Question

12. (07.06 LC) A library building is in the shape of a rectangle. Its floor has a length of (3x + 5) meters and a width of (5x − 1) meters. The expression below represents the area of the floor of the building in square meters: (3x + 5)(5x − 1) Which of the following simplified expressions represents the area of the floor of the library building in square meters? (5 points) 28x − 5 15x2 − 5 15x2 + 28x − 5 15x2 + 22x − 5

Answer 1

D. 15x^2 + 22x -5

Explanation:

I just took the test

Answer 2

`15 {x}^(2) + 22x - 5`

EXPLANATION

It was given that, the length of the rectangular building is

`(3x + 5) \: meters`

and the width of the is

`(5x - 1) \: meters`

The area of a rectangular building is calculated using the formula for finding the area of a rectangle.

`A = l * w`

Since the dimensions are given in terms of x, the area is also a function of x,

`A(x) = (3x +5 )(5x - 1)`

We expand to get,

`A(x) = 3x(5x - 1) + 5(5x - 1)`

`A(x) = 15 {x}^(2) - 3x + 25x - 5`

`A(x) = 15 {x}^(2) + 22x - 5`

meters square