Answer:
6x^2+2x
Step-by-step explanation:
Find the equation of the inverse.
![y = {2}^{x + 5} - 6](https://tex.z-dn.net/?f=y%20%3D%20%20%7B2%7D%5E%7Bx%20%2B%205%7D%20%20-%206)
we have
![y=\mleft\{2\mright\}^{\mleft\{x+5\mright\}}-6](https://tex.z-dn.net/?f=y%3D%5Cmleft%5C%7B2%5Cmright%5C%7D%5E%7B%5Cmleft%5C%7Bx%2B5%5Cmright%5C%7D%7D-6)
step 1
Exchange the variables
x for y and y for x
![x=\{2\}^{\{y+5\}}-6](https://tex.z-dn.net/?f=x%3D%5C%7B2%5C%7D%5E%7B%5C%7By%2B5%5C%7D%7D-6)
step 2
Isolate the variable y
![(x+6)=2^{(y+5)}](https://tex.z-dn.net/?f=%28x%2B6%29%3D2%5E%7B%28y%2B5%29%7D)
apply log both sides
![\begin{gathered} \log (x+6)=(y+5)\cdot\log (2) \\ y+5=\frac{\log (x+6)}{\log (2)} \\ \\ y=\frac{\log(x+6)}{\log(2)}-5 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Clog%20%28x%2B6%29%3D%28y%2B5%29%5Ccdot%5Clog%20%282%29%20%5C%5C%20y%2B5%3D%5Cfrac%7B%5Clog%20%28x%2B6%29%7D%7B%5Clog%20%282%29%7D%20%5C%5C%20%20%5C%5C%20y%3D%5Cfrac%7B%5Clog%28x%2B6%29%7D%7B%5Clog%282%29%7D-5%20%5Cend%7Bgathered%7D)
step 3
Let
![f^{(-1)}(x)=y](https://tex.z-dn.net/?f=f%5E%7B%28-1%29%7D%28x%29%3Dy)
therefore
the inverse function is
I'm pretty sure it would be 40,000 because if i'm not mistaken you meant the nearest 10,000 since the number is 39,892.
Answer:
2)
![2x + 6x + 8 = 32](https://tex.z-dn.net/?f=2x%20%2B%206x%20%2B%208%20%3D%2032)
collect like terms
![8x + 8 = 32](https://tex.z-dn.net/?f=8x%20%2B%208%20%3D%2032)
move the constant to the right hand side and change its sign.
![8x = 32 - 8](https://tex.z-dn.net/?f=8x%20%3D%2032%20-%208)
Subtract the numbers
![8x = 24](https://tex.z-dn.net/?f=8x%20%3D%2024)
Divide both sides of the equation by 8
![x = 3](https://tex.z-dn.net/?f=x%20%3D%203)
Answer:
X = 46
Step-by-step explanation:
X + 43 + 35 + 56 =180
X + 134 = 180
X = 180 - 134
X = 46