The ratio of the angle measures of a triangle is 5:6:9. Find the measure of each angle of the triangle.

5 : 45

6 : 54

9 : 81

Step-by-step explanation:

Let the angles be 5x, 6x and 9x

Now

5x+6x+9x=180 (Sum of angle of a triangle)

20x = 180

x = 180/20

x=9

Now replacing the value of x

5x = 5*9 =45

6x = 6*9 =54

9x = 9*9 =81

step-by-step explanation:

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