Answer:
The second picture
hope this helps
have a good day :)
Step-by-step explanation:
Answer:
we conclude:
![f(g(7)) =85](https://tex.z-dn.net/?f=f%28g%287%29%29%20%3D85)
Step-by-step explanation:
Given
![f(x) = 4x + 21](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%20%2B%2021)
![g(x) = 2x + 2](https://tex.z-dn.net/?f=g%28x%29%20%3D%202x%20%2B%202)
To determine
In order to determine f(g(7)), the first step we need to do is to determine g(7)
so substitute x = 7 in g(x) = 2x + 2
![g(x) = 2x + 2](https://tex.z-dn.net/?f=g%28x%29%20%3D%202x%20%2B%202)
![g(7) = 2(7) + 2](https://tex.z-dn.net/?f=g%287%29%20%3D%202%287%29%20%2B%202)
![g(7) = 14 + 2](https://tex.z-dn.net/?f=g%287%29%20%3D%2014%20%2B%202)
![g(7) = 16](https://tex.z-dn.net/?f=g%287%29%20%3D%2016)
so now we have
![f(g(7)) =f(16)](https://tex.z-dn.net/?f=f%28g%287%29%29%20%3Df%2816%29)
The next step to do is to substitute x = 16 in f(x) = 4x + 21
![f(x) = 4x + 21](https://tex.z-dn.net/?f=f%28x%29%20%3D%204x%20%2B%2021)
![f(16) = 4(16) + 21](https://tex.z-dn.net/?f=f%2816%29%20%3D%204%2816%29%20%2B%2021)
![f(16) = 64 + 21](https://tex.z-dn.net/?f=f%2816%29%20%3D%2064%20%2B%2021)
![f(16) = 85](https://tex.z-dn.net/?f=f%2816%29%20%3D%2085)
so we have
![f(g(7)) =f(16)=85](https://tex.z-dn.net/?f=f%28g%287%29%29%20%3Df%2816%29%3D85)
Therefore, we conclude:
![f(g(7)) =85](https://tex.z-dn.net/?f=f%28g%287%29%29%20%3D85)
It is 7 1/6 hope this helps
Answer:
![\bigg(\frac{2}{3} {y} \bigg)^{2}](https://tex.z-dn.net/?f=%5Cbigg%28%5Cfrac%7B2%7D%7B3%7D%20%20%7By%7D%20%5Cbigg%29%5E%7B2%7D)
STEP BY STEP EXPLANATION
![\frac{1}{4} {x}^{2} - \bigg( \frac{2}{3} \bigg)xy \\ \\ = \bigg(\frac{1}{2} {x} \bigg)^{2} - 2. \bigg(\frac{1}{2} {x} \bigg)\bigg( \frac{2}{3} y \bigg ) + \bigg(\frac{2}{3} {y} \bigg)^{2} \\ \\ = \bigg(\frac{1}{2} {x} - \frac{2}{3} y\bigg)^{2} \\](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B4%7D%20%20%7Bx%7D%5E%7B2%7D%20%20-%20%20%5Cbigg%28%20%5Cfrac%7B2%7D%7B3%7D%20%20%5Cbigg%29xy%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%20%5Cbigg%28%5Cfrac%7B1%7D%7B2%7D%20%20%7Bx%7D%20%5Cbigg%29%5E%7B2%7D%20%20-%202.%20%5Cbigg%28%5Cfrac%7B1%7D%7B2%7D%20%20%7Bx%7D%20%5Cbigg%29%5Cbigg%28%20%5Cfrac%7B2%7D%7B3%7D%20y%20%5Cbigg%20%29%20%2B%20%20%5Cbigg%28%5Cfrac%7B2%7D%7B3%7D%20%20%7By%7D%20%5Cbigg%29%5E%7B2%7D%20%5C%5C%20%20%5C%5C%20%20%3D%20%5Cbigg%28%5Cfrac%7B1%7D%7B2%7D%20%20%7Bx%7D%20%20-%20%20%5Cfrac%7B2%7D%7B3%7D%20y%5Cbigg%29%5E%7B2%7D%20%20%5C%5C%20)
To make
a perfect square we should add ![\purple{\bold{\bigg(\frac{2}{3} {y} \bigg)^{2}}}](https://tex.z-dn.net/?f=%5Cpurple%7B%5Cbold%7B%5Cbigg%28%5Cfrac%7B2%7D%7B3%7D%20%20%7By%7D%20%5Cbigg%29%5E%7B2%7D%7D%7D)
All of them would be correct except for the third option, Angle BCA is not equivalent to Angle DCE.