Answer:
(g o f)(x) =
(not simplified)
Step-by-step explanation:
(g o f)(x) = g(f(x))
g(x) =
f(x) = ![x^{3} + 9x](https://tex.z-dn.net/?f=x%5E%7B3%7D%20%2B%209x)
g(f(-5)) = g(
=
= ![-170](https://tex.z-dn.net/?f=-170)
g(-170) =
= ![\sqrt{-510}](https://tex.z-dn.net/?f=%5Csqrt%7B-510%7D)
If the question is y = blank(x) + blank (I can’t see the left of the equation
Then the answer is y = 2x + -4
Answer:
![\large\boxed{r^2=(x+5)^2+(y-4)^2}](https://tex.z-dn.net/?f=%5Clarge%5Cboxed%7Br%5E2%3D%28x%2B5%29%5E2%2B%28y-4%29%5E2%7D)
Step-by-step explanation:
The equation of a circle:
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
<em>(h, k)</em><em> - center</em>
<em>r</em><em> - radius</em>
<em />
We have diameter endpoints.
Half the length of the diameter is the length of the radius.
The center of the diameter is the center of the circle.
The formula of a distance between two points:
![d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%28x_2-x_1%29%5E2%2B%28y_2-y_1%29%5E2%7D)
Substitute the coordinates of the given points (-8, 2) and (-2, 6):
![d=\sqrt{(6-2)^2+(-2-(-8))^2}=\sqrt{4^2+6^2}=\sqrt{16+36}=\sqrt{52}](https://tex.z-dn.net/?f=d%3D%5Csqrt%7B%286-2%29%5E2%2B%28-2-%28-8%29%29%5E2%7D%3D%5Csqrt%7B4%5E2%2B6%5E2%7D%3D%5Csqrt%7B16%2B36%7D%3D%5Csqrt%7B52%7D)
The radius:
![r=\dfrac{d}{2}\to r=\dfrac{\sqrt{52}}{2}](https://tex.z-dn.net/?f=r%3D%5Cdfrac%7Bd%7D%7B2%7D%5Cto%20r%3D%5Cdfrac%7B%5Csqrt%7B52%7D%7D%7B2%7D)
The formula of a midpoint:
![\left(\dfrac{x_1+x_2}{2},\ \dfrac{y_1+y_2}{2}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cdfrac%7Bx_1%2Bx_2%7D%7B2%7D%2C%5C%20%5Cdfrac%7By_1%2By_2%7D%7B2%7D%5Cright%29)
Substitute:
![x=\dfrac{-8+(-2)}{2}=\dfrac{-10}{2}=-5\\\\y=\dfrac{2+6}{2}=\dfrac{8}{2}=4](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B-8%2B%28-2%29%7D%7B2%7D%3D%5Cdfrac%7B-10%7D%7B2%7D%3D-5%5C%5C%5C%5Cy%3D%5Cdfrac%7B2%2B6%7D%7B2%7D%3D%5Cdfrac%7B8%7D%7B2%7D%3D4)
![(-5,\ 4)\to h=-5,\ k=4](https://tex.z-dn.net/?f=%28-5%2C%5C%204%29%5Cto%20h%3D-5%2C%5C%20k%3D4)
Finally:
![(x-(-5))^2+(y-4)^2=\left(\dfrac{\sqrt{52}}{2}\right)^2\\\\(x+5)^2+(y-4)^2=\dfrac{52}{4}\\\\(x+5)^2+(y-4)^2=13](https://tex.z-dn.net/?f=%28x-%28-5%29%29%5E2%2B%28y-4%29%5E2%3D%5Cleft%28%5Cdfrac%7B%5Csqrt%7B52%7D%7D%7B2%7D%5Cright%29%5E2%5C%5C%5C%5C%28x%2B5%29%5E2%2B%28y-4%29%5E2%3D%5Cdfrac%7B52%7D%7B4%7D%5C%5C%5C%5C%28x%2B5%29%5E2%2B%28y-4%29%5E2%3D13)
Answer:
2. 10
3. D. 1 for all n
Step-by-step explanation:
2. The applicable rules of exponents are ...
(a^b)(a^c) = a^(b+c)
a^b = 1/a^-b
__
![\dfrac{4^8}{(4^2)^{-3}}\div 4^4=\dfrac{4^8}{4^{-6}\cdot4^4}=\dfrac{4^8}{4^{-2}}\\\\=4^8\cdot4^2=4^{10}](https://tex.z-dn.net/?f=%5Cdfrac%7B4%5E8%7D%7B%284%5E2%29%5E%7B-3%7D%7D%5Cdiv%204%5E4%3D%5Cdfrac%7B4%5E8%7D%7B4%5E%7B-6%7D%5Ccdot4%5E4%7D%3D%5Cdfrac%7B4%5E8%7D%7B4%5E%7B-2%7D%7D%5C%5C%5C%5C%3D4%5E8%5Ccdot4%5E2%3D4%5E%7B10%7D)
The value of n is 10.
__
3. Using the above rules of exponents, the expression simplifies to ...
6^(-n+n) = 6^0 = 1
The value is 1 for any n.
Answer:
8
Step-by-step explanation:
= ![\frac{x}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B12%7D)
We make the denominator the same by multiplying
by 4.
= ![\frac{x}{12}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B12%7D)
Thus, x = 8.