Answer:
The center of the circle is at;
![(1,-3)](https://tex.z-dn.net/?f=%281%2C-3%29)
The radius of the circle is;
![r=4](https://tex.z-dn.net/?f=r%3D4)
Explanation:
Given the equation of circle;
![x^2+y^2-2x+6y-6=0](https://tex.z-dn.net/?f=x%5E2%2By%5E2-2x%2B6y-6%3D0)
we want to re-write it in the form;
![(x-h)^2+(y-k)^2=r^2](https://tex.z-dn.net/?f=%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2)
where;
![\begin{gathered} (h,k)\text{ is the center of the circle} \\ r\text{ is the radius} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%28h%2Ck%29%5Ctext%7B%20is%20the%20center%20of%20the%20circle%7D%20%5C%5C%20r%5Ctext%7B%20is%20the%20radius%7D%20%5Cend%7Bgathered%7D)
Applying Completing the square method;
![\begin{gathered} x^2+y^2-2x+6y-6=0 \\ x^2-2x+1+y^2+6y+9=6+1+9 \\ (x-1)^2+(y+3)^2=16 \\ (x-1)^2+(y+3)^2=4^2 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2%2By%5E2-2x%2B6y-6%3D0%20%5C%5C%20x%5E2-2x%2B1%2By%5E2%2B6y%2B9%3D6%2B1%2B9%20%5C%5C%20%28x-1%29%5E2%2B%28y%2B3%29%5E2%3D16%20%5C%5C%20%28x-1%29%5E2%2B%28y%2B3%29%5E2%3D4%5E2%20%5Cend%7Bgathered%7D)
comparing the derived equation to the general form we have;
![\begin{gathered} h=1 \\ k=-3 \\ r=4 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20h%3D1%20%5C%5C%20k%3D-3%20%5C%5C%20r%3D4%20%5Cend%7Bgathered%7D)
Therefore;
The center of the circle is at;
![(1,-3)](https://tex.z-dn.net/?f=%281%2C-3%29)
The radius of the circle is;
The right answer is the first circle
Answer:
The correct answer is 8,Have a nice day!!!
Step-by-step explanation:
1 40 divided 5/4= 8
2 40 divided by 5 out of 4 = 8
you welcome
Answer:
6/3 as an Improper Fraction.
2 as a whole number.
Step-by-step explanation:
2/3 multiplied by 3 is as shown below.
2/3 + 2/3 + 2/3.
As an Improper Fraction, the sum would be expressed as:
2 + 2 + 2 = 6. 6/3
2/3 • 3 = 2, since 6/3 = 2 as well.
Answer: 48
Step-by-step explanation:
First, you multiply 75% by 64
Then, since 75% is 75 out of 100, you go ahead and multiply 75 by 64, then divide what you got by 100.
Now, you should have gotten 4800, so you divide 4800 by 100
So, your answer is 48