A. Write the algebraic expressions representing the length and width of Marlien’s house. b. Write the algebraic expression representing the perimeter of Marlien’s house in simplest form.
c. If the perimeter is 142 feet, find the value of x.
d. Using the algebraic expression for area found in Exercise 2b, find the area of the living room.
e. Show how the Distributive Property can be used to find the area of Marlien’s living room.
f. Write an algebraic expression for the area of the living room.

(Please answer all, I'm putting all of my points into this!) (if you answer just for the points and it's something not very nice, I'll report you.)

it could be a ..idk tho

312312

step-by-step explanation:

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