as you may already know, to get the inverse of any expression, we start off by doing a quick switcheroo on the variables, and then solve for "y".
![\bf \stackrel{f(x)}{y}=x^3-9\implies \stackrel{\textit{quick switcheroo}}{\underline{x}=\underline{y}^3-9}\implies x+9=y^3\implies \sqrt[3]{x+9}=\stackrel{f^{-1}(x)}{y}](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bf%28x%29%7D%7By%7D%3Dx%5E3-9%5Cimplies%20%5Cstackrel%7B%5Ctextit%7Bquick%20switcheroo%7D%7D%7B%5Cunderline%7Bx%7D%3D%5Cunderline%7By%7D%5E3-9%7D%5Cimplies%20x%2B9%3Dy%5E3%5Cimplies%20%5Csqrt%5B3%5D%7Bx%2B9%7D%3D%5Cstackrel%7Bf%5E%7B-1%7D%28x%29%7D%7By%7D)
You plug 11 in where x is.
r(11) = (11 + 1)(11 - 3)
= (12)(8)
= 96
175 mL at 25% concentration of alcohol contains 0.25 (175 mL) = 43.75 mL of alcohol. If <em>v</em> is the amount of the 70% solution that you use, then that amount contains 0.7<em>v</em> mL of alcohol.
Mixing these two yields a total volume of 175 mL + <em>v</em>, and it contains 43.75 mL + 0.7<em>v</em> alcohol. You want to end up with a concentration of 45%, which means the ratio of the amount of alcohol to the total volume needs to be 0.45:
(43.75 mL + 0.7<em>v</em>) / (175 mL + <em>v</em>) = 0.45
Solve for <em>v</em> :
43.75 mL + 0.7<em>v</em> = 0.45 (175 mL + <em>v</em>)
43.75 mL + 0.7<em>v</em> = 78.75 mL + 0.45<em>v</em>
0.25<em>v</em> = 35 mL
<em>v</em> = 140 mL
Answer: bottom left
4x+2y+15
Step-by-step explanation:
3x + x=4x
5 + 10= 15
2y=2y
4x+2y+15
