2 of a number decreased by twice a number
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]1/2 of a number: x/2
[*]Twice a number means we multiply x by 2: 2x
[*]The phrase [I]decreased by[/I] means we subtract
[/LIST]
[B]x/2 - 2x[/B]
1/3 a number increased by 10 times by that same number1/3 a number increased by 10 times by that same number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
1/3 a number
1/3 * x = x/3
That same number means the same arbitrary variable as above:
x
10 times that same number:
10x
The phrase [I]increased by[/I] means we add:
[B]x/3 + 10x
[MEDIA=youtube]29TGt3i28jw[/MEDIA][/B]
1/3 of the sum of a number and 2 plus 5 is -201/3 of the sum of a number and 2 plus 5 is -20
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
the sum of a number and 2:
x + 2
1/3 of the sum of a number and 2
1/3(x + 2)
1/3 of the sum of a number and 2 plus 5
1/3(x + 2) + 5
The phrase [I]is[/I] means equal to, so we set 1/3(x + 2) + 5 equal to -20:
[B]1/3(x + 2) + 5 = -20[/B]
1/4 of the difference of 6 and a number is 2001/4 of the difference of 6 and a number is 200
Take this [B]algebraic expression[/B] in 4 parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The difference of 6 and a number means we subtract x from 6: 6 - x
[*]1/4 of the difference means we divide 6 - x by 4: (6 - x)/4
[*]Finally, the phrase [I]is[/I] means an equation, so we set (6 - x)/4 equal to 200
[/LIST]
[B](6 - x)/4 = 200[/B]
10 more than a number z, divided by k10 more than a number z, divided by k
The phrase [I]a number[/I] means an arbitrary variable, lets call it x.
10 more than a number means we add 10 to x:
x + 10
We divide this quantity by k:
[B](x + 10)/k[/B]
10 times a number is 42010 times a number is 420
A number denotes an arbitrary variable, let's call it x.
10 times a number:
10x
The phrase is means equal to, so we set 10x equal to 420
[B]10x = 420 <-- This is our algebraic expression
[/B]
If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=10x%3D420&pl=Solve']equation calculator[/URL]
We get x = 42
12 is multiplied by some number, that product is reduced by 9, and the total is equal to 3712 is multiplied by some number, that product is reduced by 9, and the total is equal to 37
The phrase [I]some number[/I] means an arbitrary variable, let's call it x.
12 multiplied by this number:
12x
The product of 12x is reduced by 9
12x - 9
The phrase [I]the total is equal to[/I] means an equation, so we set 12x - 9 equal to 37:
[B]12x - 9 = 37[/B]
12 plus 6 times a number is 9 times the number12 plus 6 times a number is 9 times the number
The phrase [I]a number [/I]means an arbitrary variable. Let's call it x.
6 times a number is written as:
6x
12 plus 6 times the number means we add 6x to 12:
12 + 6x
9 times a number is written as:
9x
The phrase [I]is[/I] means an equation, so we set 12 + 6x equal to 9x
[B]12 + 6x = 9x <-- This is our algebraic expression[/B]
[B][/B]
If the problem asks you to solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B6x%3D9x&pl=Solve']type this expression into our search engine[/URL] and you get:
x = [B]4[/B]
12 plus the product of 4 and a number is greater than 72A number means an arbitrary variable, let's call it x.
The product of 4 and a number is 4x.
12 plus that product is 4x + 12
Is greater than means an inequality, so we set the entire expression greater than 72
4x + 12 > 72
14 increased by twice Carlos’s age. Use the variable c to represent Carlos age14 increased by twice Carlos’s age. Use the variable c to represent Carlos age
Twice means me multiply a by 2:
2a
14 increased by twice Carlos's age means we add 2a to 14:
[B]14 + 2a[/B]
15 added to a number is 16 times the number15 added to a number is 16 times the number
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]15 added to a number: 15 + x
[*]16 times the number: 16x
[*]The phrase [I]is[/I] means equal to. So we set 15 + x equal to 16x
[/LIST]
[B]15 + x = 16x[/B]
15 added to the quotient of 8 and a number is 7.15 added to the quotient of 8 and a number is 7.
Take this algebraic expression in pieces:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[*]The quotient of 8 and a number: 8/x
[*]15 added to this quotient: 8/x + 15
[*]The word [I]is[/I] means an equation, so we set 8/x + 15 equal to 7
[/LIST]
[B]8/x + 15 = 7[/B]
15 less than a number squared15 less than a number squared
A number is denoted by an arbitrary variable, let's call it x.
x
Squared means we raise that number to a power of 2
x^2
15 less means we subtract
[B]x^2 -15[/B]
16 decreased by 3 times the sum of 3 and a number16 decreased by 3 times the sum of 3 and a number
Take this algebraic expression in parts:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[*]The sum of 3 and a number: 3 + x
[*]3 times the sum: 3(3 + x)
[*]16 decreased by... means we subtract 3(3 + x) from 16
[/LIST]
[B]3(3 + x) from 16[/B]
19 increased by twice Greg’s score use the variable g to represent Greg’s score19 increased by twice Greg’s score use the variable g to represent Greg’s score
Use g for Greg's score
g
Twice g means we multiply g by 2:
2g
19 increased by means we add 2g to 19
[B]2g + 19
[MEDIA=youtube]E9a_U7z-fHE[/MEDIA][/B]
2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than twice a number of home runs the second player hit. how many home runs did each player hit?
Declare variables:
Let the first players home runs be a
Let the second players home runs be b
We're given two equations:
[LIST=1]
[*]a = 2b + 3
[*]a + b = 60
[/LIST]
To solve this system of equations, we substitute equation (1) into equation (2) for a:
2b + 3 + b = 60
Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B3%2Bb%3D60&pl=Solve']type this equation[/URL] in and get:
b = [B]19
[/B]
To solve for a, we substitute b = 19 into equation (1):
a = 2(19) + 3
a = 38 + 3
a = [B]41[/B]
2 less than half a numberA number means we pick an arbitrary variable, let's call it "x".
Half a number is 1/2x.
2 less than that is [B]1/2x - 2[/B]
2 minus 7 times a numberA number is represented by an arbitrary variable, let's call it x.
7 times x means we multiply 7 times x.
7x
2 minus 7x is written:
2 - 7x
2 more than twice the sum of 10 and a number2 more than twice the sum of 10 and a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of 10 and a number means we add x to 10:
10 + x
Twice the sum means we multiply 10 + x by 2:
2(10 + x)
2 more than twice the sum means we add 2 to 2(10 + x):
[B]2(10 + x) + 2[/B]
2 numbers that are equal have a sum of 602 numbers that are equal have a sum of 60
Let's choose 2 arbitrary variables for the 2 numbers
x, y
Were given 2 equations:
[LIST=1]
[*]x = y <-- Because we have the phrase [I]that are equal[/I]
[*]x + y = 60
[/LIST]
Because x = y in equation (1), we can substitute equation (1) into equation (2) for x:
y + y = 60
Add like terms to get:
2y = 60
Divide each side by 2:
2y/2 = 60/2
Cancel the 2's and we get:
y = [B]30
[/B]
Since x = y, x = y = 30
x = [B]30[/B]
2 times a number added to another number is 25. 3 times the first number minus the other number is 22 times a number added to another number is 25. 3 times the first number minus the other number is 20.
Let the first number be x. Let the second number be y. We're given two equations:
[LIST=1]
[*]2x + y = 25
[*]3x - y = 20
[/LIST]
Since we have matching opposite coefficients for y (1 and -1), we can add both equations together and eliminate a variable.
(2 + 3)x + (1 - 1)y = 25 + 20
Simplifying, we get:
5x = 45
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D45&pl=Solve']Typing this equation into the search engine[/URL], we get:
[B]x = 9[/B]
To find y, we plug in x = 9 into equation (1) or (2). Let's choose equation (1):
2(9) + y = 25
y + 18 = 25
[URL='https://www.mathcelebrity.com/1unk.php?num=y%2B18%3D25&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]y = 7[/B]
So we have (x, y) = (9, 7)
Let's check our work for equation (2) to make sure this system works:
3(9) - 7 ? 20
27 - 7 ? 20
20 = 20 <-- Good, we match!
2 times a number equals that number plus 52 times a number equals that number plus 5
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
2 times a number means we multiply 2 by x:
2x
That number plus 5 means we add 5 to the number x
x + 5
The phrase [I]equals[/I] means we set both expressions equal to each other
[B]2x = x + 5[/B] <-- This is our algebraic expression
If you want to take this further and solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3Dx%2B5&pl=Solve']type this expression in the search engine[/URL] and we get:
[B]x = 5[/B]
2 times a number subtracted by x2 times a number subtracted by x
The phrase [I]a number[/I] means an arbitrary variable, let's call it n.
n
2 times a number means we multiply n by 2:
2n
The phrase [I]subtracted by[/I] means we subtract 2n from x:
[B]x - 2n[/B]
2 times half of a numberA number means an arbitrary variable, let's call it x.
Half of x means we divide x by 2, or multiply by 0.5
x/2
2 times half x is written:
[B]2(x/2)[/B]
If we simplify by cancelling the 2's, we just get x.
2 times the sum of 1 and some number is 30. What is the number?2 times the sum of 1 and some number is 30. What is the number?
We let the phrase "some number" equal the variable x.
The sum of 1 and some number is:
x + 1
2 times the sum:
2(x + 1)
The word "is" means equal to, so we set [B]2(x + 1) = 30[/B]
2 times the sum of 7 times a number and 42 times the sum of 7 times a number and 4
This is an algebraic expression. Let's take it in 4 parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]7 times a number means we multiply x by 7: 7x
[*]The sum of 7 times a number and 4 means we add 4 to 7x: 7x + 4
[*]Finally, we multiply the sum in #3 by 2
[/LIST]
Build our final algebraic expression:
[B]2(7x + 4)[/B]
2 times the sum of a number and 3 is equal to 3x plus 42 times the sum of a number and 3 is equal to 3x plus 4
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 3 means we add 3 to x:
x + 3
2 times this sum means we multiply the quantity x + 3 by 2
2(x + 3)
3x plus 4 means 3x + 4 since the word plus means we use a (+) sign
3x + 4
The phrase [I]is equal to[/I] means an equation, where we set 2(x + 3) equal to 3x + 4
[B]2(x + 3) = 3x + 4[/B]
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2/3 of a number 17 is at least 292/3 of a number 17 is at least 29
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
2/3 of a number means we multiply x by 2/3:
2x/3
The phrase [I]is at least[/I] also means greater than or equal to, so we set up the inequality:
[B]2x/3 >= 29[/B]
2/5 the cube of a number2/5 the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The cube of a number means we raise x to the power of 3:
x^3
2/5 of the cube means we multiply x^3 by 2/5:
[B](2x^3)/5[/B]
217 times u, reduced by 180 is the same as q217 times u, reduced by 180 is the same as q.
Take this algebraic expression pieces:
Step 1: 217 times u
We multiply the variable u by 217
217u
Step 2: reduced by 180
Subtract 180 from 217u
217u - 180
The phrase [I]is the same as[/I] means an equation, so we set 217u - 180 equal to q
[B]217u - 180 = q[/B]
26 increased by 12 times a number26 increased by 12 times a number
A number is represented by an arbitrary variable, let's call it x
12 times a number is written as 12x
26 increased by 12 times a number means we add:
[B]26 + 12x[/B]
28 less than twice a number[U]A number means an arbitrary variable, let's call it x.[/U]
[LIST]
[*]x
[/LIST]
[U]Twice a number means multiply by 2[/U]
[LIST]
[*]2x
[/LIST]
[U]28 less than twice a number means we subtract 28[/U]
[LIST]
[*][B]2x - 28[/B]
[/LIST]
2n + 1 = n + 102n + 1 = n + 10
Solve for [I]n[/I] in the equation 2n + 1 = n + 10
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 2n and n. To do that, we subtract n from both sides
2n + 1 - n = n + 10 - n
[SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE]
n + 1 = 10
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 1 and 10. To do that, we subtract 1 from both sides
n + 1 - 1 = 10 - 1
[SIZE=5][B]Step 4: Cancel 1 on the left side:[/B][/SIZE]
n = [B]9[/B]
2n + 10 = 3n + 52n + 10 = 3n + 5
Solve for [I]n[/I] in the equation 2n + 10 = 3n + 5
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 2n and 3n. To do that, we subtract 3n from both sides
2n + 10 - 3n = 3n + 5 - 3n
[SIZE=5][B]Step 2: Cancel 3n on the right side:[/B][/SIZE]
-n + 10 = 5
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 10 and 5. To do that, we subtract 10 from both sides
-n + 10 - 10 = 5 - 10
[SIZE=5][B]Step 4: Cancel 10 on the left side:[/B][/SIZE]
-n = -5
[SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE]
-1n/-1 = -5/-1
n = [B]5[/B]
2n = 4n2n = 4n
Solve for [I]n[/I] in the equation 2n = 4n
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 2n and 4n. To do that, we subtract 4n from both sides
2n - 4n = 4n - 4n
[SIZE=5][B]Step 2: Cancel 4n on the right side:[/B][/SIZE]
-2n = 0
[SIZE=5][B]Step 3: Divide each side of the equation by -2[/B][/SIZE]
-2n/-2 = 0/-2
n = [B]0[/B]
2x increased by 3 times a number2x increased by 3 times a number
The phrase [I]a number[/I] means an arbitary variable, let's call it x.
3 times a number means we multiply x by 3:
3x
The phrase [I]increased by[/I] means we add 3x to 2x:
2x + 3x
Simplifying, we get:
[B]5x[/B]
3 decreased by 7 times a number3 decreased by 7 times a number
A number signifies an arbitrary variable, let's call it x.
7 times a number:
7x
3 decreased by this means we subtract 7x
[B]3 - 7x[/B]
3 is subtracted from square of a number3 is subtracted from square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Square of a number means we raise x to the 2nd power:
x^2
3 is subtracted from square of a number
[B]x^2 - 3[/B]
3 less than a number times itself3 less than a number times itself
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Itself means the same variable as above. So we have:
x * x
x^2
3 less than this means we subtract 3 from x^2:
[B]x^2 - 3[/B]
3 times a number increased by 1 is between -8 and 133 times a number increased by 1 is between -8 and 13.
Let's take this algebraic expression in [U]4 parts[/U]:
Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Part 2 - 3 times this number means we multiply x by 3:
3x
Part 3 - Increased by 1 means we add 1 to 3x:
3x + 1
The phrase [I]between[/I] means we have an inequality:
[B]-8 <= 3x + 1 <=13[/B]
3 times a number is 3 more a number3 times a number is 3 more a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
3 times a number:
3x
3 more than a number means we add 3 to x:
x + 3
The word [I]is[/I] means and equation, so we set 3x equal to x + 3
[B]3x = x + 3[/B]
30 increased by 3 times the square of a numberLet "a number" equal the arbitrary variable x.
The square of that is x^2.
3 times the square of that is 3x^2.
Now, 30 increased by means we add 3x^2 to 30
30 + 3x^2
30 increased by 3 times the square of a number30 increased by 3 times the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The square of a number means we raise x to the power of 2:
x^2
3 times the square:
3x^2
The phrase [I]increased by[/I] means we add 3x^2 to 30:
[B]30 + 3x^2[/B]
324 times z, reduced by 12 is z324 times z, reduced by 12 is z.
Take this algebraic expression in pieces:
324 [I]times[/I] z means we multiply 324 by the variable z.
324z
[I]Reduced by[/I] 12 means we subtract 12 from 324z
324z - 12
The word [I]is[/I] means we have an equation, so we set 324z - 12 equal to z
[B]324z - 12 = z [/B] <-- This is our algebraic expression
3abc^4/12a^3(b^3c^2)^2 * 8ab^-4c/4a^2b3abc^4/12a^3(b^3c^2)^2 * 8ab^-4c/4a^2b
Expand term 1:
3abc^4/12a^3(b^3c^2)^2
3abc^4/12a^3b^6c^4
Now simplify term 1:
3/12 = 1/4
c^4 terms cancel
Subtract powers from variables since the denominator powers are higher:
b^(6 - 1) = b^5
a^(3 - 1) = a^2
1/4a^2b^5
Now simplify term 2:
8ab^-4c/4a^2b
8/4 = 2
2c/a^(2 - 1)b^(1 - -4)
2c/ab^5
Now multiply simplified term 1 times simplified term 2:
1/4a^2b^5 * 2c/ab^5
(1 * 2c)/(4a^2b^5 * ab^5)
2c/4a^(2 + 1)b^(5 + 5)
2c/4a^3b^10
2/4 = 1/2, so we have:
[B]c/2a^3b^10[/B]
3f,subtract g from the result, then divide what you have by h3f,subtract g from the result, then divide what you have by h
Take this algebraic expression in pieces:
3f subtract g means we subtract the variable g from the expression 3f:
3f - g
Divide what we have by h, means we take the result above, 3f - g, and divide it by h:
[B](3f - g)/h[/B]
4 times a number added to 8 times a number equals 364 times a number added to 8 times a number equals 36
Let [I]a number[/I] be an arbitrary variable, let us call it x.
4 times a number:
4x
8 times a number:
8x
We add these together:
4x + 8x = 12x
We set 12x equal to 36 to get our final algebraic expression of:
[B]12x = 36
[/B]
If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/1unk.php?num=12x%3D36&pl=Solve']type this algebraic expression into our search engine[/URL] and get:
x = [B]3[/B]
4 times a number cubed decreased by 74 times a number cubed decreased by 7
A number is denoted as an arbitrary variable, let's call it x
x
Cubed means raise x to the third power
x^3
Decreased by 7 means subtract 7
x^3 - 7
4 times a number is the same as the number increased by 784 times a number is the same as the number increased by 78.
Let's take this algebraic expression in parts:
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]4 times a number is written as 4x
[*]The number increased by 78 means we add 78 to x: x + 78
[*]The phrase [I]the same as[/I] mean an equation, so we set #2 equal to #3
[/LIST]
[B]4x = x + 78[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further, then [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3Dx%2B78&pl=Solve']we type this equation into our search engine [/URL]and get:
x = 26
4 times a number plus 9A number means an arbitrary variable, let's call it "x".
4 times a number is 4x.
Plus 9 means we add:
4x + 9
4 times b increased by 9 minus twice y4 times b increased by 9 minus twice y
Take this algebraic expression in parts:
Step 1: 4 times b means we multiply the variable b by 4:
4b
Step 2: Increased by 9 means we add 9 to 4b:
4b + 9
Step 3: Twice y means we multiply the variable y by 2:
2y
Step 4: The phrase [I]minus[/I] means we subtract 2y from 4b + 9
[B]4b + 9 - 2y[/B]
4 times the difference of 6 times a number and 74 times the difference of 6 times a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times a number
6x
The difference of 6x and 7 means we subtract 7 from 6x:
6x - 7
Now we multiply this difference by 4:
[B]4(6x - 7)[/B]
4 times the quantity of a number plus 64 times the quantity of a number plus 6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The word [I]plus[/I] means we addd 6 to x
x + 6
The phrase [I]4 times the quantity [/I]means we multiply x + 6 by 4
[B]4(x + 6)[/B]
4n - 8 = n + 14n - 8 = n + 1
Solve for [I]n[/I] in the equation 4n - 8 = n + 1
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4n and n. To do that, we subtract n from both sides
4n - 8 - n = n + 1 - n
[SIZE=5][B]Step 2: Cancel n on the right side:[/B][/SIZE]
3n - 8 = 1
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants -8 and 1. To do that, we add 8 to both sides
3n - 8 + 8 = 1 + 8
[SIZE=5][B]Step 4: Cancel 8 on the left side:[/B][/SIZE]
3n = 9
[SIZE=5][B]Step 5: Divide each side of the equation by 3[/B][/SIZE]
3n/3 = 9/3
n = [B]3[/B]
4subtractedfrom6timesanumberis324 subtracted from 6 times a number is 32.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
6 times this number means we multiply by x by 6
6x
4 subtracted from this expression means we subtract 4
6x - 4
The phrase [I]is[/I] means an equation, so we set 6x - 4 equal to 32
[B]6x - 4 = 32
[/B]
If you need to solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=6x-4%3D32&pl=Solve']type it in the search engine here[/URL].
5 more than the reciprocal of a number5 more than the reciprocal of a number
Take this algebraic expression in pieces:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of this number means we divide 1 over x:
1/x
5 more means we add 5 to 1/x
[B]1/x + 5[/B]
5 more than twice the cube of a number5 more than twice the cube of a number.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The cube of a number means we raise it to a power of 3
x^3
Twice the cube of a number means we multiply x^3 by 2
2x^3
5 more than twice the cube of a number means we multiply 2x^3 by 5
5(2x^3)
Simplifying, we get:
10x^3
5 more than twice the cube of a number5 more than twice the cube of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The cube of a number means we raise x to the power of 3:
x^3
Twice the cube means we multiply x^3 by 2
2x^3
Finally, 5 more than twice the cube means we add 5 to 2x^3:
[B]2x^3 + 5[/B]
5 squared minus a number x5 squared minus a number x
5 squared is written as 5^2
Minus a number x means we subtract the variable x
[B]5^2 - x[/B]
5 subtracted from 3 times a number is 445 subtracted from 3 times a number is 44.
The problem asks for an algebraic expression.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
3 times this number is 3x.
5 subtracted from this is written as 3x - 5.
The phrase [I]is[/I] means an equation, so we set 3x - 5 equal to 44
[B]3x - 5 = 44[/B]
5 times a number increased by 135 times a number increased by 13
A number is denoted as an arbitrary variable, let's call it x
x
5 times that number
5x
Increased by 13 means we add
5x + 13
5 times a number increased by 4 is divided by 6 times the same number5 times a number increased by 4 is divided by 6 times the same number
Take this algebraic expression in parts.
Part 1: 5 times a number increased by 4
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x
[*]5 times the number means multiply x by 5: 5x
[*][I]Increased by 4[/I] means we add 4 to 5x: 5x + 4
[/LIST]
Part 2: 6 times the same number
[LIST]
[*]From above, [I]a number[/I] is x: x
[*]6 times the number means we multiply x by 6: 6x
[/LIST]
The phrase [I]is divided by[/I] means we have a quotient, where 5x + 4 is the numerator, and 6x is the denominator.
[B](5x + 4)/6x[/B]
5 times a number is 4 more than twice a number5 times a number is 4 more than twice a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
5 times a number:
5x
Twice a number means we multiply x by 2:
2x
4 more than twice a number
2x + 4
The word [I]is[/I] means equal to, so we set 5x equal to 2x + 4
[B]5x = 2x + 4[/B]
5 times a number is that number minus 35 times a number is that number minus 3
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
[LIST]
[*]5 times a number: 5x
[*]That number means we use the same number from above which is x
[*]That number minus 3: x - 3
[*]The phrase [I]is[/I] means an equation, so we set 5x equal to x - 3
[/LIST]
[B]5x = x - 3[/B]
5 times the product of 2 numbers a and b5 times the product of 2 numbers a and b
The product of 2 numbers a and be means we multiply the variables together:
ab
5 times the product means we multiply ab by 5:
[B]5ab[/B]
5 times the sum of 3 times a number and -55 times the sum of 3 times a number and -5
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
3 times a number means we multiply x by 3:
3x
the sum of 3 times a number and -5 means we add -5 to 3x:
3x - 5
5 times the sum means we multiply 3x - 5 by 5:
[B]5(3x - 5)[/B]
50 is more than the product of 4 and w50 is more than the product of 4 and w
Take this algebraic expression in pieces:
The product of 4 and w mean we multiply the variable w by 4:
4w
The phrase [I]is more than[/I] means an inequality using the (>) sign, where 50 is greater than 4w:
[B]50 > 4w[/B]
51 decreased by twice a numberA number is denoted as an arbitrary variable, let's call it x.
Twice a number means we multiply by 2, so 2x.
51 decreased by twice a number means we subtract 2x from 51
[B]51 - 2x
[MEDIA=youtube]xqZzYvxmj5w[/MEDIA][/B]
54 is the sum of 24 and Julies score. Use the variable J to represent Julies score.54 is the sum of 24 and Julies score. Use the variable J to represent Julies score.
Sum of 24 and Julie's score:
24 + J
The phrase [I]is[/I] means an equation, so we set 24 + J equal to 54 to get an algebraic expression:
[B]24 + J = 54[/B]
56 is the sum of 20 and Donnie's savings. Use the variable d to represent Donnie's savings56 is the sum of 20 and Donnie's savings. Use the variable d to represent Donnie's savings
The sum of 20 and Donnie's savings using [I]d[/I] to represent Donnie's savings:
20 + d
The word [I]is[/I] means equal to, so we set 20 + d equal to 56:
[B]20 + d = 56[/B]
59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.
The phrase [I]the sum of[/I] means we add Donnie's savings of d to 16:
d + 16
The phrase [I]is[/I] means an equation, so we set d + 16 equal to 59
d + 16 = 59 <-- [B]This is our algebraic expression[/B]
Now, if the problem asks you to solve for d, then you[URL='https://www.mathcelebrity.com/1unk.php?num=d%2B16%3D59&pl=Solve'] type the algebraic expression into our search engine to get[/URL]:
d = [B]43[/B]
6 is divided by square of a number6 is divided by square of a number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
x
the square of this means we raise x to the power of 2:
x^2
Next, we divide 6 by x^2:
[B]6/x^2[/B]
6 plus twice the sum of a number and 7.6 plus twice the sum of a number and 7.
The phrase [I]a number[/I] mean an arbitrary variable, let's call it x.
The sum of a number and 7 means we add 7 to the variable x.
x + 7
Twice the sum means we multiply the sum by 2:
2(x + 7)
6 plus means we add 6 to 2(x + 7)
[B]6 + 2(x + 7)[/B]
6 subtracted from the product of 5 and a number is 686 subtracted from the product of 5 and a number is 68
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The product of 5 and this number is:
5x
We subtract 6 from 5x:
5x - 6
The phrase [I]is[/I] means an equation, so we set 5x - 6 equal to 68
[B]5x - 6 = 68[/B]
6 times a number multiplied by 3 all divided by 46 times a number multiplied by 3 all divided by 4
Take this algebraic expression in parts:
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]6 times a number: 6x
[*]Multiplied by 3: 3(6x) = 18x
[*]All divided by 4: 18x/4
[/LIST]
We can simplify this:
We type 18/4 into our search engine, simplify, and we get 9/2. So our answer is:
[B]9x/2[/B]
6 times j squared minus twice j squared6 times j squared minus twice j squared
j squared means we raise the variable j to the power of 2:
j^2
6 times j squared means we multiply j^2 by 6:
6j^2
Twice j squared means we multiply j^2 by 2:
2j^2
The word [I]minus[/I] means we subtract 2j^2 from 6j^2
6j^2 - 2j^2
So if you must simplify, we group like terms and get:
(6 - 2)j^2
[B]4j^2[/B]
6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number6 times the reciprocal of a number equals 2 times the reciprocal of 7. What is the number
We've got two algebraic expressions here. Let's take it in parts:
Term 1:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The reciprocal is 1/x
Multiply this by 6: 6/x
Term 2:
Reciprocal of 7: 1/7
2 times this: 2/7
We set these terms equal to each other:
6/x = 2/7
[URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=2&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']Type this proportion into the search engine[/URL], and we get:
[B]x = 21[/B]
6 times the reciprocal of a number equals 3 times the reciprocal of 7 .6 times the reciprocal of a number equals 3 times the reciprocal of 7 .
This is an algebraic expression. Let's take it in parts:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of a number x means we divide 1 over x:
1/x
6 times the reciprocal means we multiply 6 by 1/x:
6/x
The reciprocal of 7 means we divide 1/7
1/7
3 times the reciprocal means we multiply 1/7 by 3:
3/7
Now, the phrase [I]equals[/I] mean an equation, so we set 6/x = 3/7
[B]6/x = 3/7[/B] <-- This is our algebraic expression
If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=3&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion in our search engine[/URL] and get:
x = 14
6 times the sum of a number and 3 is equal to 42. What is this number?6 times the sum of a number and 3 is equal to 42. What is this number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The sum of a number and 3 means we add 3 to x:
x + 3
6 times the sum:
6(x + 3)
The word [I]is[/I] means an equation, so we set 6(x + 3) equal to 42 to get our [I]algebraic expression[/I] of:
[B]6(x + 3) = 42[/B]
[B][/B]
If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/1unk.php?num=6%28x%2B3%29%3D42&pl=Solve']you type this equation into our search engine[/URL] and you get:
x = [B]4[/B]
6 times the sum of a number and 5 is 166 times the sum of a number and 5 is 16
A number represents an arbitrary variable, let's call it x
x
The sum of x and 5
x + 5
6 times the sum of x and 5
6(x + 5)
Is means equal to, so set 6(x + 5) equal to 16
[B]6(x + 5) = 16 <-- This is our algebraic expression
Solve for x[/B]
Multiply through:
6x + 30 = 16
Subtract 30 from each side:
6x - 30 + 30 = 16 - 30
6x = -14
Divide each side by 6
6x/6 = -14/6
Simplify this fraction by dividing top and bottom by 2:
x = [B]-7/3
[MEDIA=youtube]oEx5dsYK7DY[/MEDIA][/B]
60 is the sum of 22 and Helenas height. Use the variable h to represent Helenas height.60 is the sum of 22 and Helenas height. Use the variable h to represent Helenas height.
If height is represented by h, we have: 22 and h
22 + h
When they say "is the sum of", we set 22 + h equal to 60
[B]22 + h = 60[/B]
60 percent of a number minus 17 is -6560 percent of a number minus 17 is -65
Using our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=60&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percent to decimal calculator[/URL], we see that 60% is 0.6, so we have:
0.6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So 60% of a number is:
0.6x
Minus 17:
0.6x - 17
The word [I]is[/I] means an equation, so we set 0.6x - 17 equal to -65 to get our algebraic expression of:
[B]0.6x - 17 = -65[/B]
[B][/B]
If you want to solve for x in this equation, you [URL='https://www.mathcelebrity.com/1unk.php?num=0.6x-17%3D-65&pl=Solve']type it in our search engine and you get[/URL]:
[B]x = -80[/B]
7 is 1/4 of some number7 is 1/4 of some number
The phrase [I]some number[/I] means an arbitrary variable, let's call it x.
1/4 of this is written as:
x/4
The word [I]is[/I] means an equation, so we set x/4 equal to 7:
[B]x/4 = 7[/B]
7 minus a number all divided by 47 minus a number all divided by 4
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
7 minus a number
7 - x
All divided by 4:
[B](7 - x)/4[/B]
7 plus the quantity of 9 increased by a number7 plus the quantity of 9 increased by a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
9 increased by a number means we add 9 to x
9 + x
7 plus this quantity means we add (9 + x) to 7
[B]7 + (9 + x)[/B]
7 times a number and 2 is equal to 4 times a number decreased by 87 times a number and 2 is equal to 4 times a number decreased by 8
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
7 times a number:
7x
and 2 means we add 2:
7x + 2
4 times a number
4x
decreased by 8 means we subtract 8:
4x - 8
The phrase [I]is equal to[/I] means an equation, so we set 7x + 2 equal to 4x - 8:
[B]7x + 2 = 4x - 8[/B]
7 times a number increased by 4 times the number7 times a number increased by 4 times the number
Let [I]a number[/I] and [I]the number[/I] be an arbitrary variable. Let's call it x. We have an algebraic expression. Let's take it in pieces:
[LIST]
[*]7 times a number: 7x
[*]4 times the number: 4x
[*]The phrase [I]increased by[/I] means we add 4x to 7x:
[*]7x + 4x
[*]Simplifying, we get: (7 + 4)x
[*][B]11x[/B]
[/LIST]
7 times a number is the same as 12 more than 3 times a number7 times a number is the same as 12 more than 3 times a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[B][U]Algebraic Expression 1:[/U][/B]
7 times a number means we multiply 7 by x:
7x
[B][U]Algebraic Expression 2:[/U][/B]
3 times a number means we multiply 3 by x:
3x
12 more than 3 times a number means we add 12 to 3x:
3x + 12
The phrase [I]is the same as[/I] means an equation, so we set 7x equal to 3x + 12
[B]7x = 3x + 12[/B] <-- Algebraic Expression
7 times the quantity of 3 times a number reduced by 107 times the quantity of 3 times a number reduced by 10
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
3 times a number:
3x
Reduced by 10 means we subtract 10:
3x - 10
7 times this quantity:
[B]7(3x - 10)[/B]
76 decreased by twice a number. Use the variable n to represent the unknown number76 decreased by twice a number. Use the variable n to represent the unknown number.
Twice a number (n) means we multiply the unknown number n by 2:
2n
76 decreased by twice a number means we subtract 2n from 76 using the (-) operator
[B]76 - 2n[/B]
76 subtracted from p is equal to the total of g and 22776 subtracted from p is equal to the total of g and 227
We've got two algebraic expressions. Take them in pieces:
Part 1:
76 subtracted from p
We subtract 76 from the variable p
p - 76
Part 2:
The total of g and 227
The total means a sum, so we add 227 to g
g + 227
Now the last piece, the phrase [I]is equal to[/I] means an equation. So we set both algebraic expressions equal to each other:
[B]p - 76 = g + 227[/B]
8 increased by the product of a number and 7 is greater than or equal to -18Take this in parts:
First, the phrase, "a number" means we pick an arbitrary variable, let's call it x.
The product of a number and 7 is 7x.
8 increased by the product of 7x means we add them together.
7x + 8
Finally that entire expression is greater than [U]or equal to[/U] -18
[B]7x + 8 >=-18[/B]
8 is subtracted from thrice a numberThrice a number means we multiply by 3. A number means an arbitrary variable, let's call it x
3x
8 is subtracted from 3x
[B]3x - 8[/B]
8 is subtracted from twice a numberTwice a number:
[LIST]
[*]Choose an arbitrary variable, let's call it x
[*]Twice x means multiply by 2
[*]2x
[/LIST]
8 subtracted from 2x:
[B]2x - 8[/B]
8 more than twice a number is less than 6 more than the number8 more than twice a number is less than 6 more than the number.
This is an algebraic expression, let's take it in pieces...
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
8 more than twice a number:
Twice a number means multiply x by 2: 2x
Then add 8: 2x + 8
6 more than the number, means we add 6 to x
x + 6
The phrase [I]is less than[/I] means an inequality, where we set 2x + 8 less than x + 6
[B]2x + 8 < x + 6[/B]
8 times the sum of 5 times a number and 98 times the sum of 5 times a number and 9
Take this algebraic expression in parts:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
5 times a number means:
5x
The sum of this and 9 means we add 9 to 5x:
5x + 9
Now we multiply 8 times this sum:
[B]8(5x + 9)[/B]
9 is the sum of 7 and twice a number9 is the sum of 7 and twice a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Twice a number means we multiply x by 2:
2x
The sum of 7 and twice a number
7 + 2x
The word [I]is[/I] mean equal to, so we set 7 + 2x equal to 9:
[B]7 + 2x = 9[/B]
9 less than 5 times a number is 3 more than 2x9 less than 5 times a number is 3 more than 2x
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
5 times a number means we multiply x by 5:
5x
9 less than 5x means we subtract 9 from 5x:
5x - 9
3 more than 2x means we add 3 to 2x:
2x + 3
The word [I]is[/I] means an equation, so we set 5x - 9 equal to 2x + 3:
[B]5x - 9 = 2x + 3 <-- This is our algebraic expression[/B]
[B][/B]
If you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-9%3D2x%2B3&pl=Solve']type this equation into the search engine[/URL], and we get:
x = [B]4[/B]
9 subtracted from the product of 3 and a number is greater than or equal to 169 subtracted from the product of 3 and a number is greater than or equal to 16
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The product of 3 and a number means we multiply 3 times x: 3x
[*]9 subtracted from the product: 3x - 9
[*]The phrase is greater than or equal to means an inequality. So we set up an inequality with >= for the greater than or equal to sign in relation to 3x - 9 and 16
[/LIST]
Our algebraic expression (inequality) becomes:
[B]3x - 19 >= 16[/B]
9 times a number is that number minus 109 times a number is that number minus 10
The phrase [I]a number[/I] means we define a random/arbitrary variable, let's call it x:
x
9 times a number means we multiply x by 9:
9x
The phrase [I]that number[/I] refers back to the original arbitrary variable we defined above, which is x:
x
That number minus 10 means we subtract 10 from x:
x - 10
The word [I]is[/I] means equal to, so we set 9x equal to x - 10
[B]9x = x - 10[/B]
9 times a number is that number minus 39 times a number is that number minus 3
Let [I]a number[/I] be an arbitrary variable, let's call it x. We're given:
9 times a number is 9x
The number minus 3 is x - 3
The word [I]is[/I] means an equation, so we set 9x equal to x - 3 to get our [I]algebraic expression[/I]:
[B]9x = x - 3[/B]
To solve for x, we type this equation into our search engine and we get:
x = [B]-0.375 or -3/8[/B]
A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the otA 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the other. How long should the pieces be?
The key phrase in this problem is [B]two pieces[/B].
Declare Variables:
[LIST]
[*]Let the short piece length be s
[*]Let the long piece length be l
[/LIST]
We're given the following
[LIST=1]
[*]s = l - 10
[*]s + l = 98 (Because the two pieces add up to 98)
[/LIST]
Substitute equation (1) into equation (2) for s:
l - 10+ l = 98
Group like terms:
2l - 10 = 98
Solve for [I]l[/I] in the equation 2l - 10 = 98
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants -10 and 98. To do that, we add 10 to both sides
2l - 10 + 10 = 98 + 10
[SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE]
2l = 108
[SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE]
2l/2 = 108/2
l = [B]54[/B]
To solve for s, we substitute l = 54 into equation (1):
s = 54 - 10
s = [B]44[/B]
Check our work:
The shorter piece is 10 inches shorter than the longer piece since 54 - 44 = 10
Second check: Do both pieces add up to 98
54 + 44 ? 98
98 = 98
A bakery has a fixed cost of $119.75 per a day plus $2.25 for each pastry. The bakery would like toA bakery has a fixed cost of $119.75 per a day plus $2.25 for each pastry. The bakery would like to keep its daily costs at or below $500 per day. Which inequality shows the maximum number of pastries, p, that can be baked each day.
Set up the cost function C(p), where p is the number of pastries:
C(p) = Variable Cost + Fixed Cost
C(p) = 2.25p + 119.75
The problem asks for C(p) at or below $500 per day. The phrase [I]at or below[/I] means less than or equal to (<=).
[B]2.25p + 119.75 <= 500[/B]
a bicycle store costs $3600 per month to operate. The store pays an average of $60 per bike. the avea bicycle store costs $3600 per month to operate. The store pays an average of $60 per bike. the average selling price of each bicycle is $100. how many bicycles must the store sell each month to break even?
Cost function C(b) where b is the number of bikes:
C(b) = Variable Cost + Fixed Cost
C(b) = Cost per bike * b + operating cost
C(b) = 60b + 3600
Revenue function R(b) where b is the number of bikes:
R(b) = Sale price * b
R(b) = 100b
Break Even is when Cost equals Revenue, so we set C(b) = R(b):
60b + 3600 = 100b
To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B3600%3D100b&pl=Solve']type it in our math engine[/URL] and we get:
b = [B]90[/B]
A book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The booksA book publishing company has fixed costs of $180,000 and a variable cost of $25 per book. The books they make sell for $40 each.
[B][U]Set up Cost Function C(b) where b is the number of books:[/U][/B]
C(b) = Fixed Cost + Variable Cost x Number of Units
C(b) = 180,000 + 25(b)
[B]Set up Revenue Function R(b):[/B]
R(b) = 40b
Set them equal to each other
180,000 + 25b = 40b
Subtract 25b from each side:
15b = 180,000
Divide each side by 15
[B]b = 12,000 for break even[/B]
A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat.A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat. They sell boats for $75 a piece. How many boats must be sold each month to break even?
[U]Set up Cost function C(b) where t is the number of tapestries:[/U]
C(b) = Cost per boat * number of boats + Fixed Cost
C(b) = 50b + 1500
[U]Set up Revenue function R(b) where t is the number of tapestries:[/U]
R(b) = Sale Price * number of boats
R(b) = 75b
[U]Break even is where Revenue equals Cost, or Revenue minus Cost is 0, so we have:[/U]
R(b) - C(b) = 0
75b - (50b + 1500) = 0
75b - 50b - 1500 = 0
25b - 1500 = 0
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-1500%3D0&pl=Solve']type this equation in our math engine[/URL] and we get:
b = [B]60[/B]
A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each lA company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each lamp, and the selling price is $150 per lamp.
Set up the Cost Equation C(l) where l is the price of each lamp:
C(l) = Variable Cost x l + Fixed Cost
C(l) = 90l + 1800
Determine the revenue function R(l)
R(l) = 150l
Determine the profit function P(l)
Profit = Revenue - Cost
P(l) = 150l - (90l + 1800)
P(l) = 150l - 90l - 1800
[B]P(l) = 60l - 1800[/B]
Determine the break even point:
Breakeven --> R(l) = C(l)
150l = 90l + 1800
[URL='https://www.mathcelebrity.com/1unk.php?num=150l%3D90l%2B1800&pl=Solve']Type this into the search engine[/URL], and we get [B]l = 30[/B]
A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixeA corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000?
[U]Set up the cost function C(t) where t is the number of tons of cattle feed:[/U]
C(t) = Variable Cost * t + Fixed Costs
C(t) = 84t + 110000
[U]Set up the revenue function R(t) where t is the number of tons of cattle feed:[/U]
R(t) = Sale Price * t
R(t) = 132t
[U]Set up the profit function P(t) where t is the number of tons of cattle feed:[/U]
P(t) = R(t) - C(t)
P(t) = 132t - (84t + 110000)
P(t) = 132t - 84t - 110000
P(t) = 48t - 110000
[U]The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:[/U]
48t - 110000 = 560000
[U]To solve for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=48t-110000%3D560000&pl=Solve']type this equation into our search engine[/URL] and we get:[/U]
t =[B] 13,958.33
If the problem asks for whole numbers, we round up one ton to get 13,959[/B]
A first number plus twice a second number is 10. Twice the first number plus the second totals 35. FA first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers.
[U]The phrase [I]a number[/I] means an arbitrary variable[/U]
A first number is written as x
A second number is written as y
[U]Twice a second number means we multiply y by 2:[/U]
2y
[U]A first number plus twice a second number:[/U]
x + 2y
[U]A first number plus twice a second number is 10 means we set x + 2y equal to 10:[/U]
x + 2y = 10
[U]Twice the first number means we multiply x by 2:[/U]
2x
[U]Twice the first number plus the second:[/U]
2x + y
[U]Twice the first number plus the second totals 35 means we set 2x + y equal to 35:[/U]
2x + y = 35
Therefore, we have a system of two equations:
[LIST=1]
[*]x + 2y = 10
[*]2x + y = 35
[/LIST]
Since we have an easy multiple of 2 for the x variable, we can solve this by multiply the first equation by -2:
[LIST=1]
[*]-2x - 4y = -20
[*]2x + y = 35
[/LIST]
Because the x variables are opposites, we can add both equations together:
(-2 + 2)x + (-4 + 1)y = -20 + 35
The x terms cancel, so we have:
-3y = 15
To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D15&pl=Solve']type it in our search engine[/URL] and we get:
y = [B]-5
[/B]
Now we substitute this y = -5 into equation 2:
2x - 5 = 35
To solve this equation for x, we[URL='https://www.mathcelebrity.com/1unk.php?num=2x-5%3D35&pl=Solve'] type it in our search engine[/URL] and we get:
x = [B]20[/B]
A gym membership has a $50 joining fee plus charges $17 a month for m monthsA gym membership has a $50 joining fee plus charges $17 a month for m months
Build a cost equation C(m) where m is the number of months of membership.
C(m) = Variable Cost * variable units + Fixed Cost
C(m) = Months of membership * m + Joining Fee
Plugging in our numbers and we get:
[B]C(m) = 17m + 50
[MEDIA=youtube]VGXeqd3ikAI[/MEDIA][/B]
A half is a third of it. What is it?A half is a third of it. What is it?
Let "it" be an arbitrary variable, let's call it x.
A third of 'it' means we divide x/3
The word is means equals, so we have:
x/3 = 1/2
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=x&num2=1&den1=3&den2=2&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
x = [B]1.5 or 3/2 or 1 & 1/2
[MEDIA=youtube]cCXyryWpHV0[/MEDIA][/B]
A local Dunkin’ Donuts shop reported that its sales have increased exactly 16% per year for the lastA local Dunkin’ Donuts shop reported that its sales have increased exactly 16% per year for the last 2 years. This year’s sales were $80,642. What were Dunkin' Donuts' sales 2 years ago?
Declare variable and convert numbers:
[LIST]
[*]16% = 0.16
[*]let the sales 2 years ago be s.
[/LIST]
s(1 + 0.16)(1 + 0.16) = 80,642
s(1.16)(1.16) = 80,642
1.3456s = 80642
Solve for [I]s[/I] in the equation 1.3456s = 80642
[SIZE=5][B]Step 1: Divide each side of the equation by 1.3456[/B][/SIZE]
1.3456s/1.3456 = 80642/1.3456
s = 59930.142687277
s = [B]59,930.14[/B]
A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for childrenA man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket?
Declare variables:
[LIST]
[*]Let a be the number of adult's tickets
[*]Let c be the number of children's tickets
[/LIST]
Cost = Price * Quantity
We're given two equations:
[LIST=1]
[*]a + c = 20
[*]15a + 10c = 225
[/LIST]
Rearrange equation (1) in terms of a:
[LIST=1]
[*]a = 20 - c
[*]15a + 10c = 225
[/LIST]
Now that I have equation (1) in terms of a, we can substitute into equation (2) for a:
15(20 - c) + 10c = 225
Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225
We first need to simplify the expression removing parentheses
Simplify 15(20 - c): Distribute the 15 to each term in (20-c)
15 * 20 = (15 * 20) = 300
15 * -c = (15 * -1)c = -15c
Our Total expanded term is 300-15c
Our updated term to work with is 300 - 15c + 10c = 225
We first need to simplify the expression removing parentheses
Our updated term to work with is 300 - 15c + 10c = 225
[SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE]
(-15 + 10)c = -5c
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
-5c + 300 = + 225
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 300 and 225. To do that, we subtract 300 from both sides
-5c + 300 - 300 = 225 - 300
[SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE]
-5c = -75
[SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE]
-5c/-5 = -75/-5
c = [B]15[/B]
Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a:
a = 20 - 15
a = [B]5[/B]
A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produA manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produced. The product sells for $22/unit.
The cost function for each unit u is:
C(u) = Variable Cost * Units + Fixed Cost
C(u) = 10u + 100000
The revenue function R(u) is:
R(u) = 22u
We want the break-even point, which is where:
C(u) = R(u)
10u + 100000 = 22u
[URL='https://www.mathcelebrity.com/1unk.php?num=10u%2B100000%3D22u&pl=Solve']Typing this equation into our search engine[/URL], we get:
u =[B]8333.33[/B]
A manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produA manufacturer has a monthly fixed cost of $100,000 and a production cost of $14 for each unit produced. The product sells for $20/unit.
Let u be the number of units. We have a cost function C(u) as:
C(u) = Variable cost * u + Fixed Cost
C(u) = 14u + 100000
[U]We have a revenue function R(u) with u units as:[/U]
R(u) = Sale Price * u
R(u) = 20u
[U]We have a profit function P(u) with u units as:[/U]
Profit = Revenue - Cost
P(u) = R(u) - C(u)
P(u) = 20u - (14u + 100000)
P(u) = 20u - 14u - 100000
P(u) = 6u - 1000000
a number added to 5 minus pa number added to 5 minus p
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We add 5 minus p to this number x:
[B]x + 5 - p[/B]
a number added to the product of y and xa number added to the product of y and x
Since we're already using the variables x and y, we choose another arbitrary variable for the phrase [I]a number.[/I]
a
The product of y and x isL
xy
Then add a:
[B]a + xy[/B]
a number increased by 6The phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
The phrase [I]increased by[/I] means we add 6 to x
[B]x +6[/B]
a number increased by 8 and then tripleda number increased by 8 and then tripled
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Increased by 8 means we add 8 to x:
x + 8
Then tripled means we multiply the expression x + 8 by 3:
[B]3(x + 8)[/B]
a number is twice another numbera number is twice another number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
The phrase [I]another number [/I]means another arbitrary variable, let's call it y
Twice means we multiply y by 2:
2y
The phrase [I]is [/I]means an equation, so we set x equal to 2y:
[B]x = 2y[/B]
A number multiplied by 6 and divided by 5 give four more than a number?A number multiplied by 6 and divided by 5 give four more than a number?
A number is represented by an arbitrary variable, let's call it x.
Multiply by 6:
6x
Divide by 5
6x/5
The word "gives" means equals, so we set this equal to 4 more than a number, which is x + 4.
6x/5 = x + 4
Now, multiply each side of the equation by 5, to eliminate the fraction on the left hand side:
6x(5)/5 = 5(x + 4)
The 5's cancel on the left side, giving us:
6x = 5x + 20
Subtract 5x from each side
[B]x = 20[/B]
Check our work from our original equation:
6x/5 = x + 4
6(20)/5 ? 20 + 4
120/5 ?24
24 = 24 <-- Yes, we verified our answer
a number of pennies splits into 4 equal groupsa number of pennies splits into 4 equal groups
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take x and divide it by 4 to get 4 equal groups:
[B]x/4[/B]
A number y increased by itselfA number y increased by itself
increased by itself means we add the variable y to itself to get our final algebraic expression of:
[B]y + y
[/B]
[I]If[/I] the problem asks you to simplify, we group like terms and get:
[B]2y[/B]
A peanut vendor has initial start up costs of $7600 and variable costs of $0.70 per bag of peanuts.A peanut vendor has initial start up costs of $7600 and variable costs of $0.70 per bag of peanuts. What is the cost function?
We set up the cost function C(b) where b is the number of bags:
C(b) = Cost per bag * b + Start up costs
Plugging in our numbers, we get:
[B]C(b) = 0.70b + 7600[/B]
A quarter of a number is greater than or equal to 38A quarter of a number is greater than or equal to 38.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
A quarter of a number means 1/4, so we have:
x/4
The phrase [I]is greater than or equal to[/I] means an inequality, so we use the >= sign in relation to 38:
[B]x/4 >= 38 <-- This is our algebraic expression
[/B]
If you want to solve this inequality, [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=38&propsign=%3E%3D&den1=4&den2=1&pl=Calculate+missing+proportion+value']we type it in the search engine[/URL] to get:
x >= [B]152[/B]
A random variable X follows the uniform distribution with a lower limit of 670 and an upper limitA random variable X follows the uniform distribution with a lower limit of 670 and an upper limit
a. Calculate the mean and standard deviation of this distribution. (Round intermediate calculation for standard deviation to 4 decimal places and final answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/uniform.php?a=+670&b=+770&x=+680&t=+3&pl=PDF']uniform distribution calculator[/URL], we get:
[B]Mean = 720
Standard deviation = 28.87
[/B]
b. What is the probability that X is less than 730? (Do not round intermediate calculations. Round your answer to 2 decimal places.)
Using our [URL='http://www.mathcelebrity.com/uniform.php?a=+670&b=+770&x=+730&t=+3&pl=CDF']uniform distribution calculator[/URL], we get:
[B]0.6[/B]
a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.
Declare variables:
[LIST]
[*]Let f be the father's age
[*]Let s be the son's age
[/LIST]
We're given two equations:
[LIST=1]
[*]s = f/4
[*]f - s = 30. [I]The reason why we subtract s from f is the father is older[/I]
[/LIST]
Using substitution, we substitute equaiton (1) into equation (2) for s:
f - f/4 = 30
To remove the denominator/fraction, we multiply both sides of the equation by 4:
4f - 4f/4 = 30 *4
4f - f = 120
3f = 120
To solve for f, we divide each side of the equation by 3:
3f/3 = 120/3
Cancel the 3's on the left side and we get:
f = [B]40[/B]
A sum greater than 5A sum greater than 5
A sum implies two variables or more. Let's use 2, x and y
[B]x + y > 5[/B]
a textbook store sold a combined total of 296 sociology and history text books in a week. the numbera textbook store sold a combined total of 296 sociology and history text books in a week. the number of history textbooks sold was 42 less than the number of sociology textbooks sold. how many text books of each type were sold?
Let h = history book and s = sociology books. We have 2 equations:
(1) h = s - 42
(2) h + s = 296
Substitute (1) to (2)
s - 42 + s = 296
Combine variables
2s - 42 = 296
Add 42 to each side
2s = 338
Divide each side by 2
s = 169
So h = 169 - 42 = 127
A tire repair shop charges $5 for tool cost and $2 for every minute the worker spends on the repair.A tire repair shop charges $5 for tool cost and $2 for every minute the worker spends on the repair. A) Write an equation of the total cost of repair, $y, in terms of a total of x minutes of repair.
y = Variable Cost + Fixed Cost
y = Cost per minute of repair * minutes of repair + Tool Cost
[B]y = 2x + 5[/B]
a variable tripled less 40a variable tripled less 40
[I]A variable[/I] means we pick an arbitrary variable, let's call it x
x
Tripled means we multiply by 3
3x
Less 40 means we subtract 40:
[B]3x - 40[/B]
a ^5 x a ^2 without exponentsa ^5 x a ^2 without exponents
When we multiply the same variable or number, we add exponents, so we have:
a^(5 + 2)
a^7
To write a variable raised to an exponent without exponents, we break it up. The formula to do this is:
a^n = a times itself n times
a^7 = [B]a * a * a * a * a * a * a[/B]
A=a+b+c+d÷4 for cA=a+b+c+d÷4 for c
Assume A and a are different variables:
Cross multiply:
a + b + c + d = 4A
Subtract a, b, and d from each side:
a + b + c + d - (a + b + d) = 4A - (a + b + d)
Cancel the a + b + d on the left side
[B]c = 4A - a - b - d[/B]
ab/d + c = e for dab/d + c = e for d
I know this is a literal equation because we are asked to solve for a variable [U]in terms of[I] another variable
[/I][/U]
Subtract c from each side to isolate the d term:
ab/d + c - c = e - c
Cancel the c's on the left side and we get:
ab/d = e - c
Cross multiply:
ab = d(e - c)
Divide each side of the equation by (e - c):
ab/(e - c)= d(e - c)/(e - c)
Cancel the (e - c) on the right side, and we get:
d = [B]ab/(e - c)[/B]
Absolute value of x less than 8These are now available as shortcuts. You can type any number or variable in the following forms:
[LIST]
[*]Absolute value of x less than 8
[*]Absolute value of x less than or equal to 8
[*]Absolute value of x greater than 8
[*]Absolute value of x greater than or equal to 8
[*]Absolute value of x equal to 8
[/LIST]
Alberto’s salary was $1500 greater than 5 times Nick’s salary. Write an equation stating Alberto’s aAlberto’s salary was $1500 greater than 5 times Nick’s salary. Write an equation stating Alberto’s and Nick’s salaries in terms of x and y.
Let x be Alberto's salary. Let y be Nick's salary. We have:
Let's break this down:
[LIST=1]
[*]5 times Nick's salary (y), means we multiply the variable y by 5
[*]$1500 greater means we add $1500 to 5y
[/LIST]
[B]x = 5y - 1500[/B]
Algebraic SubstitutionsFree Algebraic Substitutions Calculator - Given an algebraic statement with variables [a-z], this calculator takes a set of given substitution values, i.e., x=2,y=3,z=4, and evaluates your statement using the substitution values.
Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. WhatAngad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What was the original number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it n.
[LIST]
[*]Start with n
[*]Add 20 to it: n + 20
[*]Double it means we multiply the expression by 2: 2(n + 20)
[*]Get an answer of 53: means an equation, so we set 2(n + 20) equal to 53
[/LIST]
2(n + 20) = 53
To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%28n%2B20%29%3D53&pl=Solve']type this equation into our search engine[/URL] and we get:
n = [B]6.5[/B]
Angular MomentumFree Angular Momentum Calculator - Solves for any of the 4 variables in the angular momentum equation, L, V, M, and R
b/3d - h = 343 for bb/3d - h = 343 for b
A literal equation means we solve for one variable in terms of another variable or variables
Add h to each side to isolate the b term:
b/3d - h + h = 343 + h
Cancel the h's on the left side, we get:
b/3d = 343 + h
Cross multiply:
b = [B]3d(343 + h)[/B]
Barbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants coBarbra is buying plants for her garden. She notes that potato plants cost $3 each and corn plants cost $4 each. If she plans to spend at least $20 and purchase less than 15 plants in total, create a system of equations or inequalities that model the situation. Define the variables you use.
[U]Define variables[/U]
[LIST]
[*]Let c be the number of corn plants
[*]Let p be the number of potato plants
[/LIST]
Since cost = price * quantity, we're given two inequalities:
[LIST=1]
[*][B]3p + 4c >= 20 (the phrase [I]at least[/I] means greater than or equal to)[/B]
[*][B]c + p < 15[/B]
[/LIST]
Binomial Multiplication (FOIL)Free Binomial Multiplication (FOIL) Calculator - Multiplies out the product of 2 binomials in the form (a + b)(c + d) with 1 unknown variable.
This utilizes the First-Outside-Inside-Last (F.O.I.L.) method. Also calculates using the FOIL Box Method.
Break EvenFree Break Even Calculator - Given a fixed cost, variable cost, and revenue function or value, this calculates the break-even point
Carmen is serving her child french fries and chicken wings for lunch today. Let f be the number of fCarmen is serving her child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Carmen wants the total calorie count from the french fries and chicken wings to be less than 500 calories. Using the values and variables given, write an inequality describing this.
We have:
25f + 100c < 50
Note: We use < and not <= because it states less than in the problem.
Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double herCasey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her daughter's age
Declare variables for each age:
[LIST]
[*]Let Casey's age be c
[*]Let her daughter's age be d
[*]Let n be the number of years from now where Casey will be double her daughter's age
[/LIST]
We're told that:
26 + n = 2(4 + n)
26 + n = 8 + 2n
Solve for [I]n[/I] in the equation 26 + n = 8 + 2n
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables n and 2n. To do that, we subtract 2n from both sides
n + 26 - 2n = 2n + 8 - 2n
[SIZE=5][B]Step 2: Cancel 2n on the right side:[/B][/SIZE]
-n + 26 = 8
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 26 and 8. To do that, we subtract 26 from both sides
-n + 26 - 26 = 8 - 26
[SIZE=5][B]Step 4: Cancel 26 on the left side:[/B][/SIZE]
-n = -18
[SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE]
-1n/-1 = -18/-1
n = [B]18[/B]
Check our work for n = 18:
26 + 18 ? 8 + 2(18)
44 ? 8 + 36
44 = 44
Chang is serving his child french fries and chicken wings for lunch today. Let f be the number of fChang is serving his child french fries and chicken wings for lunch today. Let f be the number of french fries in the lunch, and let c be the number of chicken wings. Each french fry has 25 calories, and each chicken wing has 100 calories. Chang wants the total calorie count from the french fries and chicken wings to be less than 600 calories. Using the values and variables given, write an inequality describing this.
We have [B]25f + 100c < 600[/B] as our inequality.
Chebyshevs TheoremFree Chebyshevs Theorem Calculator - Using Chebyshevs Theorem, this calculates the following:
Probability that random variable X is within k standard deviations of the mean.
How many k standard deviations within the mean given a P(X) value.
Combination with VariableFree Combination with Variable Calculator - Calculates the following:
Solves for r given n and the combination value.
Solves for n given r and the combination value
Compute a 75% Chebyshev interval around the mean for x values and also for y values.Compute a 75% Chebyshev interval around the mean for [I]x[/I] values and also for [I]y[/I] values.
[B][U]Grid E: [I]x[/I] variable[/U][/B]
11.92 34.86 26.72 24.50 38.93 8.59 29.31
23.39 24.13 30.05 21.54 35.97 7.48 35.97
[B][U]Grid H: [I]y[/I] variable[/U][/B]
27.86 13.29 33.03 44.31 16.58 42.43
39.61 25.51 39.14 16.58 47.13 14.70 57.47 34.44
According to Chebyshev's Theorem,
[1 - (1/k^2)] proportion of values will fall between Mean +/- (k*SD)
k in this case equal to z
z = (X-Mean)/SD
X = Mean + (z*SD)
1 - 1/k^2 = 0.75
- 1/k^2 = 0.75 - 1= - 0.25
1/k^2 = 0.25
k^2 = 1/0.25
k^2 = 4
k = 2
Therefore, z = k = 2
First, [URL='http://www.mathcelebrity.com/statbasic.php?num1=11.92%2C34.86%2C26.72%2C24.50%2C38.93%2C8.59%2C29.31%2C23.39%2C24.13%2C30.05%2C21.54%2C35.97%2C7.48%2C35.97&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']determine the mean and standard deviation of x[/URL]
Mean(x) = 25.24
SD(x) = 9.7873
Required Interval for x is:
Mean - (z * SD) < X < Mean + (z * SD)
25.24 - (2 * 9.7873) < X < 25.24 - (2 * 9.7873)
25.24 - 19.5746 < X < 25.24 + 19.5746
5.6654 < X < 44.8146
Next, [URL='http://www.mathcelebrity.com/statbasic.php?num1=27.86%2C13.29%2C33.03%2C44.31%2C16.58%2C42.43%2C39.61%2C25.51%2C39.14%2C16.58%2C47.13%2C14.70%2C57.47%2C34.44&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']determine the mean and standard deviation of y[/URL]
Mean(y) = 32.29
SD(y) = 9.7873
Required Interval for y is:
Mean - (z * SD) < Y < Mean + (z * SD)
32.29 - (2 * 13.1932) < Y < 32.29 - (2 * 13.1932)
32.29 - 26.3864 < Y < 32.29 + 26.3864
5.9036 < X < 58.6764
Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solveConsider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve for a, b, or h? Why? Solve for each of these variables to demonstrate.
The variable "h" is the easiest to solve for. Because you only have one step. Let's review:
Divide each side of the equation by 12(a + b)
h = 12(a + b)/A
Solving for "a", we two steps. Divide each side by 12h:
A/12h = a + b
Subtract b from each side
a = A/12h - b
Solving for "b" takes two steps as well. Divide each side by 12h:
A/12h = a + b
Subtract a from each side
b = A/12h - a
Cost Revenue ProfitFree Cost Revenue Profit Calculator - Given a total cost, variable cost, revenue amount, and profit unit measurement, this calculates profit for each profit unit
cube root of a number and 7cube root of a number and 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Cube root of a number means we raise x to the 1/3 power:
x^1/3
And 7 means we add 7:
[B]x^1/3 + 7[/B]
d - f^3 = 4a for ad - f^3 = 4a for a
Solve this literal equation for a:
Divide each side of the equation by 4:
(d - f^3)/4 = 4a/4
Cancel the 4's on the right side, and rewrite with our variable to solve for on the left side:
a = [B](d - f^3)/4[/B]
d squared is greater than or equal to 17d squared is greater than or equal to 17
d squared means we raise the variable d to the power of 2:
d^2
The phrase [I]greater than or equal to[/I] means an inequality. So we set this up using the >= in relation to 17:
[B]d^2 >= 17[/B]
Decrease 12 by a numberDecrease 12 by a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take 12 and decrease it by x, meaning we subtract x from 12:
[B]12 - x[/B]
decrease a number by 7 and multiply by 6.decrease a number by 7 and multiply by 6.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Decrease a number by 7:
x - 7
Multiply by 6
[B]6(x - 7)[/B]
Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened upDeon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up her account with a starting amount of $850 and is going to take out $65 per month. When would the two accounts have the same amount of money?
We set up a balance equation B(m) where m is the number of months.
[U]Set up Deon's Balance equation:[/U]
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 650 - 40m
[U]Set up Mai's Balance equation:[/U]
Withdrawals mean we subtract from our current balance
B(m) = Starting Balance - Withdrawal Amount * m
B(m) = 850 - 65m
When the two accounts have the same amount of money, we can set both balance equations equal to each other and solve for m:
650 - 40m = 850 - 65m
Solve for [I]m[/I] in the equation 650 - 40m = 850 - 65m
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables -40m and -65m. To do that, we add 65m to both sides
-40m + 650 + 65m = -65m + 850 + 65m
[SIZE=5][B]Step 2: Cancel -65m on the right side:[/B][/SIZE]
25m + 650 = 850
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 650 and 850. To do that, we subtract 650 from both sides
25m + 650 - 650 = 850 - 650
[SIZE=5][B]Step 4: Cancel 650 on the left side:[/B][/SIZE]
25m = 200
[SIZE=5][B]Step 5: Divide each side of the equation by 25[/B][/SIZE]
25m/25 = 200/25
m = [B]8[/B]
Determine the formula of the given statement by following the procedures. Choose any number then addDetermine the formula of the given statement by following the procedures. Choose any number then add 2. Multiply your answer to 3 and minus 2
For the phrase [I]choose any number[/I] we can use an arbitrary variable, let's call it x.
Add 2:
x + 2
Multiply your answer to 3:
3(x + 2)
And minus 2 which means we subtract:
[B]3(x + 2) - 2[/B]
Determine whether the random variable is discrete or continuous. In each case, state the possible vDetermine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable.
(a) The number of customers arriving at a bank between noon and 1:00 P.M.
(i) The random variable is continuous. The possible values are x >= 0.
(ii) The random variable is discrete. The possible values are x = 0, 1, 2,...
(iii) The random variable is continuous. The possible values are x = 0, 1, 2,...
(iv) The random variable is discrete. The possible values are x >= 0.
(b) The amount of snowfall
(i) The random variable is continuous. The possible values are s = 0, 1, 2,...
(ii) The random variable is discrete. The possible values are s >= 0.
(iii) The random variable is discrete. The possible values are s = 0, 1, 2,...
(iv) The random variable is continuous. The possible values are s >= 0.
[B](a) (ii) The random variable is discrete. The possible values are x = 0, 1, 2,...
Discrete variables are limited in the values they can take between 9 and ∞
(b) (iv) The random variable is continuous. The possible values are s >= 0. Snowfall can be a decimal and can vary between 0 and ∞[/B]
Diegos savings increased by 9 is 68 . Use the variable to represent Diegos savings.Diegos savings increased by 9 is 68 . Use the variable to represent Diegos savings.
Let Diego's savings be s.
The phrase [I]increased by[/I] means add, so we add 9 to s
s + 9
The phrase [I]is [/I]means equal to, so we set 2 + 9 = 68
[B]s + 9 = 68[/B]
difference between 2 positive numbers is 3 and the sum of their squares is 117difference between 2 positive numbers is 3 and the sum of their squares is 117
Declare variables for each of the two numbers:
[LIST]
[*]Let the first variable be x
[*]Let the second variable be y
[/LIST]
We're given 2 equations:
[LIST=1]
[*]x - y = 3
[*]x^2 + y^2 = 117
[/LIST]
Rewrite equation (1) in terms of x by adding y to each side:
[LIST=1]
[*]x = y + 3
[*]x^2 + y^2 = 117
[/LIST]
Substitute equation (1) into equation (2) for x:
(y + 3)^2 + y^2 = 117
Evaluate and simplify:
y^2 + 3y + 3y + 9 + y^2 = 117
Combine like terms:
2y^2 + 6y + 9 = 117
Subtract 117 from each side:
2y^2 + 6y + 9 - 117 = 117 - 117
2y^2 + 6y - 108 = 0
This is a quadratic equation:
Solve the quadratic equation 2y2+6y-108 = 0
With the standard form of ax2 + bx + c, we have our a, b, and c values:
a = 2, b = 6, c = -108
Solve the quadratic equation 2y^2 + 6y - 108 = 0
The quadratic formula is denoted below:
y = -b ± sqrt(b^2 - 4ac)/2a
[U]Step 1 - calculate negative b:[/U]
-b = -(6)
-b = -6
[U]Step 2 - calculate the discriminant Δ:[/U]
Δ = b2 - 4ac:
Δ = 62 - 4 x 2 x -108
Δ = 36 - -864
Δ = 900 <--- Discriminant
Since Δ is greater than zero, we can expect two real and unequal roots.
[U]Step 3 - take the square root of the discriminant Δ:[/U]
√Δ = √(900)
√Δ = 30
[U]Step 4 - find numerator 1 which is -b + the square root of the Discriminant:[/U]
Numerator 1 = -b + √Δ
Numerator 1 = -6 + 30
Numerator 1 = 24
[U]Step 5 - find numerator 2 which is -b - the square root of the Discriminant:[/U]
Numerator 2 = -b - √Δ
Numerator 2 = -6 - 30
Numerator 2 = -36
[U]Step 6 - calculate your denominator which is 2a:[/U]
Denominator = 2 * a
Denominator = 2 * 2
Denominator = 4
[U]Step 7 - you have everything you need to solve. Find solutions:[/U]
Solution 1 = Numerator 1/Denominator
Solution 1 = 24/4
Solution 1 = 6
Solution 2 = Numerator 2/Denominator
Solution 2 = -36/4
Solution 2 = -9
[U]As a solution set, our answers would be:[/U]
(Solution 1, Solution 2) = (6, -9)
Since one of the solutions is not positive and the problem asks for 2 positive number, this problem has no solution
Direct Current (Electrical Engineering) Ohms LawFree Direct Current (Electrical Engineering) Ohms Law Calculator - Enter two of the following items from the DIRECT CURRENT(DC) electrical engineering set of variables, and this will solve for the remaining two:
* I = current(amps.)
* V = Electricity potential of voltage(volts)
* R = resistance(ohms)
* P = power(watts)
Distance Rate and TimeFree Distance Rate and Time Calculator - Solves for distance, rate, or time in the equation d=rt based on 2 of the 3 variables being known.
Divide a number by 10. Then, add 10.Divide a number by 10. Then, add 10.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Divide the number by 10 mean we have a quotient, of x over 10
x / 10
Then, add 10:
[B](x / 10) + 10[/B]
Do the phrases 7 less than a number and a number less than 7 mean the same thing explainDo the phrases 7 less than a number and a number less than 7 mean the same thing explain
No, they are different, here's how:
First, the phrase [I]a number[/I] means an arbitrary variable, let's call it x.
7 less than a number means we subtract 7 from x:
x - 7
A number less than 7 means we subtract x from 7:
7 - x
As you can see:
x - 7 <> 7 - x so [B]they are different[/B]
Dotty McGinnis starts up a small business manufacturing bobble-head figures of famous soccer playersDotty McGinnis starts up a small business manufacturing bobble-head figures of famous soccer players. Her initial cost is $3300. Each figure costs $4.50 to make. a. Write a cost function, C(x), where x represents the number of figures manufactured.
Cost function is the fixed cost plus units * variable cost.
[B]C(x) = 3300 + 4.50x[/B]
double v, add u, then divide t by what you havedouble v, add u, then divide t by what you have
Double v means we multiply the variable v by 2:
2v
Add u:
2v + u
We build a fraction, with t as the numerator, and 2v + u as the denominator
[B]t/(2v + u)[/B]
Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offersDunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers business cards for $0.15 each with a setup charge of $10. What numbers of business cards cost the same from either company
Declare variables:
[LIST]
[*]Let b be the number of business cards.
[/LIST]
[U]Set up the cost function C(b) for Dunder Mifflin:[/U]
C(b) = Cost to print each business card * b + Setup Charge
C(b) = 0.1b + 15
[U]Set up the cost function C(b) for Werham Hogg:[/U]
C(b) = Cost to print each business card * b + Setup Charge
C(b) = 0.15b + 10
The phrase [I]cost the same[/I] means we set both C(b)'s equal to each other and solve for b:
0.1b + 15 = 0.15b + 10
Solve for [I]b[/I] in the equation 0.1b + 15 = 0.15b + 10
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 0.1b and 0.15b. To do that, we subtract 0.15b from both sides
0.1b + 15 - 0.15b = 0.15b + 10 - 0.15b
[SIZE=5][B]Step 2: Cancel 0.15b on the right side:[/B][/SIZE]
-0.05b + 15 = 10
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 15 and 10. To do that, we subtract 15 from both sides
-0.05b + 15 - 15 = 10 - 15
[SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE]
-0.05b = -5
[SIZE=5][B]Step 5: Divide each side of the equation by -0.05[/B][/SIZE]
-0.05b/-0.05 = -5/-0.05
b = [B]100[/B]
Each piece of candy costs 25 cents. The cost of x pieces of candy is $2.00. Use variable x to translEach piece of candy costs 25 cents. The cost of x pieces of candy is $2.00. Use variable x to translate the above statements into algebraic equation.
Our algebraic expression is:
[B]0.25x = 2
[/B]
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.25x%3D2&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]8[/B]
Earnings Before Interest and Taxes (EBIT) and Net IncomeFree Earnings Before Interest and Taxes (EBIT) and Net Income Calculator - Given inputs of sales, fixed costs, variable costs, depreciation, and taxes, this will determine EBIT and Net Income and Profit Margin
Eighteen times the difference of a number and tenThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
The difference of a number and ten
x - 10
Eighteen times the difference of a number and ten
[B]18(x - 10)[/B]
El triple de la diferencia de dos númerosEl triple de la diferencia de dos números
La frase 2 números significa variables arbitrarias.
Llamémoslos xey.
La diferencia significa que restamos y de x:
x - y
Triple significa multiplicar la diferencia por 3
[B]3(x - y)[/B]
Equation and InequalitiesFree Equation and Inequalities Calculator - Solves an equation or inequality with 1 unknown variable and no exponents as well as certain absolute value equations and inequalities such as |x|=c and |ax| = c where a and c are constants. Solves square root, cube root, and other root equations in the form ax^2=c, ax^2 + b = c. Also solves radical equations in the form asqrt(bx) = c. Also solves open sentences and it will solve one step problems and two step equations. 2 step equations and one step equations and multi step equations
Equation of ExchangeFree Equation of Exchange Calculator - Solves for any of the 4 variables in the Equation of Exchange: money, velocity, price, quantity
Expand Master and Build Polynomial EquationsFree Expand Master and Build Polynomial Equations Calculator - This calculator is the ultimate expansion tool to multiply polynomials. It expands algebraic expressions listed below using all 26 variables (a-z) as well as negative powers to handle polynomial multiplication. Includes multiple variable expressions as well as outside multipliers.
Also produces a polynomial equation from a given set of roots (polynomial zeros).
* Binomial Expansions c(a + b)x
* Polynomial Expansions c(d + e + f)x
* FOIL Expansions (a + b)(c + d)
* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)
Expected ValueFree Expected Value Calculator - This lesson walks you through what expected value is, expected value notation, the expected value of a discrete random variable, the expected value of a continuous random variable, and expected value properties.
F varies directly as g and inversely as r^2F varies directly as g and inversely as r^2
[U]Givens and assumptions[/U]
[LIST]
[*]We take a constant of variation called k.
[*][I]Varies directly means we multiply our variable term by k[/I]
[*][I]Varies inversely means we divide k by our variable term[/I]
[/LIST]
The phrase varies directly or varies inversely means we have a constant k such that:
[B]F = kg/r^2[/B]
Factoring and Root FindingFree Factoring and Root Finding Calculator - This calculator factors a binomial including all 26 variables (a-z) using the following factoring principles:
* Difference of Squares
* Sum of Cubes
* Difference of Cubes
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* Factor by Grouping
* Common Term
This calculator also uses the Rational Root Theorem (Rational Zero Theorem) to determine potential roots
* Factors and simplifies Rational Expressions of one fraction
* Determines the number of potential positive and negative roots using Descarte’s Rule of Signs
Fifty-two less than 75% of a numberFifty-two less than 75% of a number
A number means an arbitrary variable, let's call it x.
75% of this is 0.75x
Fifty-two less is:
[B]0.75x - 52[/B]
Five less than a number is at least -7 and at most 7.Five less than a number is at least -7 and at most 7.
A number signifies an arbitrary variable, let's call it x.
Five less than a number: x - 5
Is at least -7 means greater than or equal to and at most 7 means less than or equal to, so we have a joint inequality:
[B]-7 <= x - 5 <= 7[/B]
Four less than five times a numberThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
5 times a number:
5x
Four less means we subtract 4 from 5x:
[B]5x - 4[/B]
Four more then double a number is greater than 2Four more then double a number is greater than 2
Double a number:
A number implies an arbitrary variable, let's call it "x". Double means multiply this by 2
2x
Four more than this:
2x + 4
Now, we set this expression as an inequality greater than 2
[B]2x + 4 > 2[/B]
Fraction with variable x in numerator and 6 in the denominator.Fraction with variable x in numerator and 6 in the denominator.
The numerator is the top of the fraction.
The denominator is the bottom of the fraction.
[B]x/6[/B]
Frank is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. FindFrank is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. Find a linear function that expresses the total cost C for plumbing services for h hours.
Cost functions include a flat rate and a variable rate. The flat rate is $35 and the variable rate per hour is 15. The cost function C(h) where h is the number of hours Frank works is:
[B]C(h) = 15h + 35[/B]
g equals 232 subtracted from the quantity 377 times gg equals 232 subtracted from the quantity 377 times g
377 times g:
377g
232 subtracted from 377 times g:
377g - 232
We set the variable g equal to this expression:
[B]g = 377g - 232[/B]
Georgie joins a gym. she pays $25 to sign up and then $15 each month. Create an equation using thisGeorgie joins a gym. she pays $25 to sign up and then $15 each month. Create an equation using this information.
Let m be the number of months Georgie uses the gym. Our equation G(m) is the cost Georgie pays for m months.
G(m) = Variable Cost * m (months) + Fixed Cost
Plug in our numbers:
[B]G(m) = 15m + 25[/B]
Golden RatioFree Golden Ratio Calculator - Solves for 2 out of the 3 variables for a segment broken in 2 pieces that satisfies the Golden Ratio (Golden Mean).
(a) Large Segment
(b) Small Segment
(a + b) Total Segment
H multiplied by 2xH multiplied by 2x
h * 2x
If we arrange variables alphabetically, we have:
[B]2hx[/B]
Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $1Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $2.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours.
Happy Paws Cost: C = 16 + 1.5h
Woof Watchers: C = 11 + 2.75h
Setup the equation where there costs are equal
16 + 1.5h = 11 + 2.75h
Subtract 11 from each side:
5 + 1.5h = 2.75h
Subtract 1.5h from each side
1.25h = 5
Divide each side by 1.25
[B]h = 4[/B]
Happy Paws charges $19.00 plus $5.50 per hour to keep a dog during the day. Woof Watchers charges $1Happy Paws charges $19.00 plus $5.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $6.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours.
[B]Happy Paws cost equation:[/B]
5.50h + 19
[B]Woof Watchers cost equation:[/B]
6.75h + 11
[B]Set them equal to each other:[/B]
5.50h + 19 = 6.75h + 11
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=5.50h%2B19%3D6.75h%2B11&pl=Solve']equation solver[/URL], we get [B]h = 6.4[/B].
High and Low MethodFree High and Low Method Calculator - Calculates the variable cost per unit, total fixed costs, and the cost volume formula
High-Low MethodFree High-Low Method Calculator - Calculates Variable Cost per Unit, Total Fixed Cost, and Cost Volume using the High-Low Method
HomeWork Help Please Respond ASAP!!!The phrase a number means an arbitrary variable, let's call it x.
Three times a number:
3x
And 18 means we add 18
3x + 18
The word is means equal to, so we set 3x + 18 equal to -39
3x + 18 = -39
This is your algebraic expression. If you want to solve for x, plug it into the [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']search engine[/URL] and you get x = -19
how many sixths equal one-thirdhow many sixths equal one-third
We have a variable x where we want to solve for in the following equation:
x/6 = 1/3
[URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=1&den1=6&den2=3&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this proportion into our math engine[/URL], we get:
x = [B]2[/B]
If 11 times a number is added to twice the number, the result is 104If 11 times a number is added to twice the number, the result is 104
Let [I]the number[/I] be an arbitrary variable we call x.
11 times a number:
11x
Twice the number (means we multiply x by 2):
2x
The phrase [I]is added to[/I] means we add 2x to 11x:
11x + 2x
Simplify by grouping like terms:
(11 + 2)x = 13x
The phrase [I]the result is[/I] means an equation, so we set 13x equal to 104:
13x = 104 <-- This is our algebraic expression
To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=13x%3D104&pl=Solve']we type it in our search engine[/URL] and we get:
x = [B]8[/B]
If 2x + y = 7 and y + 2z = 23, what is the average of x, y, and z?If 2x + y = 7 and y + 2z = 23, what is the average of x, y, and z?
A. 5
B. 7.5
C. 15
D. 12.25
Add both equations to get all variables together:
2x + y + y + 2z = 23 + 7
2x + 2y + 2z = 30
We can divide both sides by 2 to simplify:
(2x + 2y + 2z)/2= 30/2
x + y + z = 15
Notice: the average of x, y, and z is:
(x + y + z)/3
But x + y + z = 15, so we have:
15/3 = [B]5, answer A[/B]
[MEDIA=youtube]tOCAhhfMCLI[/MEDIA]
If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3If 3 times a number added to 2 is divided by the number plus 4 the result is 4/3
Take this in pieces, where "a number" means an arbitrary variable, let's call it "x".
[LIST=1]
[*]3 times a number --> 3x
[*]3 times a number added to 2 --> 3x + 2
[*]The number plus 4 --> x + 4
[*]is divided by --> (3x + 2)/(x + 4)
[*]the result is 4/3 --> (3x + 2)/(x + 4) = 4/3
[/LIST]
If 4 times a number is added to 9, the result is 49If 4 times a number is added to 9, the result is 49.
[I]A number[/I] means an arbitrary variable, let's call it x.
4 [I]times a number[/I] means we multiply x by 4
4x
[I]Added to[/I] 9 means we add 9 to 4x
4x + 9
[I]The result is[/I] means we have an equation, so we set 4x + 9 equal to 49
[B]4x + 9 = 49[/B] <-- This is our algebraic expression
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D49&pl=Solve']we type it in the search engine[/URL] and get x = 10
If 72 is added to a number it will be 4 times as large as it was originallyIf 72 is added to a number it will be 4 times as large as it was originally
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
72 added to a number:
x + 72
4 times as large as it was originally means we take the original number x and multiply it by 4:
4x
Now, the phrase [I]it will be[/I] means an equation, so we set x + 72 equal to 4x to get our final algebraic expression:
[B]x + 72 = 4x[/B]
[B][/B]
If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B72%3D4x&pl=Solve']type this equation into our search engine[/URL] and we get:
x = [B]24[/B]
If 9 is added to 1/3 of a number, the result is 15. What is the number?If 9 is added to 1/3 of a number, the result is 15. What is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
1/3 of a number means we multiply x by 1/3:
x/3
9 is added to 1/3 of a number:
x/3 + 9
The phrase [I]the result is[/I] means an equation. so we set x/3 + 9 equal to 15
x/3 + 9 = 15
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2F3%2B9%3D15&pl=Solve']type it in our search engine[/URL] and we get:
x = [B]18[/B]
if 9 times a number is decreased by 6, the result is 111if 9 times a number is decreased by 6, the result is 111
A number means an arbitrary variable, let's call it x.
9 times a number:
9x
Decreased by 6
9x - 6
The result is 11, this means we set 9x - 6 equal to 11
[B]9x - 6 = 11
[/B]
To solve this equation for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=9x-6%3D11&pl=Solve']equation calculator[/URL]
if a number is added to its square, it equals 20if a number is added to its square, it equals 20.
Let the number be an arbitrary variable, let's call it n.
The square of the number means we raise n to the power of 2:
n^2
We add n^2 to n:
n^2 + n
It equals 20 so we set n^2 + n equal to 20
n^2 + n = 20
This is a quadratic equation. So [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn%3D20&pl=Solve+Quadratic+Equation&hintnum=+0']we type this equation into our search engine[/URL] to solve for n and we get two solutions:
[B]n = (-5, 4)[/B]
if a number is decreased by 5, and then the result is multiplied by 2, the result is 26If a number is decreased by 5, and then the result is multiplied by 2, the result is 26
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
[I]Decreased by[/I] means we subtract 5 from x:
x - 5
Multiply the result by 2:
2(x - 5)
The result is 26 means we set 2(x - 5) equal to 26:
[B]2(x - 5) = 26[/B]
if a number is tripled the result is 60if a number is tripled the result is 60
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Triple the number means we multiply by 3:
3x
The phrase [I]the result is[/I] means an equation, so we set 3x equal to 60:
[B]3x = 60 <-- This is our algebraic expression
[/B]
If you want to solve this equation, then [URL='https://www.mathcelebrity.com/1unk.php?num=3x%3D60&pl=Solve']you type in 3x = 60 into the search engine[/URL] and get:
x = 20
If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?
By segment addition, we know that:
EF + FG = EG
Substituting in our values for the 3 segments, we get:
9x - 17 + 17x - 14 = 20x + 17
Group like terms and simplify:
(9 + 17)x + (-17 - 14) = 20x - 17
26x - 31 = 20x - 17
Solve for [I]x[/I] in the equation 26x - 31 = 20x - 17
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 26x and 20x. To do that, we subtract 20x from both sides
26x - 31 - 20x = 20x - 17 - 20x
[SIZE=5][B]Step 2: Cancel 20x on the right side:[/B][/SIZE]
6x - 31 = -17
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants -31 and -17. To do that, we add 31 to both sides
6x - 31 + 31 = -17 + 31
[SIZE=5][B]Step 4: Cancel 31 on the left side:[/B][/SIZE]
6x = 14
[SIZE=5][B]Step 5: Divide each side of the equation by 6[/B][/SIZE]
6x/6 = 14/6
x = [B]2.3333333333333[/B]
If from twice a number you subtract four, the difference is twentyThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number means we multiply x by 2:
2x
Subtract four:
2x - 4
The word [I]is [/I]means equal to. We set 2x - 4 equal to 20 for our algebraic expression:
[B]2x - 4 = 20
[/B]
If the problem asks you to solve for x:
we [URL='https://www.mathcelebrity.com/1unk.php?num=2x-4%3D20&pl=Solve']plug this equation into our calculator [/URL]and get x = [B]12[/B]
If the correlation between two variables is close to minus one, the association is: Strong ModerateIf the correlation between two variables is close to minus one, the association is:
Strong
Moderate
Weak
None
[B]Strong[/B] - Coefficient near +1 or -1 indicate a strong correlation
If the difference of a number and 4 is multiplied by 3 the result is 19If the difference of a number and 4 is multiplied by 3 the result is 19
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The difference of a number and 4:
x - 4
The phrase [I]is multiplied by[/I] means we multiply x - 4 by 3:
3(x - 4)
The phrase [I]the result is[/I] means equals, so we set 3(x - 4) equal to 19
[B]3(x - 4) = 19
[MEDIA=youtube]Q8bnVJuWeVk[/MEDIA][/B]
If thrice a number is increased by 11,the result is 35. What is the numberIf thrice a number is increased by 11,the result is 35. What is the number?
[LIST]
[*]The phrase [I]a number [/I]means an arbitrary variable. Let's call it x.
[*]Thrice means multiply by 3, so we have 3x
[*]Increased by 11 means we add 11, so we have 3x + 11
[*]The [I]result is[/I] means an equation, so we set 3x + 11 equal to 35
[/LIST]
3x + 11 = 35 <-- This is our algebraic expression
The problem ask us to solve the algebraic expression.
[URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B11%3D35&pl=Solve']Typing this problem into our search engine[/URL], we get [B]x = 8[/B].
If twice a number is divided by 7, the result is -28If twice a number is divided by 7, the result is -28.
The phrase [I]a number[/I] means an arbitrary variable, let's call it "x".
Twice x means we multiply x by 2: 2x
Divide this by 7: 2x/7
We set this equal to -28, and we have our algebraic expression:
[B]2x/7 = -28 [/B]
if you add 35 to twice a number, the result is 17. What is the number?if you add 35 to twice a number, the result is 17. What is the number?
A number is represented by a variable, let's call it "x".
Twice a number means we multiply by 2 --> 2x
Add 35
2x + 35
Now set that entire expression equal to 17
2x + 35 = 17
[URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B35%3D17&pl=Solve']Plug that into the search engine to solve for x[/URL]
[B]x = -9[/B]
If you multiply me by 33 and subtract 20, the result is 46. Who am I?If you multiply me by 33 and subtract 20, the result is 46. Who am I?
[LIST]
[*]Start with the variable x
[*]Multiply me by 33 = 33x
[*]Subtract 20: 33x - 20
[*]The result is 46, means we set this expression equal to 46: 33x - 20 = 46
[/LIST]
Run this through our [URL='http://www.mathcelebrity.com/1unk.php?num=33x-20%3D46&pl=Solve']equation calculator[/URL], and we get:
[B]x = 2[/B]
In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there iIn a class there are 5 more boys than girls. There are 13 students in all. How many boys are there in the class?
We start by declaring variables for boys and girls:
[LIST]
[*]Let b be the number of boys
[*]Let g be the number of girls
[/LIST]
We're given two equations:
[LIST=1]
[*]b = g + 5
[*]b + g = 13
[/LIST]
Substitute equation (1) for b into equation (2):
g + 5 + g = 13
Grouping like terms, we get:
2g + 5 = 13
Subtract 5 from each side:
2g + 5 - 5 = 13 - 5
Cancel the 5's on the left side and we get:
2g = 8
Divide each side of the equation by 2 to isolate g:
2g/2 = 8/2
Cancel the 2's on the left side and we get:
g = 4
Substitute g = 4 into equation (1) to solve for b:
b = 4 + 5
b = [B]9[/B]
In order to test if there is a difference between means from two populations, which of following assIn order to test if there is a difference between means from two populations, which of following assumptions are NOT required?
a. The dependent variable scores must be a continuous quantitative variable.
b. The scores in the populations are normally distributed.
c. Each value is sampled independently from each other value.
d. The two populations have similar means
[B]a and d
[/B]
[I]because b and c [U]are[/U] required[/I]
is 6x a monomial?[B]Yes[/B]. It's an algebraic expression consisting of one term.
The constant is 6, and the variable is x.
it costs $75.00 for a service call from shearin heating and air conditioning company. the charge forit costs $75.00 for a service call from shearin heating and air conditioning company. the charge for labor is $60.00 . how many full hours can they work on my air conditioning unit and still stay within my budget of $300.00 for repairs and service?
Our Cost Function is C(h), where h is the number of labor hours. We have:
C(h) = Variable Cost * Hours + Fixed Cost
C(h) = 60h + 75
Set C(h) = $300
60h + 75 = 300
[URL='https://www.mathcelebrity.com/1unk.php?num=60h%2B75%3D300&pl=Solve']Running this problem in the search engine[/URL], we get [B]h = 3.75[/B].
Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combinedJenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined distance thrown by the 3 friends is 124 metres, how far did Angus throw the javelin?
Assumptions and givens:
[LIST]
[*]Let a be the distance Angus threw the javelin
[*]Let c be the distance Cameron threw the javelin
[*]Let j be the distance Jenny threw the javelin
[/LIST]
We're given 3 equations:
[LIST=1]
[*]j = a + 4
[*]j = c - 5
[*]a + c + j = 124
[/LIST]
Since j is the common variable in all 3 equations, let's rearrange equation (1) and equation (2) in terms of j as the dependent variable:
[LIST=1]
[*]a = j - 4
[*]c = j + 5
[*]a + c + j = 124
[/LIST]
Now substitute equation (1) and equation (2) into equation (3) for a and c:
j - 4 + j + 5 + j = 124
To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=j-4%2Bj%2B5%2Bj%3D124&pl=Solve']type it in our math engine[/URL] and we get:
j = 41
The question asks how far Angus (a) threw the javelin. Since we have Jenny's distance j = 41 and equation (1) has j and a together, let's substitute j = 41 into equation (1):
a = 41 - 4
a = [B]37 meters[/B]
Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worthJinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 76 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.
At least means greater than or equal to, so we have:
[B]3x + 4y >= 76[/B]
Joint Variation EquationsFree Joint Variation Equations Calculator - Given a joint variation (jointly proportional) of a variable between two other variables with a predefined set of conditions, this will create the joint variation equation and solve based on conditions.
Also called combined variation.
Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15%Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month?
[U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
10% written as a decimal is 0.1. We want decimals to solve equations easier.
S(m) = 0.1m + 1500
[U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U]
S(m) = Commission percentage * m + Base Salary
15% written as a decimal is 0.15. We want decimals to solve equations easier.
S(m) = 0.15m + 1200
[U]The question asks what is m when both S(m)'s equal each other[/U]:
The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other
0.1m + 1500 = 0.15m + 1200
We want to isolate m terms on one side of the equation.
Subtract 1200 from each side:
0.1m + 1500 - 1200 = 0.15m + 1200 - 1200
Cancel the 1200's on the right side and we get:
0.1m - 300 = 0.15m
Next, we subtract 0.1m from each side of the equation to isolate m
0.1m - 0.1m + 300 = 0.15m - 0.1m
Cancel the 0.1m terms on the left side and we get:
300 = 0.05m
Flip the statement since it's an equal sign to get the variable on the left side:
0.05m = 300
To solve for m, we divide each side of the equation by 0.05:
0.05m/0.05 = 300/0.05
Cancelling the 0.05 on the left side, we get:
m = [B]6000[/B]
larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2 numbers
Declare Variables for each number:
[LIST]
[*]Let l be the larger number
[*]Let s be the smaller number
[/LIST]
We're given two equations:
[LIST=1]
[*]l = s + 12
[*]l + s = 74
[/LIST]
Equation (1) already has l solved for. Substitute equation (1) into equation (2) for l:
s + 12 + s = 74
Solve for [I]s[/I] in the equation s + 12 + s = 74
[SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE]
(1 + 1)s = 2s
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
2s + 12 = + 74
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 12 and 74. To do that, we subtract 12 from both sides
2s + 12 - 12 = 74 - 12
[SIZE=5][B]Step 4: Cancel 12 on the left side:[/B][/SIZE]
2s = 62
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2s/2 = 62/2
s = [B]31[/B]
To solve for l, we substitute in s = 31 into equation (1):
l = 31 + 12
l = [B]43[/B]
larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?
Declare variables for the 2 numbers:
[LIST]
[*]Let l be the larger number
[*]Let s be the smaller number
[/LIST]
We're given two equations:
[LIST=1]
[*]l = s + 4
[*]l + s = 40
[/LIST]
To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l.
Subtract 4 from each side in equation (1)
l - 4 = s + 4 - 4
Cancel the 4's and we get:
s = l - 4
Our given equations are now:
[LIST=1]
[*]s = l - 4
[*]l + s = 40
[/LIST]
Substitute equation (1) into equation (2) for s:
l + l - 4 = 40
Grouping like terms for l, we get:
2l - 4 = 40
Add 4 to each side:
2l - 4 + 4 = 40 + 4
Cancelling the 4's on the left side, we get
2l = 44
Divide each side of the equation by 2 to isolate l:
2l/2 = 44/2
Cancel the 2's on the left side and we get:
l = [B]22[/B]
let x be the variable, an age that is at least 57 years oldlet x be the variable, an age that is at least 57 years old
At least means greater than or equal to
x >= 57
Literal EquationsFree Literal Equations Calculator - Solves literal equations with no powers for a variable of your choice as well as open sentences.
Logarithms and Natural Logarithms and Eulers Constant (e)Free Logarithms and Natural Logarithms and Eulers Constant (e) Calculator - This calculator does the following:
* Takes the Natural Log base e of a number x Ln(x) → logex
* Raises e to a power of y, ey
* Performs the change of base rule on logb(x)
* Solves equations in the form bcx = d where b, c, and d are constants and x is any variable a-z
* Solves equations in the form cedx=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z
* Exponential form to logarithmic form for expressions such as 53 = 125 to logarithmic form
* Logarithmic form to exponential form for expressions such as Log5125 = 3
M is the sum of a and its reciprocalM is the sum of a and its reciprocal
The reciprocal of a variable is 1 divided by the variable
1/a
The sum of a and its reciprocal means we add:
a + 1/a
The phrase [I]is[/I] means an equation, so we set M equal to the sum of a + 1/a:
[B]M = 1 + 1/a[/B]
Match each variable with a variable by placing the correct letter on each line.Match each variable with a variable by placing the correct letter on each line.
a) principal
b) interest
c) interest rate
d) term/time
2 years
1.5%
$995
$29.85
[B]Principal is $995
Interest is $29.85 since 995 * .0.15 * 2 = 29.85
Interest rate is 1.5%
Term/time is 2 year[/B]s
Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she cMelissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month?
Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is:
C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have:
C(x) = 264
The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns.
Now, profit is Revenue - Cost. Our profit function is:
P(x) = 53x - 264
To make a profit of $800 per month, we set P(x) = 800.
53x - 264 = 800
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=53x-264%3D800&pl=Solve']equation solver[/URL], we get:
[B]x ~ 21 lawns[/B]
Mr. Chris’s new app “Tick-Tock” is the hottest thing to hit the app store since...ever. It costs $5Mr. Chris’s new app “Tick-Tock” is the hottest thing to hit the app store since...ever. It costs $5 to buy the app and then $2.99 for each month that you subscribe (a bargain!). How much would it cost to use the app for one year? Write an equation to model this using the variable “m” to represent the number of months that you use the app.
Set up the cost function C(m) where m is the number of months you subscribe:
C(m) = Monthly Subscription Fee * months + Purchase fee
[B]C(m) = 2.99m + 5[/B]
multiply a number by 4 and then subtract the answer from 30multiply a number by 4 and then subtract the answer from 30
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Multiply this number by 4:
4x
Subtract the answer from 30:
[B]30 - 4x[/B]
Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and suMultiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and subtracting 4. Find the number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
multiply a number by 6 and subtract 6:
6x - 6
Multiply a number by 3 and subtract 4:
3x - 4
The phrase [I]gives the same result[/I] means an equation. So we set 6x - 6 equal to 3x - 4
6x - 6 = 3x - 4
To solve this equation for x, we type it in our search engine and we get:
x = [B]2/3[/B]
Multiply the difference of 3 and q by pMultiply the difference of 3 and q by p.
Take this algebraic expression in pieces:
[B][U]Step 1: The difference of 3 and q[/U][/B]
The word [I]difference[/I] means we subtract the variable q from 3
3 - q
[B][U]Step 2: Multiply the expression 3 - q by p:[/U]
p(3 - q)[/B]
Multiplying a number by 6 is equal to the number increased by 9Multiplying a number by 6 is equal to the number increased by 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Multiply it by 6 --> 6x
We set this equal to the same number increased by 9. Increased by means we add:
[B]6x = x + 9 <-- This is our algebraic expression
[/B]
To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3Dx%2B9&pl=Solve']type it into the search engine [/URL]and get x = 1.8.
n + 9n - 8 - 5 = 2n + 3n + 9n - 8 - 5 = 2n + 3
Solve for [I]n[/I] in the equation n + 9n - 8 - 5 = 2n + 3
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(1 + 9)n = 10n
[SIZE=5][B]Step 2: Group the constant terms on the left hand side:[/B][/SIZE]
-8 - 5 = -13
[SIZE=5][B]Step 3: Form modified equation[/B][/SIZE]
10n - 13 = 2n + 3
[SIZE=5][B]Step 4: Group variables:[/B][/SIZE]
We need to group our variables 10n and 2n. To do that, we subtract 2n from both sides
10n - 13 - 2n = 2n + 3 - 2n
[SIZE=5][B]Step 5: Cancel 2n on the right side:[/B][/SIZE]
8n - 13 = 3
[SIZE=5][B]Step 6: Group constants:[/B][/SIZE]
We need to group our constants -13 and 3. To do that, we add 13 to both sides
8n - 13 + 13 = 3 + 13
[SIZE=5][B]Step 7: Cancel 13 on the left side:[/B][/SIZE]
8n = 16
[SIZE=5][B]Step 8: Divide each side of the equation by 8[/B][/SIZE]
8n/8 = 16/8
n = [B]2[/B]
n - n = 10 - nn - n = 10 - n
Solve for [I]n[/I] in the equation n - n = 10 - n
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(1 - 1)n = 0n = 0
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
= - n + 10
[SIZE=5][B]Step 3: Group variables:[/B][/SIZE]
We need to group our variables and -n. To do that, we add n to both sides
+ n = -n + 10 + n
[SIZE=5][B]Step 4: Cancel -n on the right side:[/B][/SIZE]
n = [B]10[/B]
n = 3n - 1/2n = 3n - 1/2
Solve for [I]n[/I] in the equation n = 3n - 1/2
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables n and 3n. To do that, we subtract 3n from both sides
n - 3n = 3n - 0.5 - 3n
[SIZE=5][B]Step 2: Cancel 3n on the right side:[/B][/SIZE]
-2n = -0.5
[SIZE=5][B]Step 3: Divide each side of the equation by -2[/B][/SIZE]
-2n/-2 = -0.5/-2
n = [B]0.25 or 1/4[/B]
n = b + d^2a for an = b + d^2a for a
Let's start by isolating the one term with the a variable.
Subtract b from each side:
n - b = b - b + d^2a
Cancel the b terms on the right side and we get:
n - b = d^2a
With the a term isolated, let's divide each side of the equation by d^2:
(n - b)/d^2 = d^2a/d^2
Cancel the d^2 on the right side, and we'll display this with the variable to solve on the left side:
a = [B](n - b)/d^2
[MEDIA=youtube]BCEVsZmoKoQ[/MEDIA][/B]
Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daugNancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daughter?
Declare variables for each age:
[LIST]
[*]Let Nancy's age be n
[*]Let her daughter's age be d
[/LIST]
We're given two equations:
[LIST=1]
[*]n = 3d - 10
[*]n = 41
[/LIST]
We set 3d - 10 = 41 and solve for d:
Solve for [I]d[/I] in the equation 3d - 10 = 41
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants -10 and 41. To do that, we add 10 to both sides
3d - 10 + 10 = 41 + 10
[SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE]
3d = 51
[SIZE=5][B]Step 3: Divide each side of the equation by 3[/B][/SIZE]
3d/3 = 51/3
d = [B]17[/B]
Nine less than a number is no more than 8 and no less than 3Nine less than a number is no more than 8 and no less than 3
A number is denoted as an arbitrary variable, let's call it x.
We have a double inequality:
[LIST=1]
[*]No more than 8 means less than or equal to 8
[*]No less than 3 means greater than or equal to 3
[/LIST]
[B]3 <= x <= 8[/B]
Nine times the sum of a number and 6Nine times the sum of a number and 6
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 6 means we add 6 to x:
x + 6
9 times the sum:
[B]9(x + 6)[/B]
Normal DistributionFree Normal Distribution Calculator - Calculates the probability that a random variable is less than or greater than a value or between 2 values using the Normal Distribution z-score (z value) method (Central Limit Theorem).
Also calculates the Range of values for the 68-95-99.7 rule, or three-sigma rule, or empirical rule. Calculates z score probability
One fifth of the square of a numberOne fifth of the square of a number
We have an algebraic expression. Let's break this into parts.
[LIST=1]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x
[*]The square of a number means we raise it to the power of 2. So we have x^2
[*]One-fifth means we have a fraction, where we divide our x^2 in Step 2 by 5. So we get our final answer below:
[/LIST]
[B]x^2/5[/B]
One-half a number is fiftyThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
One-half a number means we divide x by2:
x/2
The word [I]is[/I] means equal to. We set x/2 equal to 50 for our algebraic expression
[B]x/2 = 50
[/B]
If the problem asks us to solve for x, we cross multiply:
x = 2 * 50
x = [B]100[/B]
One-half a number times fifteenThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
One-half a number means we multiply x by 1/2:
x/2
Times fifteen means we multiply:
[B]15x/2[/B]
One-third a number less twoThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
One-third a number means we multiply x by 1/3:
x/3
Less two means we subtract 2
[B]x/3 - 2[/B]
Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% eachPenny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each year since. Let x = the number of years since 2010 and y = the value of the car. What will the value of the car be in 2020? Write the equation, using the variables above, that represents this situation and solve the problem, showing the calculation you did to get your solution. Round your answer to the nearest whole number.
We have the equation y(x):
y(x) = 25,000(0.97)^x <-- Since a 3 % decrease is the same as multiplying the starting value by 0.97
The problem asks for y(2020). So x = 2020 - 2010 = 10.
y(10) = 25,000(0.97)^10
y(10) = 25,000(0.73742412689)
y(10) = [B]18,435.60[/B]
PolynomialFree Polynomial Calculator - This calculator will take an expression without division signs and combine like terms.
It will also analyze an polynomial that you enter to identify constant, variables, and exponents. It determines the degree as well.
Prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and twImagine you are in a game show. Prizes hidden on a game board with 10 spaces. One prize is worth $100, another is worth $50, and two are worth $10. You have to pay $20 to the host if your choice is not correct. Let the random variable x be the winning
(a) What is your expected winning in this game?
(b) Determine the standard deviation of x. (Round the answer to two decimal places)
(a) 100(0.1) + 50(0.1) + 10(0.2) - 20 = 10 + 5 + 2 - 20 = [B]-3[/B]
(b) 3.3 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=+100,50,10&num2=+0.1,0.1,0.2&usep=usep&pl=Number+Set+Basics']standard deviation calculator[/URL]
product of a number and its reciprocal is increased by 7product of a number and its reciprocal is increased by 7
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Its reciprocal means we take the reciprocal of x:
1/x
product of a number and its reciprocal:
x * 1/x
x/x
The x's cancel giving us:
1
is increased by 7 means we add 7:
1 + 7
[B]8[/B]
quotient of the sum of 2 numbers and 6quotient of the sum of 2 numbers and 6
The phrase [I]two numbers[/I] means we choose 2 arbitrary variables, let's call them x and y
x, y
The sum of 2 numbers:
x + y
quotient of the sum of 2 numbers and 6
[B](x + y)/6[/B]
quotient of the sum of 3 numbers and 3quotient of the sum of 3 numbers and 3
The phrase [I]3 numbers[/I] means we choose 3 arbitrary variables:
a, b,c
The sum of the 3 numbers:
a + b + c
quotient of the sum of 3 numbers and 3
[B](a + b + c)/3[/B]
raise t to the 10th power, then find the quotient of the result and sraise t to the 10th power, then find the quotient of the result and s
Raise t to the 10th power means we use t as our variable and 10 as our exponent:
t^10
The quotient means a fraction, where the numerator is t^10 and the denominator is s:
[B]t^10/s[/B]
Rational Exponents - Fractional IndicesFree Rational Exponents - Fractional Indices Calculator - This calculator evaluates and simplifies a rational exponent expression in the form ab/c where a is any integer or any variable [a-z] while b and c are integers. Also evaluates the product of rational exponents
Rearrange the following equation to make x the subject, and select the correct rearrangement from thRearrange the following equation to make x the subject, and select the correct rearrangement from the list below
3x + 2y 1
-------- = ---
4x + y 3
[LIST]
[*]x = 7y/13
[*]x = 7y/5
[*]x = -7y
[*]x = -3y
[*]x = 3y/5
[*]x = -5y/13
[*]x = -y
[/LIST]
Cross multiply:
3(3x - 2y) = 4x + y
Multiply the left side through
9x - 6y = 4x + y
Subtract 4x from each side and add 6y to each side
5x = 7y
Divide each side by 5 to isolate x, the subject of an equation is the variable to the left
[B]x = 7y/5[/B]
Rectangle Word ProblemFree Rectangle Word Problem Calculator - Solves word problems based on area or perimeter and variable side lengths
Sam purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost cSam purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Sam paid.
Cost Function is:
[B]c = 4n[/B]
Or, using n as a function variable, we write:
c(n) = 4n
Seven less than 1/4 of a number is 9.Seven less than 1/4 of a number is 9.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
1/4 of a number means we multiply x by 1/4:
x/4
Seven less than this means we subtract 7 from x/4:
x/4 - 7
The word [I]is[/I] means an equation, so we set x/4 - 7 equal to 9:
[B]x/4 - 7 = 9[/B]
Seven subtracted from the product of 3 and a number is greater than or equal to -26Seven subtracted from the product of 3 and a number is greater than or equal to -26
[LIST=1]
[*]A number means an arbitrary variable, let's call it x.
[*]The product of 3 and a number is written as 3x
[*]Seven subtracted from 3x is written as 3x - 7
[*]Finally, that entire expression is greater than or equal to -26: [B]3x - 7 >= - 26[/B]
[/LIST]
Six less than twice a number is at least -1 and at most 1First, the phrase [I]a number[/I] means we choose an arbitrary variable, let's call it x.
Twice a number means we multiply it by 2.
2x
Six less than that means we subtract 6
2x - 6
Now, the last piece, we set up an inequality. At least -1 means greater than or equal to 1. At most 1 means less than or equal to 1. Notice, for both points, we include the number.
-1 <= 2x - 6 <= 1
Sixteen subtracted from five times a number equals the number plus fourThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
5 times a number
5x
Sixteen subtracted from five times a number
5x - 16
the number plus 4:
x + 4
Equals means we set 5x - 16 equals to x + 4 for our algebraic expression:
[B]5x - 16 = x + 4[/B]
[B][/B]
If you have to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-16%3Dx%2B4&pl=Solve']type this expression into our math solver[/URL] and we get:
x = [B]5[/B]
Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cSoda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point.
Calculate the revenue function R(c) where s is the number of sodas sold:
R(s) = Sale Price * number of units sold
R(s) = 50s
Calculate the cost function C(s) where s is the number of sodas sold:
C(s) = Variable Cost * s + Fixed Cost
C(s) = 0.25s + 900
Our break-even point is found by setting R(s) = C(s):
0.25s + 900 = 50s
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]18.09[/B]
square root of the sum of 2 variablessquare root of the sum of 2 variables
The phrase [I]2 variables[/I] means we choose 2 arbitrary variables, let's call them x and y:
x, y
The sum of 2 variables means we add:
x + y
Square root of the sum of 2 variables is written as:
[B]sqrt(x + y)[/B]
Squaring a number equals 5 times that numberSquaring a number equals 5 times that number.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Squaring this number:
x^2
5 times this number means we multiply by 5:
5x
The phrase [I]equals[/I] means we set both expressions equal to each other:
[B]x^2 = 5x [/B] <-- This is our algebraic expression
If you want to solve for x, then we subtract 5x from each side:
x^2 - 5x = 5x - 5x
Cancel the 5x on the right side, leaving us with 0:
x^2 - 5x = 0
Factor out x:
x(x - 5)
So we get x = 0 or [B]x = 5[/B]
Start with t and cube it.Start with t and cube it.
Cubing a variable means raising it to the power of 3:
[B]t^3[/B]
Substitute the given values into given formula and solve for the unknown variable. S=4LW + 2 WH; S=Substitute the given values into given formula and solve for the unknown variable. S = 4LW + 2 WH; S= 144, L= 8, W= 4. H=
S = 4LW + 2 WH
Substituting our given values, we have:
144 = 4(8)(4) + 2(4)H
144 = 128 + 8H
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=128%2B8h%3D144&pl=Solve']equation calculator[/URL], we get:
[B]H = 2[/B]
subtract half of a number from 10subtract half of a number from 10
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
half of a number means we divide x by 2:
x/2
subtract half of a number from 10
[B]10 - x/2[/B]
sum of 3 consecutive odd integers equals 1 hundred 17sum of 3 consecutive odd integers equals 1 hundred 17
The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers?
1) Set up an equation where our [I]odd numbers[/I] are n, n + 2, n + 4
2) We increment by 2 for each number since we have [I]odd numbers[/I].
3) We set this sum of consecutive [I]odd numbers[/I] equal to 117
n + (n + 2) + (n + 4) = 117
[SIZE=5][B]Simplify this equation by grouping variables and constants together:[/B][/SIZE]
(n + n + n) + 2 + 4 = 117
3n + 6 = 117
[SIZE=5][B]Subtract 6 from each side to isolate 3n:[/B][/SIZE]
3n + 6 - 6 = 117 - 6
[SIZE=5][B]Cancel the 6 on the left side and we get:[/B][/SIZE]
3n + [S]6[/S] - [S]6[/S] = 117 - 6
3n = 111
[SIZE=5][B]Divide each side of the equation by 3 to isolate n:[/B][/SIZE]
3n/3 = 111/3
[SIZE=5][B]Cancel the 3 on the left side:[/B][/SIZE]
[S]3[/S]n/[S]3 [/S]= 111/3
n = 37
Call this n1, so we find our other 2 numbers
n2 = n1 + 2
n2 = 37 + 2
n2 = 39
n3 = n2 + 2
n3 = 39 + 2
n3 = 41
[SIZE=5][B]List out the 3 consecutive odd numbers[/B][/SIZE]
([B]37, 39, 41[/B])
37 ← 1st number, or the Smallest, Minimum, Least Value
39 ← 2nd number
41 ← 3rd or the Largest, Maximum, Highest Value
sum of a number and 7 is subtracted from 15 the result is 6.Sum of a number and 7 is subtracted from 15 the result is 6.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
We take this expression in pieces. Sum of a number and 7
x + 7
Subtracted from 15
15 - (x + 7)
The result is means an equation, so we set this expression above equal to 6
[B]15 - (x + 7) = 6 <-- This is our algebraic expression[/B]
If the problem asks you to solve for x, we Group like terms
15 - x - 7 = 6
8 - x = 6
[URL='https://www.mathcelebrity.com/1unk.php?num=8-x%3D6&pl=Solve']Type 8 - x = 6 into the search engine[/URL], and we get [B]x = 2[/B]
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gaSuppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2012 pounds. When carrying 55 gallons of fuel, it weighs 2208 pounds. How much does the airplane weigh if it is carrying 65 gallons of fuel?
Linear functions are written in the form of one dependent variable and one independent variable. Using g as the number of gallons and W(g) as the weight, we have:
W(g) = gx + c where c is a constant
We are given:
[LIST]
[*]W(20) = 2012
[*]W(55) = 2208
[/LIST]
We want to know W(65)
Using our givens, we have:
W(20) = 20x + c = 2012
W(55) = 55x + c = 2208
Rearranging both equations, we have:
c = 2012 - 20x
c = 2208 - 55x
Set them both equal to each other:
2012 - 20x = 2208 - 55x
Add 55x to each side:
35x + 2012 = 2208
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=35x%2B2012%3D2208&pl=Solve']equation solver[/URL], we see that x is 5.6
Plugging x = 5.6 back into the first equation, we get:
c = 2012 - 20(5.6)
c = 2012 - 112
c = 2900
Now that we have all our pieces, find W(65)
W(65) = 65(5.6) + 2900
W(65) = 264 + 2900
W(65) = [B]3264[/B]
Ten subtracted from the product of 9 and a number is less than −24Ten subtracted from the product of 9 and a number is less than −24.
A number means an arbitrary variable, let's call it x
x
The product of 9 and a number:
9x
Ten subtracted from that
9x - 10
Finally, is less than means we set our entire expression less than -24
[B]9x - 10 < -24[/B]
Ten times the sum of twice a number and sixThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number means we multiply x by 2:
2x
The sum of twice a number and 6:
2x + 6
Ten times the sum of twice a number and six
[B]10(2x + 6)[/B]
The cost of having a plumber spend h hours atThe cost of having a plumber spend h hours at your house if the plumber charges $60 for coming to the house and $70 per hour labor:
We have a fixed cost of $60 plus the variable cost of $70h. We add both for our total cost C(h):
[B]C(h) = $70h + 60[/B]
The cost to rent a boat is $10. There is also charge of $2 for each person. Which expresion represenThe cost to rent a boat is $10. There is also charge of $2 for each person. Which expresion represents the total cost to rent a boat for p persons?
The cost function includes a fixed cost of $10 plus a variable cost of 2 persons for p persons:
[B]C(p) = 2p + 10[/B]
the cube of c decreased by a^2the cube of c decreased by a^2
The cube of means we raise the variable c to the power of 3:
c^3
The phrase [I]decreased by[/I] means we subtract:
[B]c^3 - a^2[/B]
the difference between 7 times a number and 9 less than a numberthe difference between 7 times a number and 9 less than a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
7 times a number means we multiply x by 7
7x
9 less than a number means we subtract 9 from x
x - 9
The difference between the two expressions means we subtract (x - 9) from 7x
7x - (x - 9)
Simplifying this, we have:
7x - x + 9
Grouping like terms, we get:
[B]6x + 9[/B]
The difference between a number and 9 is 27. Find that numberThe difference between a number and 9 is 27. Find that number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The difference between a number and 9
x - 9
The word [I]is[/I] means equal to, so we set x - 9 equal to 27:
x - 9 = 27
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-9%3D27&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]36[/B]
The difference between the opposite of a number and 6.The difference between the opposite of a number and 6.
The phrase [I]a number means[/I] an arbitrary variable, let's call it x.
x
The opposite of a number means we multiply by x by -1
-x
The phrase [I]the difference between[/I] means we subtract 6 from -x:
[B]-x - 6[/B]
The difference between the product of 4 and a number and the square of a numberThe difference between the product of 4 and a number and the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The product of 4 and a number:
4x
The square of a number means we raise x to the power of 2:
x^2
The difference between the product of 4 and a number and the square of a number:
[B]4x - x^2[/B]
the difference between triple a number and double a numberthe difference between triple a number and double a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Triple a number means we multiply x by 3:
3x
Double a number means we multiply x by 2:
2x
The difference means we subtract 2x from 3x:
3x - 2x
Simplifying like terms, we have:
(3 - 2)x = [B]x[/B]
The difference in Julies height and 9 is 48 letting j be Julie's heightThe difference in Julies height and 9 is 48 letting j be Julie's height
Step 1: If Julie's height is represented with the variable j, then we subtract 9 from j since the phrase [I]difference[/I] means we subtract:
j - 9
Step 2: The word [I]is[/I] means an equation, so we set j - 9 equal to 48 for our final algebraic expression:
[B]j - 9 = 48[/B]
The difference of 25 and a number added to triple another numberThe difference of 25 and a number added to triple another number
The phrase [I]a number [/I]means an arbitrary variable, let's call it x:
x
The difference of 25 and a number means we subtract x from 25:
25 - x
The phrase [I]another number[/I] means a different arbitrary variable, let's call it y:
y
Triple another number means we multiply y by 3:
3y
The phrase [I]added to[/I] means we add 25 - x to 3y
[B]25 - x + 3y[/B]
the difference of 4 and the quotient of 18 and a numberthe difference of 4 and the quotient of 18 and a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The quotient of 18 and a number means we divide 18 by the variable x.
18/x
The difference of 4 and the quotient above means we subtract 18/x from 4:
[B]4 - 18/x[/B]
The difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the numThe difference of a number and 6 is the same as 5 times the sum of the number and 2. What is the number?
We have two expressions:
[U]Expression 1: [I]The difference of a number and 6[/I][/U]
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The difference of a number and 6 means we subtract 6 from x:
x - 6
[U]Expression 2: [I]5 times the sum of the number and 2[/I][/U]
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The sum of a number and 2 means we add 2 to x:
x + 2
5 times the sum means we multiply x + 2 by 5
5(x + 2)
[U]For the last step, we evaluate the expression [I]is the same as[/I][/U]
This means equal to, so we set x - 6 equal to 5(x + 2)
[B]x - 6 = 5(x + 2)[/B]
The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown nThe difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown number.
The phrase a number uses the variable w.
3 times w is written as 3w
The difference of 3w and 6 is written as 3w - 6
Set this equal to 7
[B]3w - 6 = 7
[/B]
This is our algebraic expression. To solve this equation for w, we [URL='http://www.mathcelebrity.com/1unk.php?num=3w-6%3D7&pl=Solve']type the algebraic expression into our search engine[/URL].
The difference of twice a number and 4 is at least -27The difference of twice a number and 4 is at least -27.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Twice a number means multiply the number by 2
2x
[I]and 4[/I] means we add 4 to our expression:
2x + 4
[I]Is at least[/I] means an inequality. In this case, it's greater than or equal to:
[B]2x + 4 >= -27
[/B]
To solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B4%3E%3D-27&pl=Solve']type it in the search engine[/URL].
The difference of twice a number and 6 is at most 28The difference of twice a number and 6 is at most 28
This is an algebraic expression. Let's take it in parts:
[LIST=1]
[*]The phrase [I]a number[/I], means an arbitrary variable, let's call it x
[*]Twice this number means we multiply x by 2: 2x
[*][I]The difference of[/I] means subtract, so we subtract 6 to 2x: 2x - 6
[*][I]Is at most [/I]means less than or equal to, so we create an inequality where 2x - 6 is less than or equal to 28, using the <= sign
[/LIST]
[B]2x - 6 <= 28
[/B]
If you wish to solve this inequality, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-6%3C%3D28&pl=Solve']click this link[/URL].
the difference of twice a number and 8 is at most -30the difference of twice a number and 8 is at most -30.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Twice this number means we multiply by 2, so we have 2x.
We take the difference of 2x and 8, meaning we subtract 8:
2x - 8
Finally, the phrase [I]at most[/I] means an inequality, also known as less than or equal to:
[B]2x - 8 <= 30 <-- This is our algebraic expression
[/B]
To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x-8%3C%3D30&pl=Solve']type it into the search engine[/URL] and get x <= 19.
The difference of twice a number and 9 is less than 22The difference of twice a number and 9 is less than 22
The phrase a number, means an arbitrary variable, let's call it x.
x
Twice a number
2x
The difference of twice a number and 9
2x - 9
Is less than 22
[B]2x - 9 < 22[/B]
The fixed costs to produce a certain product are 15,000 and the variable costs are $12.00 per item.The fixed costs to produce a certain product are 15,000 and the variable costs are $12.00 per item. The revenue for a certain product is $27.00 each. If the company sells x products, then what is the revenue equation?
R(x) = Revenue per item x number of products sold
[B]R(x) = 27x[/B]
The phone company charges Rachel 12 cents per minute for her long distance calls. A discount companyThe phone company charges Rachel 12 cents per minute for her long distance calls. A discount company called Rachel and offered her long distance service for 1/2 cent per minute, but will charge a $46 monthly fee. How many minutes per month must Rachel talk on the phone to make the discount a better deal?
Minutes Rachel talks = m
Current plan cost = 0.12m
New plan cost = 0.005m + 46
Set new plan equal to current plan:
0.005m + 46 = 0.12m
Solve for [I]m[/I] in the equation 0.005m + 46 = 0.12m
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 0.005m and 0.12m. To do that, we subtract 0.12m from both sides
0.005m + 46 - 0.12m = 0.12m - 0.12m
[SIZE=5][B]Step 2: Cancel 0.12m on the right side:[/B][/SIZE]
-0.115m + 46 = 0
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 46 and 0. To do that, we subtract 46 from both sides
-0.115m + 46 - 46 = 0 - 46
[SIZE=5][B]Step 4: Cancel 46 on the left side:[/B][/SIZE]
-0.115m = -46
[SIZE=5][B]Step 5: Divide each side of the equation by -0.115[/B][/SIZE]
-0.115m/-0.115 = -46/-0.115
m = [B]400
She must talk over 400 minutes for the new plan to be a better deal
[URL='https://www.mathcelebrity.com/1unk.php?num=0.005m%2B46%3D0.12m&pl=Solve']Source[/URL][/B]
the product of 2 less than a number and 7 is 13the product of 2 less than a number and 7 is 13
Take this algebraic expression in [U]4 parts[/U]:
Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Part 2 - 2 less than a number means we subtract 2 from x
x - 2
Part 3 - The phrase [I]product[/I] means we multiply x - 2 by 7
7(x - 2)
Part 4 - The phrase [I]is[/I] means an equation, so we set 7(x - 2) equal to 13
[B]7(x - 2) = 13[/B]
the product of 8 and 15 more than a numberthe product of 8 and 15 more than a number.
Take this algebraic expression in pieces.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
15 more than x means we add 15 to x:
x + 15
The product of 8 and 15 more than a number means we multiply 8 by x + 15
[B]8(x + 15)[/B]
the product of a number and 15 is not less than 15the product of a number and 15 is not less than 15
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
the product of a number and 15 means we multiply x by 15
15x
The phrase [I]not less than[/I] means greater than or equal to. We set 15x greater than prequel to 15
[B]15x >= 15 <-- This is our algebraic expression
[/B]
[U]If the problem asks you to solve for x:[/U]
Divide each side by 15:
15x/15 >= 15/15
[B]x >= 1[/B]
The product of the 2 numbers x and yThe product of the 2 numbers x and y
The phrase [I]product [/I]means we multiply the two variables, x and y.
[B]xy[/B]
The quotient of 2 and the sum of a number and 1The quotient of 2 and the sum of a number and 1.
The phrase [I]a number[/I] represents an arbitrary variable, let's call it x.
The sum of a number and 1 is written as:
x + 1
The word [I]quotient[/I] means a fraction. So we divide 2 by x + 1
2
--------
( x + 1)
[MEDIA=youtube]uPQHCKr-9vA[/MEDIA]
the quotient of 4 more than a number and 7 is 10the quotient of 4 more than a number and 7 is 10
Take this algebraic expression in pieces:
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
4 more than a number means we add 4 to x:
x + 4
The quotient of 4 more than a number and 7 means we divide x + 4 by 7
(x + 4)/7
The word [I]is[/I] means an equation, so we set (x + 4)/7 equal to 10 to get our algebraic expression of:
[B](x + 4)/7 = 10
[/B]
If the problem asks you to solve for x, then we cross multiply:
x + 4 = 10 * 7
x + 4 = 70
Subtract 4 from each side:
x + 4 - 4 = 70 - 4
x = [B]66
[MEDIA=youtube]j-GZLPVKbTM[/MEDIA][/B]
the quotient of a number and twice another numberthe quotient of a number and twice another number
The phrase[I] a number [/I]means an arbitrary variable, let's call it x.
The phrase[I] another number [/I]means another arbitrary variable, let's call it y.
Twice means we multiply y by 2:2y
The quotient means we divide x by 2y:
[B]x/2y[/B]
the quotient of a variable and 7the quotient of a variable and 7.
A variable means an arbitrary number, let's call it x.
A quotient means a fraction, where x is the numerator and 7 is the denominator:
[B] x
---
7[/B]
the quotient of the cube of a number x and 5the quotient of the cube of a number x and 5
[LIST]
[*]A number means an arbitrary variable, let's call it x
[*]The cube of a number means raise it to the 3rd power, so we have x^3
[*]Quotient means we have a fraction, so our numerator is x^3, and our denominator is 5
[/LIST]
[B]x^3
----
5[/B]
the ratio of 50 and a number added to the quotient of a number and 10the ratio of 50 and a number added to the quotient of a number and 10
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The ratio of 50 and x means we divide by 50 by x
50/x
The quotient of a number and 10 means we have a fraction:
x/10
The phrase [I]added to[/I] means we add 50/x to x/10
[B]50/x + x/10[/B]
the ratio of a number x and 4 added to 2the ratio of a number x and 4 added to 2
Take this algebraic expression in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The ratio of this number and 4 means we have a fraction:
x/4
The phrase [I]added to[/I] means we add 2 to x/4
[B]x/4 + 2[/B]
the ratio of ten to a numberthe ratio of ten to a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The ratio of 10 and this number x is written as:
[B]10/x[/B]
The square of a number added to its reciprocalThe square of a number added to its reciprocal
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
the square of x mean we raise x to the power of 2. It's written as:
x^2
The reciprocal of x is 1/x
We add these together to get our final algebraic expression:
[B]x^2 + 1/x
[MEDIA=youtube]ZHut58-AoDU[/MEDIA][/B]
The square of a number increased by 7 is 23The square of a number increased by 7 is 23
The phrase [I]a number [/I]means an arbitrary variable, let's call it x.
x
The square of a number means we raise x to the power of 2:
x^2
[I]Increased by[/I] means we add 7 to x^2
x^2 + 7
The word [I]is[/I] means an equation. So we set x^2 + 7 equal to 23:
[B]x^2 + 7 = 23[/B]
The square of the difference of a number and 4The square of the difference of a number and 4
A number means an arbitrary variable, let's call it x
The difference of a number and 4:
x - 4
The square of this difference:
[B](x - 4)^2[/B]
The sum of 13 and twice janelles ageLet Janelle's age be the variable a.
So twice Janelle's age is denoted as 2a.
We want the sum of 13 and 2a.
Sum means add.
13 + 2a
or
2a + 13
the sum of 16 and twice julies savings use the variable j to represent julies savingsThe sum of 16 and twice julies savings use the variable j to represent julies savings
Twice Julie's savings:
2j
The sum of 16 and twice Julie's savings:
[B]2j + 16[/B]
the sum of 2 times a number and -2, added to 4 times a numberthe sum of 2 times a number and -2, added to 4 times a number.
The phrase, [I]a number[/I], means an arbitrary variable, let's call it x.
2 times a number
2x
The sum of means add, so we add -2, which is the same as subtracting 2
2x - 2
Now, we add 4 times x
2x - 2 + 4x
Combining like terms, we have:
(2 + 4)x - 2
[B]6x - 2[/B]
the sum of 3 numbersSince no variable name is defined, we pick 3 arbitrary variables. Let's pick x, y, and z.
The sum of 3 numbers means we add them together:
x + y + z
the sum of 3 numbersLet's choose 3 arbitrary variables, w, x, and y. We add them up:
[B]w + x + y[/B]
the sum of 3 numbers divided by its productthe sum of 3 numbers divided by its product
The phrase [I]3 numbers[/I] means we choose [I]3[/I] arbitrary variables. Let's call them x, y, z.
The sum of of these 3 numbers is:
x + y + z
The phrase [I]its product[/I] means we multiply all 3 arbitrary variables together:
xyz
Now, the phrase [I]divided by[/I] means we divide x + y + z by xyz:
[B](x + y + z)/xyz[/B]
The sum of 3 times the square of a number and negative 7The sum of 3 times the square of a number and negative 7
[U]The phrase [I]a number[/I] means an arbitrary variable, let's call it x:[/U]
x
[U]The square of a number means we raise x to the power of 2:[/U]
x^2
[U]3 times the square of a number:[/U]
3x^2
[U]The sum of 3 times the square of a number and negative 7[/U]
[B]3x^2 - 7[/B]
The sum of 5, 8, and a number amounts to 19. Find the number.The sum of 5, 8, and a number amounts to 19. Find the number.
We represent [I]a number[/I] with the variable "x". We write our problem as:
5 + 8 + x = 19
13 + x = 19
[URL='https://www.mathcelebrity.com/1unk.php?num=13%2Bx%3D19&pl=Solve']Type this problem into our calculator[/URL], and we get [B]x = 6[/B].
the sum of 6 and 7, plus 5 times a number, is -12the sum of 6 and 7, plus 5 times a number, is -12
The sum of 6 and 7 means we add the two numbers:
6 + 7
This evaluates to 13
Next, we take 5 times a number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So we multiply x by 5:
5x
The first two words say [I]the sum[/I], so we add 13 and 5x
13 + 5x
The word [I]is[/I] means an equation, so we set 13 + 5x equal to -12
[B]13 + 5x = -12[/B] <-- This is our algebraic expression
If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=13%2B5x%3D-12&pl=Solve']type this algebraic expression into our search engine[/URL] and you get:
[B]x = -5[/B]
The sum of 6 times a number and -8, added to 3 times a numberThe sum of 6 times a number and -8, added to 3 times a number
The phrase "a number", means an arbitrary variable, let's call it x.
6 times a number:
6x
And means we add, so we have
6x - 8
Added to 3 times a number
6x - 8 + 3x
Combine like terms:
[B]9x - 8[/B]
The sum of a and d isSince it's a sum, we add our two variables a and d.
a + d
the sum of a number and 16 is eA number means an arbitrary variable, let's call it x.
The sum of x and 16 means we add:
x + 16
Is, means equal to, so we set x + 16 = e
x + 16 = e
The sum of a number and 34 times the numberThe sum of a number and 34 times the number
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
x
34 times the number:
34x
The sum of a number and 34 times the number means we add both terms together:
x + 34x
The sum of a number and 5 all divided by 2 is 17The sum of a number and 5 all divided by 2 is 17
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The sum of a number and 5:
x + 5
All divided by 2:
(x + 5)/2
The word [I]is[/I] means equal to, so we set (x + 5)/2 equal to 17:
[B](x + 5)/2 = 17[/B]
The sum of a number and 5 divided by 8The sum of a number and 5 divided by 8.
Let's take this algebraic expression in parts.
Part 1: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
Part 2: The sum of a number and 5 means we add 5 to the number x
x + 5
Part 3: Next, we divide this expression by 8
[B](x + 5)/8[/B]
the sum of a number and its reciprocal is 5/2the sum of a number and its reciprocal is 5/2
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The reciprocal of the number means 1/x.
The sum means we add them:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 52
[B]x + 1/x = 52[/B]
The sum of a number and its reciprocal is 72The sum of a number and its reciprocal is 72
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
The reciprocal of the number is written as:
1/x
The sum of a number and its reciprocal means we add:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 72
[B]x + 1/x = 72[/B]
The sum of a number and its reciprocal is five.The sum of a number and its reciprocal is five.
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The reciprocal of the number is 1/x.
The sum means we add them together:
x + 1/x
The word [I]is[/I] means an equation, so we set x + 1/x equal to 5
[B]x + 1/x = 5[/B]
the sum of a number and itself is 8A number means an arbitrary variable, let's call it x.
The sum of a number and itself means adding the number to itself
x + x
Simplified, we have 2x
The word is means equal to, so we have an algebraic expression of:
[B]2x= 8
[/B]
IF you need to solve this equation, divide each side by 2
[B]x = 4[/B]
The sum of a number and twice its reciprocal is 3The sum of a number and twice its reciprocal is 3
the phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The reciprocal of a number means we take 1 over that number:
1/x
Twice the reciprocal means we multiply 1/x by 2:
2/x
The sum of a number and twice its reciprocal
x + 2/x
The word [I]is[/I] means equal to, so we set x + 2/x equal to 3
[B]x + 2/x = 3[/B]
the sum of a number divided by 8 and 3 equals 6"A Number" means an arbitrary variable, let's call it x.
x divide d by 8 is written as a quotient
x/8
The sum of x/8 and 3 means we add:
x/8 + 3
Finally, equals means we have an equation, so we set our expression above equal to 6
x/8 + 3 = 6
The sum Of a number squared and 14The sum Of a number squared and 14.
A number means an arbitrary variable, let's call it x.
Squared means we raise x to the 2nd power: x^2
The sum means we add x^2 to 14 to get our algebraic expression below:
[B]x^2 + 14[/B]
the sum of a number times 3 and 30 is less than 17the sum of a number times 3 and 30 is less than 17
A number is denoted as an arbitrary variable, let's call it x.
x
Times 3 means we multiply x by 3:
3x
The sum of a number times 3 and 30 means we add 30 to 3x above
3x + 30
Is less than 17 means we have an inequality, so we set 3x + 30 less than 17
3x + 30 < 17
To solve for x and see the interval notation, use [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B30%3C17&pl=Solve']our calculator[/URL]:
The sum of five and twice a number is 17The sum of five and twice a number is 17
[U]The phrase a number means an arbitrary variable, let's call it x[/U]
x
[U]Twice a number means we multiply x by 2:[/U]
2x
[U]The sum of five and twice a number means we add 5 to 2x:[/U]
2x + 5
[U]The phrase [I]is[/I] means an equation, so we set 2x + 5 equal to 17 to get our algebraic expression[/U]
[B]2x + 5 = 17[/B]
[B][/B]
As a bonus, if the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D17&pl=Solve']type in this algebraic expression into our math engine[/URL] and we get:
x = 6
The sum of six times a number and 1 is equal to five times the number. Find the number.The sum of six times a number and 1 is equal to five times the number. Find the number.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
6 times a number is written as:
6x
the sum of six times a number and 1 is written as:
6x + 1
Five times the number is written as:
5x
The phrase [I]is equal to[/I] means an equation, so we set 6x + 1 equal to 5x:
6x + 1 = 5x
[URL='https://www.mathcelebrity.com/1unk.php?num=6x%2B1%3D5x&pl=Solve']Plugging this into our search engine[/URL], we get:
x = [B]-1[/B]
the sum of the cube of a number and 12the sum of the cube of a number and 12
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The cube of a number means we raise x to the power of 3:
x^3
Finally, we take the sum of x^3 and 12. Meaning, we add 12 to x^3. This is our final algebraic expression.
[B]x^3 + 12[/B]
The sum of the reciprocals of x and yThe sum of the reciprocals of x and y
The reciprocal of a variable is found by taking 1 over the variable.
[LIST]
[*]Reciprocal of x = 1/x
[*]Reciprocal of y = 1/y
[/LIST]
The sum means we add the reciprocals together
[B]1/x + 1/y[/B]
The sum of the square of a number and 7 times a numberThe sum of the square of a number and 7 times a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
Square the number:
x^2
7 times the number means we multiply x by 7:
7x
The sum means we add x^2 and 7x
[B]x^2 + 7x[/B]
The sum of three consecutive integers is 42Let the 3 integers be x, y, and z.
y = x + 1
z = y + 1, or x + 2.
Set up our equation:
x + (x + 1) + (x + 2) = 42
Group our variables and constants:
(x + x + x) + (1 + 2) = 42
3x + 3 = 42
Subtract 3 from each side:
3x = 39
Divide each side of the equation by 3:
[B]x = 13
So y = x + 1 = 14
z = x + 2 = 15
(x,y,z) = (13,14,15)[/B]
The Sum of three times a number and 18 is -39. Find the numberThe Sum of three times a number and 18 is -39. Find the number.
A number means an arbitrary variable, let us call it x.
Three times x:
3x
The sum of this and 18:
3x + 18
Is means equal to, so we set 3x + 18 = -39
3x + 18 = -39
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']equation solver[/URL], we get [B]x = -19[/B]
The sum of three times a number and twelveThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
3 times a number:
3x
The sum of three times a number and twelve means we add 12 to 3x:
[B]3x + 12[/B]
The sum of two numbers multiplied by 9Choose two variables as arbitrary numbers, let's say x and y
[U]The sum of x and y is:[/U]
x + y
[U]Multiply that by 9[/U]
[B]9(x + y)[/B]
The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define yourThe total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet.
We set up a cost function as fixed cost plus total cost. Fixed cost is the shipping charge of $9. So we have the following cost function where n is the cost of the bracelets:
C(b) = nb + 9
We are given C(9) = 72 and b = 9
9n + 9 = 72
[URL='https://www.mathcelebrity.com/1unk.php?num=9n%2B9%3D72&pl=Solve']Run this through our equation calculator[/URL], and we get [B]n = 7[/B].
The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25The total cost of producing x units for which the fixed costs are $2900 and the cost per unit is $25
[U]Set up the cost function:[/U]
Cost function = Fixed Cost + Variable Cost per Unit * Number of Units
[U]Plug in Fixed Cost = 2900 and Cost per Unit = $25[/U]
[B]C(x) = 2900 + 25x
[MEDIA=youtube]77PiD-VADjM[/MEDIA][/B]
The volleyball team and the wrestling team at Clarksville High School are having a joint car wash tThe volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take?
Set up the earnings equation for the volleyball team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 4w + 81
Set up the earnings equation for the wrestling team where w is the number of cars washed:
E = Price per cars washed * w + past fundraisers
E = 2w + 85
If the raised the same amount in total, set both earnings equations equal to each other:
4w + 81 = 2w + 85
Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides
4w + 81 - 2w = 2w + 85 - 2w
[SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE]
2w + 81 = 85
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 81 and 85. To do that, we subtract 81 from both sides
2w + 81 - 81 = 85 - 81
[SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE]
2w = 4
[SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 4/2
w = [B]2 <-- How many cars it will take
[/B]
To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2:
E = 4(2) + 81
E = 8 + 81
E = [B]89 <-- Total Earnings[/B]
There are 7 more jeeps than vans.There are 7 more jeeps than vans.
[U]Define variables[/U]
[LIST]
[*]Let j be the number of jeeps
[*]Let v be the number of vans
[/LIST]
7 more jeeps than vans means we add 7 to the number of vans:
[B]j = v + 7[/B]
thesumof9andanumberWe denoted a number using the arbitrary variable "x".
The sum of 9 and x is written:
x + 9 or 9 + x
Thirty is half of the sum of 4 and a numberThirty is half of the sum of 4 and a number.
The phrase [I]a number[/I] represents an arbitrary variable, let's call it x.
The sum of 4 and a number:
4 + x
Half of this sum means we divide by 2:
(4 + x)/2
Set this equal to 30:
[B](4 + x)/2 = 30[/B] <-- This is our algebraic expression
Three subtracted from triple a numberThree subtracted from triple a number
A number means an arbitrary variable, let's call it x
x
Triple it
3x
Three subtracted from this
[B]3x - 3[/B]
thrice the sum of x y and zthrice the sum of x y and z
The sum of x, y, and z means we add all 3 variables together:
x + y + z
The word [I]thrice[/I] means we multiply the sum of x, y, and z by 3:
3(x + y +z)
total of a number and the square of a numbertotal of a number and the square of a number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
The square of a number means we raise x to the power of 2. x^2
The total means we add x squared to x:
[B]x + x^2[/B]
translate the product of -1 and a number in mathematics expressiontranslate the product of -1 and a number in mathematics expression
The phrase [I]a number[/I] means an arbitrary variable. Let's call it x.
The product of -1 and the number;
[B]-x[/B]
Translate this phrase into an algebraic expression. 57 decreased by twice Mais savings Use the variaTranslate this phrase into an algebraic expression. 57 decreased by twice Mais savings Use the variable m to represent Mais savings.
Twice means multiply by 2
2m
57 decreased by means subtract 2m from 57
[B]57 - 2m[/B]
Translate this phrase into an algebraic expression. 58 decreased by twice Gails age. Use the variablTranslate this phrase into an algebraic expression. 58 decreased by twice Gails age. Use the variable g to represent Gails age.
Twice Gail's age:
2g
58 decreased by twice Gail's age
[B]58 - 2g[/B]
Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g toTranslate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to represent Gregs age.
The sum of 17 and Greg's age:
g + 17
The word [I]is[/I] means equal to, so we set g + 17 equal to 43
[B]g + 17 = 43[/B] <-- This is our algebraic expression
If you want to solve this equation for g, use our [URL='http://www.mathcelebrity.com/1unk.php?num=g%2B17%3D43&pl=Solve']equation calculator[/URL].
[B]g = 26[/B]
Translate this sentence into an equation. 48 is the difference of Ritas age and 11 . Use the variablTranslate this sentence into an equation. 48 is the difference of Ritas age and 11 . Use the variable r to represent Ritas age.
The difference of Rita's age and 11 is written:
r - 11
The phrase [I]is[/I] means equal to, so we set r - 11 equal to 48
r - 11 = 48
Translate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variablTranslate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variable d to represent Diegos age.
The difference means we subtract, so we have d as Diego's age minus 17
d - 17
The word "is" means an equation, so we set d - 17 equal to 49
[B]d - 17 = 49[/B]
Translate this sentence into an equation. The difference of Maliks age and 15 is 63 Use the variableTranslate this sentence into an equation. The difference of Maliks age and 15 is 63 Use the variable m to represent Malik's age.
[B]m - 15 = 63
[/B]
To solve this equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=m-15%3D63&pl=Solve']equation calculator[/URL].
triple a number and another numbertriple a number and another number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Triple a number means we multiply x by 3:
3x
The phrase [I]another number[/I] means another arbitrary variable, let's call it y:
y
The word [I]and[/I] means we add y to 3x:
[B]3x + y[/B]
triple c divide the result by atriple c divide the result by a
Take this algebraic expression in pieces.
Triple c means we multiply the variable c by 3
3c
Divide the result by a, means we take 3c, and divide by a
[B]3c/a[/B]
Twenty-five is nine more than four times a numberThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Four times a number:
4x
nine more than four times a numbrer
4x + 9
The phrase [I]is[/I] means equal to. We set 4x + 9 equal to 25 as our algebraic expression:
[B]4x + 9 = 25
[/B]
If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D25&pl=Solve']type it in our math solver[/URL] and get:
x = [B]4[/B]
Twenty-five is the same as ten added to twice a numberThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number means we multiply x by 2:
2x
ten added to twice a number
2x + 10
The phrase [I]is the same as [/I]means equal to. Set 25 equal to 2x + 10 to get our algebraic expression
[B]25 = 2x + 10
[/B]
If the problem asks you to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=25%3D2x%2B10&pl=Solve']type it in our math solver [/URL]and get
x = [B]7.5[/B]
Twice a number decreased by eight is zeroThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number:
2x
decreased by eight
2x - 8
[I]is [/I]means equal to. Set 2x - 8 equal to zero for our algebraic expression:
[B]2x - 8 = 0
[/B]
If the problem asks you to solve for x, add 8 to each side:
2x = 8
Divide each side by 2:
x= [B]4[/B]
Twice a number decreased by sixThe phrase [I]a number[/I] means an arbitrary variable. We can pick any letter a-z except for i and e.
Let's choose x.
Twice a number means we multiply x by 2:
2x
Decreased by six means we subtract 6 from 2x:
[B]2x - 6[/B]
twice a number subtracted from the square root of the same numbertwice a number subtracted from the square root of the same number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Twice a number means we multiply x by 2:
2x
Square root of the same number:
sqrt(x)
twice a number subtracted from the square root of the same number
[B]sqrt(x) - 2x[/B]
twice the difference between x and 28 is 3 times a numbertwice the difference between x and 28 is 3 times a number
The difference between x and 28:
x - 28
Twice the difference means we multiply x - 28 by 2:
2(x - 28)
The phrase [I]a number[/I] means an arbitrary variable, let's call it x
x
3 times a number:
3x
The word [I]is[/I] means equal to, so we set 2(x - 28) equal to 3x:
[B]2(x - 28) = 3x[/B]
twice the difference of a number and 3 is equal to 3 times the sum of a number and 2twice the difference of a number and 3 is equal to 3 times the sum of a number and 2.
We've got 2 algebraic expressions here. Let's take them in parts.
Left side algebraic expression: twice the difference of a number and 3
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]The word [I]difference[/I] means we subtract 3 from the variable x
[*]x - 3
[*]Twice this difference means we multiply (x - 3) by 2
[*]2(x - 3)
[/LIST]
Right side algebraic expression: 3 times the sum of a number and 2
[LIST]
[*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
[*]The word [I]sum[/I] means we add 2 to the variable x
[*]x + 2
[*]3 times the sum means we multiply (x + 2) by 3
[*]3(x + 2)
[/LIST]
Now, we have both algebraic expressions, the problem says [I]is equal to[/I]
This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer
[B]2(x - 3) = 3(x + 2)[/B]
twice the difference of a number and 55 is equal to 3 times the sum of a number and 8twice the difference of a number and 55 is equal to 3 times the sum of a number and 8
Take this algebraic expression in pieces.
Left side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The difference of this number and 55 means we subtract 55 from x
x - 55
Twice the difference means we multiply x - 55 by 2
2(x - 55)
Right side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
The sum of a number and 8 means we add 8 to x
x + 8
3 times the sum means we multiply x + 8 by 3
3(x + 8)
Now that we have the left and right side of the expressions, we see the phrase [I]is equal to[/I]. This means an equation, so we set the left side equal to the right side:
[B]2(x - 55) = 3(x + 8)[/B]
twice the product of p q and rtwice the product of p q and r
The product of p q and r means we multiply all 3 variables together:
pqr
The word [I]twice[/I] means we multiply pqr by 2:
[B]2pqr[/B]
twice the square root of a number increased by 5 is 23twice the square root of a number increased by 5 is 23
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
The square root of a number means we raise x to the 1/2 power:
sqrt(x)
the square root of a number increased by 5 means we add 5 to sqrt(x):
sqrt(x) + 5
twice the square root of a number increased by 5 means we multiply sqrt(x) + 5 by 2:
2(sqrt(x) + 5)
The phrase [I]is 23[/I] means we set 2(sqrt(x) + 5) equal to 23:
[B]2(sqrt(x) + 5) = 23[/B]
Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the[SIZE=6]Twice the sum of a number and 6 is equal to three times the difference of the number and 3. Find the number.
The phrase [/SIZE][I][SIZE=7]a number[/SIZE][/I][SIZE=6] means an arbitrary variable, let's call it x.
The sum of a number and 6 means we add 6 to x:
x + 6
Twice the sum of a number and 6 means we multiply x + 6 by 2:
2(x + 6)
the difference of the number and 3 means we subtract 3 from x
x - 3
three times the difference of the number and 3 means we multiply x - 3 by 3:
3(x- 3)
The word [I]is[/I] means we set 2(x + 6) equal to 3(x - 3)
2(x + 6) = 3(x - 3)
Use the distributive property to multiply through:
2x + 12 = 3x - 9
Subtract 2x from each side:
2x - 2x + 12 = 3x - 2x - 9
x - 9 = 12
Add 9 to each side:
x - 9 + 9 = 12 + 9
x = [B]21[/B]
[B][/B]
[B][MEDIA=youtube]CeZl_oZnSiw[/MEDIA][/B][/SIZE]
two thirds of a number is no more than -10two thirds of a number is no more than -10
The phrase [I]a number[/I] means an arbitrary variable, let's call it x:
x
Two thirds of a number mean we multiply x by 2/3:
2x/3
The phrase [I]no more than[/I] -10 means less than or equal to -10, so we have an inequality:
[B]2x/3 <= -10[/B]
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Use c for unknown variable : Sam's age plus twice his ageUse c for unknown variable : Sam's age plus twice his age
Sam's age:
c
Twice his age means we multiply c by 2:
2c
Sam's age plus twice his age
[B]c + 2c[/B]
Use set notation to describe the set of integers greater than 4Let x be our variable:
We write x, such that x is greater than 4 below:
[B]{x | x > 4}[/B]
What can we conclude if the coefficient of determination is 0.94?What can we conclude if the coefficient of determination is 0.94?
[LIST]
[*]Strength of relationship is 0.94
[*]Direction of relationship is positive
[*]94% of total variation of one variable(y) is explained by variation in the other variable(x).
[*]All of the above are correct
[/LIST]
[B]94% of total variation of one variable(y) is explained by variation in the other variable(x)[/B]. The coefficient of determination explains ratio of explained variation to the total variation.
What does y=f(x) meanWhat does y=f(x) mean
It means y = a function of the variable x.
x is the independent variable and y is the dependent variable.
f(x) means a function in terms of x
What is a VariableFree What is a Variable Calculator - This lesson walks you through what a variable is and how to use it.
Also demonstrates the let statement.
When 20 is subtracted from 3 times a certain number, the result is 43A certain number means an arbitrary variable, let's call it x
x
3 times x
3x
20 is subtracted from 3 time x
3x - 20
The result is means equal to, so we set 3x - 20 equal to 43 for our algebraic expression
[B]3x - 20 = 43
[/B]
If you need to solve this, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-20%3D43&pl=Solve']equation calculator[/URL]:
[B]x = 21[/B]
When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the numWhen 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number
The phrase [I]a number, [/I]means an arbitrary variable, let's call it "x".
4 times a number, increased by 40, means we multiply 4 times x, and then add 40
4x + 40
100 decreased by the number means we subtract x from 100
100 - x
The problem tells us both of these expressions are the same, so we set them equal to each other:
4x + 40 = 100 - x
Add x to each side:
4x + x + 40 = 100 - x + x
The x's cancel on the right side, so we have:
5x + 40 = 100
[URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B40%3D100&pl=Solve']Typing this equation into the search engine[/URL], we get [B]x = 12[/B].
When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the numWhen 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
4 times a number means we multiply x by 4:
4x
Increased by 40 means we add 40 to 4x:
4x + 40
100 decreased by the number means we subtract x from 100:
100 - x
The phrase [I]is the same as[/I] means equal to, so we set 4x + 40 equal to 100 - x
4x + 40 = 100 - x
Solve for [I]x[/I] in the equation 4x + 40 = 100 - x
[SIZE=5][B]Step 1: Group variables:[/B][/SIZE]
We need to group our variables 4x and -x. To do that, we add x to both sides
4x + 40 + x = -x + 100 + x
[SIZE=5][B]Step 2: Cancel -x on the right side:[/B][/SIZE]
5x + 40 = 100
[SIZE=5][B]Step 3: Group constants:[/B][/SIZE]
We need to group our constants 40 and 100. To do that, we subtract 40 from both sides
5x + 40 - 40 = 100 - 40
[SIZE=5][B]Step 4: Cancel 40 on the left side:[/B][/SIZE]
5x = 60
[SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE]
5x/5 = 60/5
x = [B]12[/B]
Check our work for x = 12:
4(12) + 40 ? 100 - 12
48 + 40 ? 100 - 12
88 = 88
When 54 is subtracted from the square of a number, the result is 3 times the number.When 54 is subtracted from the square of a number, the result is 3 times the number.
This is an algebraic expression. Let's take it in parts.
The phrase [I]a number[/I] means an arbitrary variable, let's call it "x".
x
Square the number, means raise it to the 2nd power:
x^2
Subtract 54:
x^2 - 54
The phrase [I]the result[/I] means an equation, so we set x^2 - 54 equal to 3
[B]x^2 - 54 = 3[/B]
When 9 is subtracted from 5 times a number ,the result is 31When 9 is subtracted from 5 times a number ,the result is 31
A number means an arbitrary variable, let's call it x.
5 times this number is written as 5x.
9 subtracted from this is written as 5x - 9
[I]The result[/I] means we have an equation, so we set [B]5x - 9 = 31[/B]. This is our algebraic expression.
Now if we want to solve for x, we [URL='http://www.mathcelebrity.com/1unk.php?num=5x-9%3D31&pl=Solve']plug this equation into the search engine [/URL]and get [B]x = 8[/B].
When twice a number is reduced by 15 you get 95 what is the numberWhen twice a number is reduced by 15 you get 95 what is the number?
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
[I]Twice[/I] x means we multiply x by 2
2x
[I]Reduced by[/I] 15 means we subtract 15
2x - 15
[I]You get[/I] means equal to, as in an equation. Set 2x - 15 = 95
2x - 15 = 95 <-- This is our algebraic expression.
[URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D95&pl=Solve']Type 2x - 15 = 95 into the search engine[/URL] and we get [B]x = 55[/B].
WorkFree Work Calculator - Solves for any of the 3 variables, Work (W), Force (F) and Distance (d) in the work formula
Write a model that utilizes all three explanatory variables with no interaction or quadratic terms.Write a model that utilizes all three explanatory variables with no interaction or quadratic terms. Choose the correct answer below.
A. y i = B0 + B1x1 + B2x2 + B3x3 + e i
B. y i = B0 + B1x1 + B2x2 + B3x3x2 + e i
C. y i = B1x1 + B2x2 + B3x3 + ei
D. None of the above equations satisfy all of the conditions
[B]A. y i = B0 + B1x1 + B2x2 + B3x3 + e i[/B]
y is the sum of twice a number and 3y is the sum of twice a number and 3
The phrase [I]a number[/I] means an arbitrary variable, let's call it x.
x
twice a number means we multiply x by 2:
2x
the sum of twice a number and 3:
2x + 3
The word [I]is[/I] means equal to, so we set 2x + 3 equal to y
[B]y = 2x + 3[/B]
y minus 10 is equal to the product of y and 8y minus 10 is equal to the product of y and 8.
Take this algebraic expression in 3 parts:
Part 1: y minus 10
Subtract 10 from the variable y
y - 10
Part 2: The product of y and 8
We multiply 8 by the variable y
8y
Part 3: The phrase [I]is equal to[/I] means an equation, so we set y - 10 equal to 8y
[B]y - 10 = 8y[/B]
You are buying boxes of cookies at a bakery. Each box of cookies costs $4. In the equation below, cYou are buying boxes of cookies at a bakery. Each box of cookies costs $4. In the equation below, c represents the number of boxes of cookies you buy, and d represents the amount the cookies will cost you (in dollars). The relationship between these two variables can be expressed by the following equation: d=4c. Identify the dependent and independent variables.
[B]The variable d is dependent, and c is independent since the value of d is determined by c.[/B]
You work for a remote manufacturing plant and have been asked to provide some data about the cost ofYou work for a remote manufacturing plant and have been asked to provide some data about the cost of specific amounts of remote each remote, r, costs $3 to make, in addition to $2000 for labor. Write an expression to represent the total cost of manufacturing a remote. Then, use the expression to answer the following question. What is the cost of producing 2000 remote controls?
We've got 2 questions here.
Question 1: We want the cost function C(r) where r is the number of remotes:
C(r) = Variable Cost per unit * r units + Fixed Cost (labor)
[B]C(r) = 3r + 2000
[/B]
Question 2: What is the cost of producing 2000 remote controls.
In this case, r = 2000, so we want C(2000)
C(2000) = 3(2000) + 2000
C(2000) = 6000 + 2000
C(2000) = [B]$8000[/B]
Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same aZalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4.
The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x):
[U]She subtracts 6 then multiplies the result by 5[/U]
[LIST]
[*]Subtract 6: x - 6
[*]Multiply the result by 5: 5(x - 6)
[/LIST]
[U]She subtracts 5 from the number then multiplying by 4[/U]
[LIST]
[*]Subtract 6: x - 5
[*]Multiply the result by 5: 4(x - 5)
[/LIST]
Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation:
5(x - 6) = 4(x - 5)
Now, let's solve the equation for x. To do this, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%28x-6%29%3D4%28x-5%29&pl=Solve']type this equation into our search engine [/URL]and we get:
x = [B]10[/B]
