Answer:
The center of the circle is
![(-\frac{3}{2},2)](https://tex.z-dn.net/?f=%28-%5Cfrac%7B3%7D%7B2%7D%2C2%29)
Step-by-step explanation:
Let the equation of the circle be
, where (-a,-b) is the center of this circle.
The points lying the circle must satisfy the equation of this circle.
A(0,0)
We substitute this point to get;
![0^2+0^2+2a(0)+2b(0)+c=0](https://tex.z-dn.net/?f=0%5E2%2B0%5E2%2B2a%280%29%2B2b%280%29%2Bc%3D0)
![\implies c=0](https://tex.z-dn.net/?f=%5Cimplies%20c%3D0)
B(-3,0)
![(-3)^2+0^2+2a(-3)+2b(0)+c=0](https://tex.z-dn.net/?f=%28-3%29%5E2%2B0%5E2%2B2a%28-3%29%2B2b%280%29%2Bc%3D0)
![\implies 9+0-6a+0+c=0](https://tex.z-dn.net/?f=%5Cimplies%209%2B0-6a%2B0%2Bc%3D0)
![\implies -6a+c=-9](https://tex.z-dn.net/?f=%5Cimplies%20-6a%2Bc%3D-9)
But c=0
![\implies -6a=-9](https://tex.z-dn.net/?f=%5Cimplies%20-6a%3D-9)
![\implies a=\frac{3}{2}](https://tex.z-dn.net/?f=%5Cimplies%20a%3D%5Cfrac%7B3%7D%7B2%7D)
C(1,2)
![1^2+2^2+2a(1)+2b(2)+c=0](https://tex.z-dn.net/?f=1%5E2%2B2%5E2%2B2a%281%29%2B2b%282%29%2Bc%3D0)
![1+4+2a+4b+c=0](https://tex.z-dn.net/?f=1%2B4%2B2a%2B4b%2Bc%3D0)
![2a+4b+c=-5](https://tex.z-dn.net/?f=2a%2B4b%2Bc%3D-5)
Put the value of 'a' and 'c' to find 'b'
![2(\frac{3}{2})+4b+0=-5](https://tex.z-dn.net/?f=2%28%5Cfrac%7B3%7D%7B2%7D%29%2B4b%2B0%3D-5)
![3+4b+0=-5](https://tex.z-dn.net/?f=3%2B4b%2B0%3D-5)
![4b=-5-3](https://tex.z-dn.net/?f=4b%3D-5-3)
![4b=-8](https://tex.z-dn.net/?f=4b%3D-8)
b=-2
Hence the center of the circle is
![(-\frac{3}{2},2)](https://tex.z-dn.net/?f=%28-%5Cfrac%7B3%7D%7B2%7D%2C2%29)
Answer:
![Z= 75*6 -250=200](https://tex.z-dn.net/?f=%20Z%3D%2075%2A6%20-250%3D200)
So then the correct answer is B. $200.
Step-by-step explanation:
Notation
Let X be the average contribution size before John makes his contribution.
Let Y be the total contribution size before John makes his contribution.
Let Z be John's contribution.
We know that for this case $ 75 represent the original average amount before the contribution with 50% increase so we can set up the following equation in order to find the original average amount
![1.5 X = 75](https://tex.z-dn.net/?f=%201.5%20X%20%3D%2075)
And solvong for X we got:
![X = \frac{75}{1.5}= 50](https://tex.z-dn.net/?f=%20X%20%3D%20%5Cfrac%7B75%7D%7B1.5%7D%3D%2050)
Now we can find the total contribution before the donation with the following proportion:
![\frac{50}{1}= \frac{Y}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B50%7D%7B1%7D%3D%20%5Cfrac%7BY%7D%7B5%7D)
![Y = 250](https://tex.z-dn.net/?f=%20Y%20%3D%20250)
And then with the formula of average taking in count the 6 values we can find the size of donation Z like this:
![\frac{Y+Z}{6}= 75](https://tex.z-dn.net/?f=%20%5Cfrac%7BY%2BZ%7D%7B6%7D%3D%2075)
![\frac{250+Z}{6}= 75](https://tex.z-dn.net/?f=%20%5Cfrac%7B250%2BZ%7D%7B6%7D%3D%2075)
![Z= 75*6 -250=200](https://tex.z-dn.net/?f=%20Z%3D%2075%2A6%20-250%3D200)
So then the correct answer is B. $200.
The word form for 2.35 is
"two point three five".
Answer:
You can't factor x or any number other than 1 out.
Step-by-step explanation: