<span>35% of $1,800 = $630 per month
12 = $7560 per year.</span>
From the given inverse function, we have
![f^{-1}(x-1) = 2x - \dfrac52 \\\\ \implies f^{-1}(x) = f^{-1}((x+1)-1) = 2(x+1) - \dfrac52 = 2x-\dfrac12](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28x-1%29%20%3D%202x%20-%20%5Cdfrac52%20%5C%5C%5C%5C%20%5Cimplies%20f%5E%7B-1%7D%28x%29%20%3D%20f%5E%7B-1%7D%28%28x%2B1%29-1%29%20%3D%202%28x%2B1%29%20-%20%5Cdfrac52%20%3D%202x-%5Cdfrac12)
By definition of inverse function,
![f\left(f^{-1}(x)\right) = x](https://tex.z-dn.net/?f=f%5Cleft%28f%5E%7B-1%7D%28x%29%5Cright%29%20%3D%20x)
so that
![f\left(2x-\dfrac12\right) = x](https://tex.z-dn.net/?f=f%5Cleft%282x-%5Cdfrac12%5Cright%29%20%3D%20x)
![a\left(2x-\dfrac12\right) + \dfrac b2 = x](https://tex.z-dn.net/?f=a%5Cleft%282x-%5Cdfrac12%5Cright%29%20%2B%20%5Cdfrac%20b2%20%3D%20x)
![2ax - \dfrac a2 + \dfrac b2 = x](https://tex.z-dn.net/?f=2ax%20-%20%5Cdfrac%20a2%20%2B%20%5Cdfrac%20b2%20%3D%20x)
![\implies\begin{cases}2a=1 \\\\ -\dfrac a2+\dfrac b2 = 0\end{cases}](https://tex.z-dn.net/?f=%5Cimplies%5Cbegin%7Bcases%7D2a%3D1%20%5C%5C%5C%5C%20-%5Cdfrac%20a2%2B%5Cdfrac%20b2%20%3D%200%5Cend%7Bcases%7D)
![\implies \boxed{a=\dfrac12}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cboxed%7Ba%3D%5Cdfrac12%7D)
![\implies \dfrac b2 = \dfrac a2 \implies \boxed{b=\dfrac12}](https://tex.z-dn.net/?f=%5Cimplies%20%5Cdfrac%20b2%20%3D%20%5Cdfrac%20a2%20%5Cimplies%20%5Cboxed%7Bb%3D%5Cdfrac12%7D)
Hello!
You solve this like an algebraic expression
Multiply both sides by 12
50/6 * 12 = 100
x = 100
Hope this helps!
Answer:
5 minutes
Step-by-step explanation:
We know that 1760 yards are in a mile. We can convert the given info into a proportion. 440/75 = 1760/x, where x is the number of seconds it takes to run a mile. Cross-multiply to get 440x = 75*1760. Divide both sides by 440 to get x = 75*4 = 300 seconds. The problem asks for how many minutes so you have to convert 300 seconds to minutes. To do this, we have to divide 300 by 60 to get 5 minutes.