Compared to last month, there was a 65% increase in the number of houses sold this month. There were x. number of houses sold last month. Write two expressions that can be used to determine the number of houses

x+0.65x and x(1 + 0.65)

Step-by-step explanation:

Given

Original number of houses last month = x

If there are 65% increase in the number of houses, then;

Increment = 65% of x

Increment = 0.65x

The number of houses sold compared to last month = Original number + Increment

The number of houses sold compared to last month = x + 0.65x

This can also be expressed as x (1+ 0.65)

Hence the required expressions are x + 0.65x and x(1 + 0.65)

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