In the figure, find the value of x that makes a ∥ b. A. 50° B. 65° C. 75° D. 95°

B

Step-by-step explanation:

Because alternate interior angles are congruent in parallel lines, the angle next to the 25° in the right triangle is 85 - 25 = 60° which makes the other angle in the right triangle 180 - 90 - 60 = 30°. Since they form a straight angle, we can write x + 30 + 85 = 180 → x + 115 = 180 → x = 65°.

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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