Recent content by math_celebrity

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

Factor the following expression: 4a(9b + 7) - 3(9b + 7) The common factor in each term is (9b + 7). Factor this out and we get: (4a - 3)(9b + 7)

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 store buys 48 candy bars. they sell the candy for .75 each Revenue = Cost per unit * # of Units Revenue = 0.75 * 48 Revenue = 36

Since we have all coefficients of 3 raised to the n, we have: 3(3^n) Using our exponent rules, we have: 3^(n + 1)

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...

a. b^(y + 1) b. b^(y + 2) c. b^(y + 3) d. b^2y e. b^3y Multiply each side by b: 3b = b^y * b 3b = b^(y + 1) answer A.

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