Solve the equation. Then check your solution. -5.4 = -1.5h a. 3.9
b. -3.9
c. 8.1
d. -6.9

Please select the best answer from the choices provided

9514 1404 393

  a. 3.9

Step-by-step explanation:

Divide by the coefficient of h:

  -5.4 = -1.5h

  -5.4/-1.5 = h = 3.6

All of the offered choices are incorrect.

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Check

  -1.5 × 3.6 = -1.5(3) + (-1.5)(.6)

  = -4.5 - 0.9 = -5.4

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The best answer from those provided is 3.9, choice A.

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