I've been stuck on this for a little while now. Could anybody help?

  7

Step-by-step explanation:

The arrows on the diagonal lines mean those lines are parallel. That means the triangles are similar, so corresponding sides have the same ratio.

There are many ways we can write the proportion expressing that fact. It is convenient to do so with the variable in the numerator:

  (3x -6)/12 = 10/8

Multiplying by 4, we have ...

  x -2 = 5

  x = 7 . . . . . . add 2

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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