2 years ago

Picture shown!

Mathematics

1 answer:

igomit [66]2 years ago

7 0

Answer:

3x^2+6x-11

Step-by-step explanation:

g(f(x)) = g(x^2+2x-4) = 3(x^2+2x-4)+1 = 3x^2+6x-11

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Let $x,y$ be the dimensions of the rectangle. We know the equations for both area and perimeter:

$A=xy=36$

$P=2(x+y)=36 \iff x+y=18$

So, we have the following system:

$\begin{cases}xy=36\\x+y=18\end{cases}$

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Both solutions are feasible, because they're both positive.

If we chose the positive solution, we have

$x=9+3\sqrt{5} \implies y=18-x=18-9-3\sqrt{5}=9-3\sqrt{5}$

If we choose the negative solution, we have

$x=9-3\sqrt{5} \implies y=18-x=18-9+3\sqrt{5}=9+3\sqrt{5}$

So, we're just swapping the role of $x$ and $y$ . The two dimensions of the rectangle are $9+3\sqrt{5}$ and $9-3\sqrt{5}$

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