26. If BD = 8x - 27 and EC-2x + 33, find BD

BD = 21

Step-by-step explanation:

8x - 27 = -2x + 33

Add 27 to both sides

8x - 27 +27 = -2x + 33 +27

Simplify

8x = -2x + 60

Add 2x to both sides

8x + 2x = -2x + 2x + 60

Simplify

10x = 60

Divide both sides by 10

10x/10 = 60/10

x = 6

Plug 6 for x into BD

8 (6) - 27

48 - 27

= 21

$27.5

step-by-step explanation:

$110.00 divided by 4

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