A computer company makes a rectangular screen with a diagonal of 20 inches. The width of the screen is 4 inches less than its length. The dimensions of the computer screen are modeled by the equation x2 + (x – 4)2 = 202. What is the value of x, the length of the screen? x = –16 x = –12 x = 12 x = 16

Step-by-step explanation:

x = length of screen

x-4 = width of screen

x² + (x-4)² = 20²

x² + (x²-8x+16) = 400

2x² - 8x - 384 =  0

x² - 4x - 192  = 0

use the quadratic formula to solve for x

x = [4 ± √(4²-4·1(-192))]/[2·1]

= [4 ± √784]/2

= 4 ±  28]/2

= 16, -12

-12 is an extraneous solution, so x = 16 inches.

Exponents need to be marked with a ^. For example, (x-4)² can be written (x-4)^2.

d. $180

step-by-step explanation:

if the dimensions of the room is 9ft by 12 ft, we have the area of the floor as,

so the area of the floor is 108 square feet, converting that into square yards we get,

the cost of carpet is $15 per square yard, therefore the cost of carpet for 12 square yards is,

hence, the cost of carpet is $180.

assuming the dimensions of the room be,

15 ft by 12 ft

so, the area of the floor of that room is,

we can convert 180 square feet into square yards, we know that,

1 sq ft = 0.111 sq yard

so, 180 square feet is,

so the area of floor is 20 square yards.

now, the cost of carpet is 15 dollars per square yard, therefore the cost of carpet for 20 square yards is,

so, it will cost $300.

2

step-by-step explanation: