On a farm, the farmer harvested 34.7 crates of apples and 25.9 crates of oranges. How much more crates of apples are harvested?
How much more means we subtract:
34.7 - 25.9 = 8.8 more craters of apples
Multiply each side by 3 to remove the fraction:
3F=3(2y-z/3)
3F = 6y - z
Subtract 6y from each side:
3F - 6y = -z
Multiply each side by -1:
z = 6y - 3F
If a is 4 and b is 6, what is the value of this expression? sqrt(a^2+2b-3)
Plug in our values for a and b:
sqrt(4^2+2(6)-3)
sqrt(16 + 12 - 3)
sqrt(25)
5
i = sqrt(-1)
i^2 = sqrt(-1)*sqrt(-1) = -1
i^3 = I^2 * I = -sqrt(-1)
i^4 = I^2 * I^2 = -1 * -1 = 1
i^100 can be broken down. The easiest way is to check for powers of 4:
100 = 25 * 4 so we have:
(i^4)^25
i^4 = 1, so we have:
(i)^25 = 1
If 2^x + 2^x + 2^x + 2^x = 2^16, what is the value of x?
Add up the left side, we get:
4(2^x) = 2^16
But 4 = 2^2, so we have:
2^2(2^x) = 2^16
Using our exponent rule, we have:
2^(x + 2) = 2^16
x + 2 = 16
Subtract 2 from each side, we get:
x = 14
A road is resurfaced at the rate of 2 1/5 km per day. if it takes 9 days to complete the job, how long is the road?
2 & 1/5 = 11/5
9 / 11/5 is the same as 9 * 5/11 - 45/11
Write in decimal form: 3 cm 7 mm = ? cm
Remember that 1 cm = 10 mm
Which means 1 mm = 1/10 cm = 0.1 cm
So 7 mm = 7/10 cm = 0.7 cm
Therefore, 3 cm 7 mm = 3.7 cm
Volume of a cube is s^3 where s is the length of one side.
V = 64
s^3 = 64
Take the cube root of each side:
s = 4 since 4^3 = 64
Surface Area of a cube is 6s^2. With s = 4, we have:
SA = 6(4)^2
SA =6(16)
SA = 96
If the perimeter of square C is triple the perimeter of square D, the area of square C is how many times the area of square D?
A. 1/3
B. 1
C. 3
D. 9
E. 27
Let side of D be s. Perimeter is 4s. Area is (4s)^2 = 16s^2
Let side of C be 3s. Perimeter is 4(3s) = 12s. Area is (12s)^2 = 144s^2...
A. 2
B. 3
C. 4
D. 5
E. 6
We have 3 conditions that all must be met:
Whole number
Prime Number
20 * number is divisible by 6
The are all whole numbers
One A, B, and D are prime, so we eliminate C and E
20(2) = 40 which is not divisible by 6 - Eliminate Answer A
20(5) = 100 which is not...
Do this without a calculator.
Notice, all numerators have a matching denominator except 2 in the first term and 14 in the last term.
So we have 2/14
Using 2 as a common factor, we have:
2/2 / 14/2
1/7