Which of the following relations is a function? OA. (3, 4), (-3, 2), (6, 1), (-8, 2)
OB. (6, 1), (-3, 4), (3, 1), (6,2)
OC. (3, 4), (-3, 6), (3, 3), (-8, 2)
OD. (3,0), (-3, 3), (6, 1), (-3,5)

A. (3, 4), (-3, 2), (6, 1), (-8, 2)

Step-by-step explanation:

OA. (3, 4), (-3, 2), (6, 1), (-8, 2) - function

OB. (6, 1), (-3, 4), (3, 1), (6,2) - this repeats the x value of 6 to two different y values so it is not a function

OC. (3, 4), (-3, 6), (3, 3), (-8, 2)- this repeats the x value of 3 to two different y values so it is not a function

OD. (3,0), (-3, 3), (6, 1), (-3,5)- this repeats the x value of -3 to two different y values so it is not a function

step-by-step explanation:

there are 36 inches in a yard

25 : 36 = 0.69 yards (you can round to 0.70)

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