Answer:D
Step-by-step explanation:
Your welcome
Answer:
Hello!!! Princess Sakura here ^^
Step-by-step explanation:
The answer is choice D. I always remember it by the bigger number is the one that is going to get divided but that doesn't always work out, but in this case it does.
CE = CD + DE = 2DE + DE = 3DE = 8.7
DE = 8.7/3 = 2.9
CD = 2DE = 5.8
For the inscribed circle, where center is point D. The radius is length DE.
This is because the circle will touch the 3 points where the bisectors intersect with sides of triangle.
radius = 2.9
For circumscribed circle, the center will also be point D. The radius is CD.
The circle will touch 3 points of triangle, A,B,C.
radius = 5.8
<span>We have the following polynomial:
![f(x)=2x^{3}+9x^{2}+7x-6](https://tex.z-dn.net/?f=f%28x%29%3D2x%5E%7B3%7D%2B9x%5E%7B2%7D%2B7x-6)
The problem states that one root is -3. Thus, it is true that
![(x+3)](https://tex.z-dn.net/?f=%28x%2B3%29)
is a factor of the polynomial. Given that this is fulfilled, it is also true that:
</span>
![f(x)=(x+3)Q(x) \therefore Q(x)=\frac{f(x)}{x+3} \\ \\ where \ Q(x) \ has \ a \ degree \ of \ 2](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B3%29Q%28x%29%20%5Ctherefore%20Q%28x%29%3D%5Cfrac%7Bf%28x%29%7D%7Bx%2B3%7D%20%5C%5C%20%5C%5C%20where%20%5C%20Q%28x%29%20%5C%20has%20%5C%20a%20%5C%20degree%20%5C%20of%20%5C%202)
<span>
We can find Q(x) by applying Ruffini's rule, thus:
</span>
![\ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ 9 \ \ \ \ \ \ \ \ 7 \ \ \ \ \ \ -6 \\ -3 \\ \rule{50mm}{0.1mm} \\ \ {} \ \ \ \ \ \ \ \ \ \ \ \ 2 \ \ \ \ \ \ \ 3 \ \ \ \ \ -2 \ \ \ \ \ \ \ \ 0](https://tex.z-dn.net/?f=%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%202%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%209%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%207%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20-6%20%20%5C%5C%20-3%20%5C%5C%20%5Crule%7B50mm%7D%7B0.1mm%7D%20%5C%5C%20%5C%20%7B%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%202%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%203%20%5C%20%5C%20%5C%20%5C%20%5C%20-2%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%200)
<span>
Therefore:
The roots of this polynomial can be get as follows:
These are the roots along with
![-3](https://tex.z-dn.net/?f=-3)
. Finally, the factored polynomial can be written as follows:
![f(x)=(x+3)(x+2)(2x-1)](https://tex.z-dn.net/?f=f%28x%29%3D%28x%2B3%29%28x%2B2%29%282x-1%29)
</span>
Answer:
45 units^2
Step-by-step explanation:
W x H = area
9 x 5 = 45 units^2