Kayla is framing a square painting with side lengths of x+5 inches. The total area of the painting and the frame has a side length of 3x-6 inches. The material for the frame will cost 0.07 per square inch

Complete question :

Kayla is framing a square painting with side lengths of x+5 inches. The total area of the painting and the frame has a side length of 3x-6. inches. Write an expression for the area of the frame. Then find the cost of the material for the frame if x = 16. The material for the frame will cost 0.07 per square inch

8x² - 46x + 11 ;

$92.61

Step-by-step explanation:

Side length of square painting = x + 5

Area of square painting = (x +5)²

Side length of Total area of square painting + frame = 3x - 6

Total area = (3x - 6)²

Area of frame :

(3x - 6)² - (x +5)²

(3x - 6)(3x-6)

9x² - 18x - 18x +. 36 = 9x² - 36x + 36

(x +5)(x+5) = x²+5x+5x+25 = x² + 10x + 25

9x² - 36x + 36 - (x² + 10x + 25)

9x² - 36x + 36 - x² - 10x - 25

8x² - 46x + 11

Area of frame = 8x² - 46x + 11

8(16^2) - 46(16) + 11

= 1323 in²

1323 * 0.07 = $92.61

twenty-six miles over two gallons because the proportion for the original 13 miles to one gallon would be written 13/1 and, doing the same thing to the top and bottom, i multiplied by 2 and got 26/2