The average (arithmetic mean) of the measures of angle x, its complementary angle, and its supplementary angle is 80 degrees. what is the measure of the complementary of angle x? (hint: the complementary angle of x can be represented as (90-x))

60°

the mean is the sum of the 3 angles divided by 3

complementary angle = 90 - x

supplementary angle = 180 - x

sum of angles = x + 90 - x + 180 - x = 270 - x

Hence

mean = = 80 ( multiply both sides by 3 )

270 - x = 240 ( subtract 270 from both sides )

- x = - 30 ( multiply both sides by - 1 )

x = 30

complement of x = 90 - 30 = 60°

x+y = 29, 5x + 2y = 100

step-by-step explanation:

i'm guessing it was a multiple first option was the correct answer

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