Which of the following equations have no solutions? Choose all answers that apply: Choose all answers that apply: (Choice A) A 45x-45=-15x+7545x−45=−15x+7545, x, minus, 45, equals, minus, 15, x, plus, 75 (Choice B) B -45x-45=-75x+75−45x−45=−75x+75minus , 45, x, minus, 45, equals, minus, 75, x, plus, 75 (Choice C) C 15x-45=15x+7515x−45=15x+7515, x, minus, 45, equals, 15, x, plus, 75 (Choice D) D 15x-45=75x+7515x−45=75x+75

a is the correct

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

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