Jeremy says (x − 9)(x^7 + x^6+x^5 +x^4 +x^3+x^2 +x +1) must equal x^7+x^6 +x^5 +x^4+x^3 +x^2 +x +1 because when x =10, multiplying by x − 9 is the same as multiplying by 1.(a)-multiply (x − 9) (x^7+x^6 +x^5 +x^4+x^3 +x^2 +x +1). (b)- substitute x =10 into your answer. (c)- is the answer to part (b) the same as the value of x^7+x^6 +x^5 +x^4+x^3 +x^2 +x +1 when x = 10? (d) was jeremy right?

3; 9 is 8 to -4

step-by-step explanation:

4+4+2x

or

2x+8

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