Wilson cuts rectangular mats for picture frames. The area of the mat before it is cut is represented by the function M(x) = 4.5x^2 + 17x + 16. The area that is cut out and removed from the middle of the mat is represented by the function N(x) = x^2 + 6x. If x is the width of the portion of the mat that is cut out, which function best describes A(x), the area of the cut mat?

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt

y/x of point b= y/x of point a

step-by-step explanation:

(i got the same question, this was the correct answer.)