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

Step-by-step 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

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

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

$x=\frac{40\pm\sqrt{(-40)^2-4\times 16\times 25}}{2\times 16}$

$x=\frac{40\pm\sqrt{1600-1600}}{32}$

$x=\frac{40\pm\sqrt{0}}{32}$

$x=\frac{40}{32}$

$x=\frac{5}{4}$

$4x=5\\4x-5=0$

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

7 0

3 years ago

I NEED HELP ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!

Artist 52 [7]

Hayden Grace and Gaytar went to the store. They did not go anymore.

8 0

3 years ago

4(x – 3) <br> need help answering this question

AVprozaik [17]

Answer:

4x-12

Step-by-step explanation:

4 x x is 4x and 4x-3 is -12

3 0

3 years ago

What is 15% of 60?? Can someone plz tell me how to calculate this as well??? Thanks!!!

earnstyle [38]

To convert a percentage to a decimal you move the decimal two places to the left. Therefore:

15.% becomes .15

You then multiply this decimal to the number you are trying to find the percentage of.

.15 × 60 = 9.

9 is 15% of 60.

4 0

3 years ago