Apicture frame goes around a picture such that it has 1 inch thickness as shown below. the width of the picture is 4 inches more than twice the height. the area of the the frame and picture is 60 square inches. determine the height in inches of the picture

The height of the picture is 3 inches.

Step-by-step explanation:

A picture frame goes around a picture such that it has 1 inch thickness. The width of the picture is 4 inches more than twice the height.

Therefore, our picture has the dimensions of height = h and width = 4 + 2h.

The area of the the frame and picture is 60 square inches. Thus, the picture frame with the picture's dimension is height (picture frame) =height of the picture + 2 (1 inch per side) and the width = width of the picture + 2 (1 inch per side).

Area = height x width

60 = (h +2) (4+ 2h + 2)

60 = (h+ 2) (2h + 6)

60 = 2h² + 6h + 4h + 12, combine like terms

2h² + 10h - 48 = 0, divide the whole equation by 2 to simplify

h² + 5h -24 = 0, factor the equation

(h+ 8)(h-3) = 0

h+8 = 0, h -3=0

h = - 8 and h = 3,  since there is no negative height therefore the height is 3 inches.

19

step-by-step explanation:

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3