We are given the following quadratic equation

The vertex is the maximum/minimum point of the quadratic equation.
The x-coordinate of the vertex is given by

Comparing the given equation with the general form of the quadratic equation, the coefficients are
a = 2
b = 7
c = -10

The y-coordinate of the vertex is given by

This means that we have a minimum point.
Therefore, the minimum point of the given quadratic equation is
565+65=630 so he needs that much to get the bike AND pay his sister back. 630 divided by $30 is 21. So, in 21 weeks, Steven Can pay back his sister and get the bike
Assuming that an exponentiation sign is missing, all you need to know is that rational exponents work like this:
![a^{\frac{b}{c}}=\sqrt[c]{a^b}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7Bb%7D%7Bc%7D%7D%3D%5Csqrt%5Bc%5D%7Ba%5Eb%7D)
So, you have

And similarly,
![81^{\frac{7}{4}}=\sqrt[4]{25^7}=\sqrt[4]{(3^4)^7}=3^7](https://tex.z-dn.net/?f=81%5E%7B%5Cfrac%7B7%7D%7B4%7D%7D%3D%5Csqrt%5B4%5D%7B25%5E7%7D%3D%5Csqrt%5B4%5D%7B%283%5E4%29%5E7%7D%3D3%5E7)
9.045 is the number added to 0.034 to obtain 9.079
2,400,000 is my answer (: I calculated it