5 times 3 equals 15 so they gained 15 yards. 12 times 2 equals 24. 24 minis 15 equals 9. So the answer in 9 yards
AB = AX+XB = 6+18 = 24
The ratio of AB to AX is AB/AX = 24/6 = 4
AC = AY+YC = 10+25 = 35
The ratio of AC to AY is AC/AY = 25/10 = 3.5
The results of each division are 4 and 3.5
We do <u>not</u> get the same result, which means that the proportion
is <u>not</u> true. This is sufficient to prove that the triangles aren't similar. We need them to be in proportion so that we can use the SAS similarity rule.
<h3>Answer: The triangles aren't similar</h3>
![(\frac{g}{f})(3)=\frac{-13}{21}\\](https://tex.z-dn.net/?f=%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-13%7D%7B21%7D%5C%5C)
2/3 will not be included in the domain of g/f
Step-by-step explanation:
Given functions are:
![g(x) =-2x^2+5\\f(x)=9x-6](https://tex.z-dn.net/?f=g%28x%29%20%3D-2x%5E2%2B5%5C%5Cf%28x%29%3D9x-6)
We have to calculate (f/g)(x) first
The steps will be as follows:
![(\frac{g}{f})(x)=\frac{g(x)}{f(x)}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bg%7D%7Bf%7D%29%28x%29%3D%5Cfrac%7Bg%28x%29%7D%7Bf%28x%29%7D)
Putting the values of functions
![(\frac{g}{f})(x)=\frac{-2x^2+5}{9x-6}\\We\ have\ to\ find\ the\ value\ of\ (\frac{g}{f})(x)\ at\ 3\\So,\\(\frac{g}{f})(3)=\frac{-2(3)^2+5}{9(3)-6}\\(\frac{g}{f})(3)=\frac{-2(9)+5}{27-6}\\(\frac{g}{f})(3)=\frac{-18+5}{27-6}\\(\frac{g}{f})(3)=\frac{-13}{21}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bg%7D%7Bf%7D%29%28x%29%3D%5Cfrac%7B-2x%5E2%2B5%7D%7B9x-6%7D%5C%5CWe%5C%20have%5C%20to%5C%20find%5C%20the%5C%20value%5C%20of%5C%20%28%5Cfrac%7Bg%7D%7Bf%7D%29%28x%29%5C%20at%5C%203%5C%5CSo%2C%5C%5C%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-2%283%29%5E2%2B5%7D%7B9%283%29-6%7D%5C%5C%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-2%289%29%2B5%7D%7B27-6%7D%5C%5C%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-18%2B5%7D%7B27-6%7D%5C%5C%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-13%7D%7B21%7D)
Domain of g/f:
![(\frac{g}{f})(x)=\frac{-2x^2+5}{9x-6}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bg%7D%7Bf%7D%29%28x%29%3D%5Cfrac%7B-2x%5E2%2B5%7D%7B9x-6%7D)
The function will be undefined if the denominator is zero.
To find the domain we will put the denominator equal to zero
So,
![9x-6=0\\Adding\ 6\ on\ both\ sides\\9x-6+6=0+6\\9x=6\\Dividing\ both\ sides\ by\ 9\\\frac{9x}{9}=\frac{6}{9}\\x=\frac{2}{3}](https://tex.z-dn.net/?f=9x-6%3D0%5C%5CAdding%5C%206%5C%20on%5C%20both%5C%20sides%5C%5C9x-6%2B6%3D0%2B6%5C%5C9x%3D6%5C%5CDividing%5C%20both%5C%20sides%5C%20by%5C%209%5C%5C%5Cfrac%7B9x%7D%7B9%7D%3D%5Cfrac%7B6%7D%7B9%7D%5C%5Cx%3D%5Cfrac%7B2%7D%7B3%7D)
Hence, the function will be undefined on x=2/3 so 2/3 will not be included in the domain of (f/g)(x)
<u>Answer:</u>
![(\frac{g}{f})(3)=\frac{-13}{21}\\](https://tex.z-dn.net/?f=%28%5Cfrac%7Bg%7D%7Bf%7D%29%283%29%3D%5Cfrac%7B-13%7D%7B21%7D%5C%5C)
2/3 will not be included in the domain of g/f
Keywords: Domain, Operations on Functions
Learn more about functions at:
#LearnwithBrainly
Answer:
x = 6
Step-by-step explanation:
5 sides all the same length
s = 22.5/5
s = 4.5
--------------------
x - 1.5 = 4.5
Add 1.5 to both sides
x = 6
Answer:
6.66666666667
Step-by-step explanation: