Hurry 50 points for correct answer
Solve the equation. Identify any extraneous situations.
x=√6x+7

1 is a solution to the original equation. The value –7 is an extraneous solution.

7 is a solution to the original equation. The value –1 is an extraneous solution.

7 and –1 are solutions.

7 and 1 are both extraneous solutions.

"7 is a solution to the original equation. The value –1 is an extraneous solution."

Step-by-step explanation:

The equation can be solved by squaring both sides:

We can see that -1 and 7 are solutions, but make sure they are not extraneous by substituting them in the original equation:

The square root of 49 equals 7, but the square root of -1 is an imaginary number.

The correct choice is "7 is a solution to the original equation. The value –1 is an extraneous solution."

oof

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