The answer is 107 because for every term the sequence is being added by 15. Therefore 62+15= 77. 77+15=92. 92+15=107, the seventh term is going to be 107
The function is given as,
![y=\frac{3}{4x}-8](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B4x%7D-8)
In order to determine the inverse of the function, first, we need to switch the variables 'x' and 'y' in the given equation. And then transform the equation to obtain the form y=f(x).
After switching the variables, the equation becomes,
![x=\frac{3}{4y}-8](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%7D%7B4y%7D-8)
Now, convert the equation in the form y=f(x) by transposing the terms.
Add 8 on both sides,
![\begin{gathered} x+8=\frac{3}{4y}-8+8 \\ x+8=\frac{3}{4y} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%2B8%3D%5Cfrac%7B3%7D%7B4y%7D-8%2B8%20%5C%5C%20x%2B8%3D%5Cfrac%7B3%7D%7B4y%7D%20%5Cend%7Bgathered%7D)
Multiply the equation by 4/3 as follows,
![\begin{gathered} (x+8)\cdot\frac{4}{3}=(\frac{3}{4y})\cdot\frac{4}{3} \\ \frac{4}{3}x+(\frac{8\cdot4}{3})=\frac{3\cdot4}{4y\cdot3} \\ \frac{4}{3}x+\frac{32}{3}=\frac{1}{y} \\ \frac{4x+32}{3}=\frac{1}{y} \\ \frac{4x+32}{3}=\frac{1}{y} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%28x%2B8%29%5Ccdot%5Cfrac%7B4%7D%7B3%7D%3D%28%5Cfrac%7B3%7D%7B4y%7D%29%5Ccdot%5Cfrac%7B4%7D%7B3%7D%20%5C%5C%20%5Cfrac%7B4%7D%7B3%7Dx%2B%28%5Cfrac%7B8%5Ccdot4%7D%7B3%7D%29%3D%5Cfrac%7B3%5Ccdot4%7D%7B4y%5Ccdot3%7D%20%5C%5C%20%5Cfrac%7B4%7D%7B3%7Dx%2B%5Cfrac%7B32%7D%7B3%7D%3D%5Cfrac%7B1%7D%7By%7D%20%5C%5C%20%5Cfrac%7B4x%2B32%7D%7B3%7D%3D%5Cfrac%7B1%7D%7By%7D%20%5C%5C%20%5Cfrac%7B4x%2B32%7D%7B3%7D%3D%5Cfrac%7B1%7D%7By%7D%20%5Cend%7Bgathered%7D)
Cross multiply the terms,
![y=\frac{3}{4x+32}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B3%7D%7B4x%2B32%7D)
Now that the function is converted into the desired form, it can be concluded that the inverse is obtained.
Therefore, the required inverse function is obtained as,
Answer:
77 + n ≥ 100
Step-by-step explanation:
We know that adding two numbers (77 and n) must be equal to or greater than (≥) 100.
So we can write the equation like:
77 + n ≥ 100
She will need 8 more barbies, to reach a total of 12.
Hope this helps!