Question

What is the side length, in inches, of the pets

Candy draws a square design with a side length of x inches
for the window at the pet shop. She takes the design to the
printer and asks for a sign that has an area of 16x - 40x +
25 square inches
4x + 5
O 4x-5
O 8x + 5
O 8x-5
16x2 - 40x-25

Answer 1

B took the test

Explanation:

Answer 2

Candy draws a square design with a side length of x inches for the window at the pet shop. She takes the design to the printer and asks for a sign that has an area of 16x2 – 40x + 25 square inches. What is the side length, in inches, of the pet shop sign?

Answer:

the length of the sign is
`4x-5` inches

Explanation:

Given

Area of the square of design =
`16x^(2) -40x+25`

First we find the roots of equation
`16x^(2) -40x+25=0`

The roots of the quadratic equation
`ax^(2) +bx^(2) +c=0` are given by

`x=(-b\pm√(b^2-4ac))/(2a)`

where
`a=16, b=-40, c=25`

`x=(40\pm√((-40)^2-4* 16* 25))/(2* 16)`

`x=(40\pm√(1600-1600))/(32)`

`x=(40\pm√(0))/(32)`

`x=(40)/(32)`

`x=(5)/(4)`

`4x=5\\4x-5=0`

That is, the factors of the polynomial
`16x^(2) -40x+25` are
`4x-5` and
`4x-5`.

So, Area of the square design =
`16x^(2) -40x+25` =
`(4x-5)^(2)`

Area of a square = Length^2

Thus, the length of the sign is
`4x-5` inches