Srael started to solve a radical equation in this way: square root of x plus 6 − 4 = x square root of x plus 6 − 4 + 4 = x + 4 square root of x plus 6 = x + 4 (square root of x plus 6)2 = (x + 4)2 x + 6 = x2 + 8x + 16 x + 6 − 6 = x2 + 8x + 16 − 6 x = x2 + 8x + 10 x − x = x2 + 8x + 10 − x 0 = x2 + 7x + 10 0 = (x + 2)(x + 5) x + 2 = 0 x + 5 = 0 x + 2 − 2 = 0 − 2 x + 5 − 5 = 0 − 5 x = −2 x = −5 Solutions = −2, −5 What error did Israel make?

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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