Stella solves the following system of equations using the substitution method. y=−4x−65x−y=10

What is the single-variable equation she solves after substituting?

5x−4x−6=10
5x−(−4x−6)=10
5x+10=−4x−6
5x+10=−(4x−6)

5x-(-4x-6) = 10

Step-by-step explanation:

Given the expression

y=−4x−6 1

5x−y=10... 2

To get the required equation we will substitute equation 1 into 2

5x-y = 10

5x-(-4x-6) = 10

5x+4x+6 = 10

9x+6 = 10

9x = 4

x = 4/9the required equation is 5x-(-4x-6) = 10

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