1) What is x - 5 = 7? 2) What is n + 3 = 18?

3) What is 9a = 45?

4) What is n fraction bar 3 = 18?

5) What is x + 10 = 35?

6) What is n - 13 = 9?

7) What is 6p = 78?

8) What is a fraction bar 7 = 3?

9) What is n - 16 = 28?

10) What is 12X = 60?

11) What is X + 32 = 40?

12) What is n fraction bar 5 = 19?

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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

you need to rotate this triangle about the origin 270 degrees clockwise to create the full square.