CubeyThePenguin

first line: 3x + 4y = -14

4y = -3x - 14

y = -3x/4 - 7/2

second line: parallel to first line, so the slope is 4/3. this line also passes through (-5, 7) so we can write this line in point slope form first:

y - 7 = 4/3(x + 5)

y - 7 = 4x/3 + 20/3

y = 4x/3 + 41/3

m + b = 4/3 + 41/3 = 15

g(5) = g(f(x))

f(x) = 5

3x - 8 = 5

x = 13/3

g(f(x)) = 2(13/3)^2 - 5(13/3) + 3 = 170/9

Combine like terms.

40x - 2x + 3x = (40 - 2 + 3)x = 41x

x^1 = x, so another one could be 81^1. 

y = f(x+3) is the same as the graph of y = f(x), just shifted to the left 3 units. So, the vertex of y = f(x+3) is (-1, -1).

There is another way to solve this problem. Notice that the left side is the square of a binomial.

\((x + 5)^2 = 64\)

\(x + 5 = 8 \qquad x + 5 = -8\)

x = 3 or -13.

Suppose Peter can finish painting the fence in x hours. That means he can paint 1/x of the fence in 1 hour, John can paint 1/6 of the fence in 1 hour, and Paul can paint 1/8 of the fence in 1 hour. We can write the following equation:

1/6 + 1/8 + 1/x = 1/2

Solving, we get x = 24/5, so it takes Peter 24/5 hours to paint the fence alone.

That's a good step, but the problem with your reasoning is that -7 by itself doesn't have a^3 + 7 in the denominator, so you would have to convert -7 to (-7(a^3 + 7))/(a^3 + 7) before solving.

Use the exponent rule \(x^{a} \cdot x^{b} = x^{a+b}\).

\(x^2 \cdot x^{-8} = x^{2-8} = x^{-6} = \boxed{\frac{1}{x^6}}\)

We have the equation y = 3x/7 + b, since we know that the slope is 3/7. Plug in the point (-14, 0):

0 = 3(-14)/7 + b

0 = -6 + b

b = 6

The line is y = 3x/7 + 6.