Answer:
x^2-4x+y^2+6y-108=0
Step-by-step explanation:
![The- equation- of- circle- with -center- at- (h,k) -and -a -radius- of- r -is: \\(x-h)^2 +(y-k)^2 = r^2\\h = 2 , \\ k = -3\\r = 11\\(x-2)^2+(y-(-3))^2 = 11^2\\(x-2)^2+(y+3)^2 = 121\\x^2-4x+4 +y^2+6y+9 = 121\\x^2 -4x+y^2+6y+4+9=121\\x^2 -4x+y^2+6y+13=121\\x^2 -4x+y^2+6y=121-13\\x^2 -4x+y^2+6y= 108\\x^2 -4x+y^2+6y-108 = 0](https://tex.z-dn.net/?f=The-%20equation-%20of-%20circle-%20with%20-center-%20at-%20%28h%2Ck%29%20-and%20-a%20-radius-%20of-%20r%20-is%3A%20%5C%5C%28x-h%29%5E2%20%2B%28y-k%29%5E2%20%3D%20r%5E2%5C%5Ch%20%3D%202%20%2C%20%5C%5C%20%20k%20%3D%20-3%5C%5Cr%20%3D%2011%5C%5C%28x-2%29%5E2%2B%28y-%28-3%29%29%5E2%20%3D%2011%5E2%5C%5C%28x-2%29%5E2%2B%28y%2B3%29%5E2%20%3D%20121%5C%5Cx%5E2-4x%2B4%20%2By%5E2%2B6y%2B9%20%3D%20121%5C%5Cx%5E2%20-4x%2By%5E2%2B6y%2B4%2B9%3D121%5C%5Cx%5E2%20-4x%2By%5E2%2B6y%2B13%3D121%5C%5Cx%5E2%20-4x%2By%5E2%2B6y%3D121-13%5C%5Cx%5E2%20-4x%2By%5E2%2B6y%3D%20108%5C%5Cx%5E2%20-4x%2By%5E2%2B6y-108%20%3D%200)
Answer:
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Step-by-step explanation:
Answer: Divide 6/42 by 6/6 to get 1/7
Step-by-step explanation: To find the numerator when dividing by 6/6, divide 6/6 to get 1. To find the denominator, divide 42/6 to get 7.
Answer:
Constant of proportionality: ![k=3](https://tex.z-dn.net/?f=k%3D3)
Equation: ![c=3d](https://tex.z-dn.net/?f=c%3D3d)
Step-by-step explanation:
By definition, Direct proportion equations have the following form:
![y=kx](https://tex.z-dn.net/?f=y%3Dkx)
Where "k" is the Constant of proportionality.
In this case, let be "c" the the amount of caffeine consumed (in mg) from a glass of Diet Pepsi and "d" the number of ounces that was drank.
So, the equation that represents this relationship will have this form:
![c=kd](https://tex.z-dn.net/?f=c%3Dkd)
Then, the first step is to find the Constant of proportionality "k".
Knowing that:
![c=24;d=8](https://tex.z-dn.net/?f=c%3D24%3Bd%3D8)
We can substitute values into the equation:
![24=k(8)](https://tex.z-dn.net/?f=24%3Dk%288%29)
Now, solving for "k", we get:
![\frac{24}{8}=k\\\\k=3](https://tex.z-dn.net/?f=%5Cfrac%7B24%7D%7B8%7D%3Dk%5C%5C%5C%5Ck%3D3)
Therefore, we can write the following equation that represents that proportional relationship:
![c=3d](https://tex.z-dn.net/?f=c%3D3d)