Answer:
![\mathrm{Vertical}:\:x=-1,\:x=2,\:\mathrm{Horizontal}:\:y=\frac{1}{4}](https://tex.z-dn.net/?f=%5Cmathrm%7BVertical%7D%3A%5C%3Ax%3D-1%2C%5C%3Ax%3D2%2C%5C%3A%5Cmathrm%7BHorizontal%7D%3A%5C%3Ay%3D%5Cfrac%7B1%7D%7B4%7D)
Step-by-step explanation:
Your equation is: ![f(x)=\frac{x^2+4}{4x^2-4x-8}](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7Bx%5E2%2B4%7D%7B4x%5E2-4x-8%7D)
![\mathrm{If\:the\:degrees\:are\:equal,\:the\:asymptote\:is:\:y=\frac{numerator's\:leading\:coefficient}{denominator's\:leading\:coefficient}}](https://tex.z-dn.net/?f=%5Cmathrm%7BIf%5C%3Athe%5C%3Adegrees%5C%3Aare%5C%3Aequal%2C%5C%3Athe%5C%3Aasymptote%5C%3Ais%3A%5C%3Ay%3D%5Cfrac%7Bnumerator%27s%5C%3Aleading%5C%3Acoefficient%7D%7Bdenominator%27s%5C%3Aleading%5C%3Acoefficient%7D%7D)
ANSWER
The radius is 4
EXPLANATION
The given equation is:
![{x}^{2} + {y}^{2} - 10y + 6x + 18 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%2B%20%20%7By%7D%5E%7B2%7D%20%20-%2010y%20%2B%206x%20%2B%2018%20%3D%200)
We complete the square to get the expression in standard form:
![{x}^{2} + 6x + {y}^{2} - 10y + 18 = 0](https://tex.z-dn.net/?f=%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%20%20%7By%7D%5E%7B2%7D%20%20-%2010y%20%20%2B%2018%20%3D%200)
![{x}^{2} + 6x + 9 + {y}^{2} - 10y + 25 = - 18 + 9 + 25](https://tex.z-dn.net/?f=%7Bx%7D%5E%7B2%7D%20%20%2B%206x%20%2B%20%209%20%2B%20%7By%7D%5E%7B2%7D%20%20-%2010y%20%20%2B%2025%20%20%3D%20%20-%2018%20%2B%209%20%2B%2025)
We factor using perfect squares to get:
![{(x + 3)}^{2} + {(y - 5)}^{2} = 16](https://tex.z-dn.net/?f=%7B%28x%20%2B%203%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28y%20-%205%29%7D%5E%7B2%7D%20%3D%20%2016)
This implies that,
![{(x + 3)}^{2} + {(y - 5)}^{2} = {4}^{2}](https://tex.z-dn.net/?f=%7B%28x%20%2B%203%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28y%20-%205%29%7D%5E%7B2%7D%20%3D%20%20%20%7B4%7D%5E%7B2%7D%20)
Comparing to
![{(x - h)}^{2} + {(y - k)}^{2} = {r}^{2}](https://tex.z-dn.net/?f=%7B%28x%20%20-%20h%29%7D%5E%7B2%7D%20%20%2B%20%20%7B%28y%20-%20k%29%7D%5E%7B2%7D%20%3D%20%20%20%7Br%7D%5E%7B2%7D%20)
The radius is r=4
Answer: It is not prime , therefor it's composite.
Step-by-step explanation:
Because....
The number 27 can be evenly divided by 1, 3, 9 and 27, with no remainder.
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