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Option (C)

Step-by-step explanation:

Equation of a line passing through a point (h, k) and slope 'm' is given by,

y - k = m(x - h)

Slope of the function passing through two points and is,

slope (m) =

Slope of the line passing through (-1, -40) and (-8, -124) will be,

m = = 12

Equation of the line passing through (-20, -268) and slope = 12 will be,

y + 268 = 12(x + 20)

Equation of the line passing through (-14, -196) and slope = 12 will be,

y + 196 = 12(x + 14)

Equation of the line passing through (-8, -124) and slope = 12 will be,

y + 124 = 12(x + 8)

Equation of the line passing through (-1, -40) and slope = 12 will be,

y + 40 = 12(x + 1)

From the given choices, option (C) is the correct one.

answer: y = 3/2 x - 3

y = 1/8 x - 3/4 that would be your correct option

step-by-step explanation: w

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