Step-by-step explanation:
You can put the value of x into the equation to solve for y. Hopes this works.
700 + 80 + 2^2?
I have no idea rly lol
It would take her 10min to finish 35 hot dogs because 21 divided by 6 equals 3.5 so in six minutes she eats 3.5 hot dogs per minute. Multiply 3.5 by ten you get 35
I'm guessing the repeating part is 89 at the end, so that
![x=0.8967\overline89\implies10^4x=8967.\overline{89}](https://tex.z-dn.net/?f=x%3D0.8967%5Coverline89%5Cimplies10%5E4x%3D8967.%5Coverline%7B89%7D)
Then
![10^4x=8967+\displaystyle89\sum_{i=1}^\infty\frac1{100^i}](https://tex.z-dn.net/?f=10%5E4x%3D8967%2B%5Cdisplaystyle89%5Csum_%7Bi%3D1%7D%5E%5Cinfty%5Cfrac1%7B100%5Ei%7D)
![10^4x=8967+89\left(\dfrac1{1-\frac1{100}}-1\right)](https://tex.z-dn.net/?f=10%5E4x%3D8967%2B89%5Cleft%28%5Cdfrac1%7B1-%5Cfrac1%7B100%7D%7D-1%5Cright%29)
![10^4x=8967+\dfrac{89}{99}](https://tex.z-dn.net/?f=10%5E4x%3D8967%2B%5Cdfrac%7B89%7D%7B99%7D)
![x=\dfrac{8967}{10^4}+\dfrac{89}{99\cdot10^4}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B8967%7D%7B10%5E4%7D%2B%5Cdfrac%7B89%7D%7B99%5Ccdot10%5E4%7D)
![x=\dfrac{443911}{495000}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B443911%7D%7B495000%7D)
###
An arguably quicker way without using geometric series:
![10^4x=8967.\overline{89}](https://tex.z-dn.net/?f=10%5E4x%3D8967.%5Coverline%7B89%7D)
![10^6x=896789.\overline{89}](https://tex.z-dn.net/?f=10%5E6x%3D896789.%5Coverline%7B89%7D)
![10^6x-10^4x=887822](https://tex.z-dn.net/?f=10%5E6x-10%5E4x%3D887822)
![x=\dfrac{887822}{10^6-10^4}=\dfrac{443911}{495000}](https://tex.z-dn.net/?f=x%3D%5Cdfrac%7B887822%7D%7B10%5E6-10%5E4%7D%3D%5Cdfrac%7B443911%7D%7B495000%7D)