Question

Annalise makes rectangular patchwork quilts out of leftover fabric scraps. The first scrap she is using to make a quilt has a width of 2x feet and a
Hength of 5x feet. When finished, the entire quilt will be 5 feet wider and 3 feet longer than the first fabric scrap used. Which of the following
functions will give the area, fx), of the quilt in square feet?

Answer 1

Answer:

Area = $f(x)=10x^2 + 31x + 15$

Step-by-step explanation:

The function is the area function of a rectangle.

Area of Rectangle = Length * Width

Length of fabric scrap = 5x

Length of rectangular patchwork will be 5x + 3

and

Width of fabric scrap = 2x

Width of rectangular patchwork will be 2x + 5

THus, Area = (5x+3)(2x+5) square feet.

Let's expand:

$Area = f(x) = (5x+3)(2x+5)\\f(x)=10x^2 + 25x + 6x + 15\\f(x)=10x^2 + 31x + 15$