The graph shows the location of jacob's, kent's, and hakim's houses. each unit on the graph represents 1 kilometer. a coordinate plane is shown. hakims house is located at negative 3, 1, jacobs house is located at 1, 5, and kents house is located at 1, 1. line segments connect the points to form a right triangle. hakim is preparing for a cross country meet. hakim is going to run from his house to jacob's, then to kent's, and finally back home. how many total kilometers did hakim run? round your answer to the nearest whole kilometer. 6 kilometers 14 kilometers 18 kilometers 22 kilometers

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step-by-step explanation:

a

step-by-step explanation:

the answer is 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