Question

A pool is being filled with a large water hose. The height of the water in a pool is determined by 8g^2 + 3g - 4. Previously, the pool had been filled up with a different hose. Then, the height was determined by 6g^2 + 2g - 1. Write an expression that determines the height of the water in the pool if both hoses are on at the same time. Simplify the expression.

a) 14g^2 + 5g - 5
b) 2g^2 + 5g - 5
c) 14g^2 - 5g + 5
d) 2g^2 - 5g + 5

Answer 1

To determine the height of the water in the pool when both hoses are on, add the expressions for each hose: 6g^2 + 2g - 1 and 8g^2 + 3g - 4. Simplify the expression by combining like terms to get 14g^2 + 5g - 5.

Step-by-step explanation:

To determine the height of the water in the pool when both hoses are on, we need to add the expressions that determine the height of the water from each hose. The expression for the first hose is 6g^2 + 2g - 1, and the expression for the second hose is 8g^2 + 3g - 4. To simplify the expression, we add the like terms: (6g^2 + 2g - 1) + (8g^2 + 3g - 4) = 14g^2 + 5g - 5.