Mrs. culland is finding the center of a circle whose equation is x2 + y2 + 6x + 4y – 3 = 0 by completing the square. her work is shown. x2 + y2 + 6x + 4y – 3 = 0 x2 + 6x + y2 + 4y – 3 = 0 (x2 + 6x) + (y2 + 4y) = 3 (x2 + 6x + 9) + (y2 + 4y + 4) = 3 + 9 + 4 which completes the work correctly? (x – 3)2 + (y – 2)2 = 42, so the center is (3, 2). (x + 3)2 + (y + 2)2 = 42, so the center is (3, 2). (x – 3)2 + (y – 2)2 = 42, so the center is (–3, –2). (x + 3)2 + (y + 2)2 = 42, so the center is (–3, –2).

1/800 is the right answer

final total: 63

step-by-step explanation:

60 times sales tax

60 times 0.05

3

60 + 3

63

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