Answer:
the answer is 8 and you are welcome
Answers with step-by-step explanation:
1. (7x + x) + 7x
= 7x + 7x + x
= 14x + x
= 15x
2. 5 * (4 * x)
= 5*4x
= 20x
3. 15y + (x + 9y)
= 15y + 9y + x
= 24y + x
4. (6x + 21) + 14
= 6x + 21 + 14
= 6x + 35
5. 3x + 2 + 11x
= 11x+ 3x + 2
= 14x + 2
6. (x + 13y) + 8y
= 13y + 8y + x
= 21y + x
7. (12y + 2x) + 4y
= 12y + 4y + 2x
= 16y + 2x
8. 8 (x4)
= 32x
9. 3 (5x)
= 15x
10. 3x + (7x + 10)
= 3x + 7x + 10
= 21x + 10
11. 5x + (2 + x)
= 6x + 2
12. 4 * x * 10
= 4 * 10 *x
= 40x
13. (x * 12) * 3
= 36x
14. 14x + 9y + 6x
= 20x + 9y
15. 5x + (24 + 14x)
= 19x + 24
Answer:
![\displaystyle f(x) = -2(x-2)(x^2+4)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20-2%28x-2%29%28x%5E2%2B4%29)
Step-by-step explanation:
We want to find a third degree polynomial with zeros <em>x </em>= 2 and <em>x</em> = 2i and f(-1) = 30.
First, note that by the Complex Root Theorem, since <em>x</em> = 2i is a root, <em>x</em> = -2i must also be a root.
Hence, we will have the three factors:
![\displaystyle f(x) = a(x-(2))(x-(2i))(x-(-2i))](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20a%28x-%282%29%29%28x-%282i%29%29%28x-%28-2i%29%29)
Where <em>a</em> is the leading coefficient.
Expand and simplify the second and third factors:
![\displaystyle \begin{aligned} (x-(2i))(x-(-2i)) &= (x-2i)(x+2i) \\ \\ &= x(x-2i)+2i(x-2i) \\ \\ &= (x^2 - 2ix) + (2ix - 4i^2) \\ \\ &=x^2 + 4\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20%28x-%282i%29%29%28x-%28-2i%29%29%20%26%3D%20%28x-2i%29%28x%2B2i%29%20%5C%5C%20%5C%5C%20%26%3D%20x%28x-2i%29%2B2i%28x-2i%29%20%5C%5C%20%5C%5C%20%26%3D%20%28x%5E2%20-%202ix%29%20%2B%20%282ix%20-%204i%5E2%29%20%5C%5C%20%5C%5C%20%26%3Dx%5E2%20%2B%204%5Cend%7Baligned%7D)
Hence:
![\displaystyle f(x) = a(x-2)(x^2+4)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20a%28x-2%29%28x%5E2%2B4%29)
Since f(-1) = 30:
![\displaystyle \begin{aligned} f(x) &= a(x-2)(x^2+4) \\ \\ (30) &= a((-1)-2)((-1)^2+4) \\ \\ 30 &= -15a \\ \\ a&= -2\end{aligned}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cbegin%7Baligned%7D%20%20f%28x%29%20%26%3D%20a%28x-2%29%28x%5E2%2B4%29%20%5C%5C%20%5C%5C%20%2830%29%20%26%3D%20a%28%28-1%29-2%29%28%28-1%29%5E2%2B4%29%20%5C%5C%20%5C%5C%2030%20%26%3D%20-15a%20%5C%5C%20%5C%5C%20a%26%3D%20-2%5Cend%7Baligned%7D)
In conclusion, third degree polynomial function is:
![\displaystyle f(x) = -2(x-2)(x^2+4)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20f%28x%29%20%3D%20-2%28x-2%29%28x%5E2%2B4%29)
The Answer Is g(x)=1/3x^2
Use (3,3) to find the equation.
3^2x1/3=3
Meaning y or g(x) equals 3. Which is true.
Answer:
gosh...…. dang brainly why do you have to be like that. you were literally trying to help ppl hippo and they just shut you down like that... ugh why rude.
Step-by-step explanation:
im sorry :(