What is the measure of angle D?

52°

Step-by-step explanation:

The trapezoid is a closed figure, meaning all the angles must equal 360°.

1. Set up the equation

128° + 126° + 54° + ∠D = 360°

2. Solve for ∠D

360 - 128- 126- 54 = 52

∠D = 52°

You can also solve this by knowing that in a trapezoid:

∠A + ∠D = 180° and ∠B + ∠C = 180°

1. Set up the equation

128 + ∠D = 180°

2. Solve

180 - 128 = 52

∠D = 52°

a=24; b=12

step-by-step explanation:

a/b=2: 1

a=2b

36/(1+2)=12

b=12

a=24

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