82.24 = -8.48 + 4x
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x = 22.68

Step-by-step explanation:

82.24 = -8.48 + 4x

82.24 + 8.48 = 4x

4x = 90.72

x = 22.68

x=22.68

Step-by-step explanation:

82.24 = -8.48 + 4x=-8.48+4x=82.24

= -8.48+4x+8.48=82.24+8.48

= 4x=90.72

=4x/4=90.72/4

=x=22.68

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

c

step-by-step explanation: