Answer:
The equation does not match the form of any conic section.
Not a Conic Section
Step-by-step explanation:
Step-by-step explanation:
Since ∠E is right angle, its opposite side is DF and the legs are DE and EF.
<u>Pythagorean applied:</u>
Given:
The functions are
![f(x)=4x^2+7x-5](https://tex.z-dn.net/?f=f%28x%29%3D4x%5E2%2B7x-5)
![g(x)=-9x^2+4x-13](https://tex.z-dn.net/?f=g%28x%29%3D-9x%5E2%2B4x-13)
To find:
The functions
and
.
Solution:
We know that,
![(f+g)(x)=f(x)+g(x)](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3Df%28x%29%2Bg%28x%29)
![(f+g)(x)=4x^2+7x-5-9x^2+4x-13](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D4x%5E2%2B7x-5-9x%5E2%2B4x-13)
![(f+g)(x)=(4x^2-9x^2)+(7x+4x)+(-5-13)](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D%284x%5E2-9x%5E2%29%2B%287x%2B4x%29%2B%28-5-13%29)
![(f+g)(x)=-5x^2+11x-18](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D-5x%5E2%2B11x-18)
And,
![(f-g)(x)=f(x)-g(x)](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3Df%28x%29-g%28x%29)
![(f-g)(x)=(4x^2+7x-5)-(-9x^2+4x-13)](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3D%284x%5E2%2B7x-5%29-%28-9x%5E2%2B4x-13%29)
![(f+g)(x)=4x^2+7x-5+9x^2-4x+13](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D4x%5E2%2B7x-5%2B9x%5E2-4x%2B13)
![(f+g)(x)=(4x^2+9x^2)+(7x-4x)+(-5+13)](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D%284x%5E2%2B9x%5E2%29%2B%287x-4x%29%2B%28-5%2B13%29)
![(f-g)(x)=13x^2+3x+8](https://tex.z-dn.net/?f=%28f-g%29%28x%29%3D13x%5E2%2B3x%2B8)
Therefore, the required functions are ![(f+g)(x)=-5x^2+11x-18](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D-5x%5E2%2B11x-18)
and
.
I think the best answer choice would be C.