R + c=24
r=3c
3c+c=24
x=6
So there are 18 rock CDs
Answer:
see below
Step-by-step explanation:
translated 3 units down whic means -3 on the y
hence T1 (2,0), T2 (-4,-8), T3 (-2, 1)
I believe you just add all the numbers then divide by how many were there. You would divide by 16.
Step-by-step explanation:
We have
![\frac{20x + 9}{25 {x}^{2} + 20x + 4 }](https://tex.z-dn.net/?f=%20%5Cfrac%7B20x%20%2B%209%7D%7B25%20%7Bx%7D%5E%7B2%7D%20%2B%2020x%20%2B%204%20%7D%20)
Let's factor the denomiator first,
the denomaitor is a perfect square so we get
![\frac{20x + 9}{(5x + 2) {}^{2} }](https://tex.z-dn.net/?f=%20%5Cfrac%7B20x%20%2B%209%7D%7B%285x%20%2B%202%29%20%7B%7D%5E%7B2%7D%20%7D%20)
Now, we must think of two fractions that
![\frac{a}{(5x + 2) {}^{2} } + \frac{b}{5x + 2}](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7B%285x%20%2B%202%29%20%7B%7D%5E%7B2%7D%20%7D%20%20%2B%20%20%5Cfrac%7Bb%7D%7B5x%20%2B%202%7D%20)
We use a perfect square term for one fraction, then a linear one for the next, because if we set both of the denomiator to the same factor, we would get a inconsistent system.
So right now, we have
![\frac{a}{(5x + 2) { }^{2} } + \frac{b}{5x + 2} = \frac{20x +9 }{25 {x}^{2} + 20x + 4 }](https://tex.z-dn.net/?f=%20%5Cfrac%7Ba%7D%7B%285x%20%2B%202%29%20%7B%20%7D%5E%7B2%7D%20%7D%20%20%2B%20%20%5Cfrac%7Bb%7D%7B5x%20%2B%202%7D%20%20%3D%20%20%5Cfrac%7B20x%20%2B9%20%7D%7B25%20%7Bx%7D%5E%7B2%7D%20%2B%2020x%20%2B%204%20%7D%20)
![a + (5x + 2)b = 20x + 9](https://tex.z-dn.net/?f=a%20%2B%20%285x%20%20%2B%202%29b%20%3D%2020x%20%2B%209)
![5b (x)= 20](https://tex.z-dn.net/?f=5b%20%28x%29%3D%2020)
![a + 2b = 9](https://tex.z-dn.net/?f=a%20%2B%202b%20%3D%209)
![b = 4](https://tex.z-dn.net/?f=b%20%3D%204)
so that means that a is
![a + (2)(4) = 9](https://tex.z-dn.net/?f=a%20%2B%20%282%29%284%29%20%3D%209)
![a + 8 = 9](https://tex.z-dn.net/?f=a%20%2B%208%20%3D%209)
![a = 1](https://tex.z-dn.net/?f=a%20%3D%201)
So our equation is
![\frac{1}{(5x + 2) {}^{2} } + \frac{4}{5x + 2}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B%285x%20%2B%202%29%20%7B%7D%5E%7B2%7D%20%7D%20%20%2B%20%20%5Cfrac%7B4%7D%7B5x%20%2B%202%7D%20)