13: 72.25
14: 52
For 14, you need to split the figure into a triangle and rectangle.
The fundamental theorem of algebra states that a polynomial with degree n has at most n solutions. The "at most" depends on the fact that the solutions might not all be real number.
In fact, if you use complex number, then a polynomial with degree n has exactly n roots.
So, in particular, a third-degree polynomial can have at most 3 roots.
In fact, in general, if the polynomial
has solutions
, then you can factor it as
![p(x) = (x-x_1)(x-x_2)\ldots (x-x_n)](https://tex.z-dn.net/?f=p%28x%29%20%3D%20%28x-x_1%29%28x-x_2%29%5Cldots%20%28x-x_n%29)
So, a third-degree polynomial can't have 4 (or more) solutions, because otherwise you could write it as
![p(x)=(x-x_1)(x-x_2)(x-x_3)(x-x_4)](https://tex.z-dn.net/?f=p%28x%29%3D%28x-x_1%29%28x-x_2%29%28x-x_3%29%28x-x_4%29)
But this is a fourth-degree polynomial.
Answer:
![f(g(-1))= 3](https://tex.z-dn.net/?f=f%28g%28-1%29%29%3D%203)
Step-by-step explanation:
![f(g(-1))= 2(-1 -1)+7](https://tex.z-dn.net/?f=f%28g%28-1%29%29%3D%202%28-1%20-1%29%2B7)
![f(g(-1))= 2(-2)+7](https://tex.z-dn.net/?f=f%28g%28-1%29%29%3D%202%28-2%29%2B7)
![f(g(-1))= -4+7](https://tex.z-dn.net/?f=f%28g%28-1%29%29%3D%20-4%2B7)
![f(g(-1))= +3](https://tex.z-dn.net/?f=f%28g%28-1%29%29%3D%20%2B3)