I think it should be C but let me know if im wrong plz
6 x 60 x 5 would be the equation and all of that put together would be 1,800 vehicles would pass by in an hour.
Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.
Step-by-step explanation:
The equation of a circle in the center-radius form is:
(1)
Where
are the coordinates of the center and
is the radius.
Now, we are given the equation of this circle as follows:
(2)
And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:
(3)
Rearranging the equation:
(4)
(5)
Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of
:
<u>For the first parenthesis:</u>
![x^{2}+6x+b^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B6x%2Bb%5E%7B2%7D)
We can rewrite this as:
![x^{2}+2(3)x+b^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B2%283%29x%2Bb%5E%7B2%7D)
Hence in this case
and
:
![x^{2}+2(3)x+3^{2}=x^{2}+6x+9=(x+3)^{2}](https://tex.z-dn.net/?f=x%5E%7B2%7D%2B2%283%29x%2B3%5E%7B2%7D%3Dx%5E%7B2%7D%2B6x%2B9%3D%28x%2B3%29%5E%7B2%7D)
<u>For the second parenthesis:</u>
![y^{2}-8y+b^{2}](https://tex.z-dn.net/?f=y%5E%7B2%7D-8y%2Bb%5E%7B2%7D)
We can rewrite this as:
![y^{2}-2(4)y+b^{2}](https://tex.z-dn.net/?f=y%5E%7B2%7D-2%284%29y%2Bb%5E%7B2%7D)
Hence in this case
and
:
![y^{2}-2(4)y+4^{2}=y^{2}-8y+16=(y-4)^{2}](https://tex.z-dn.net/?f=y%5E%7B2%7D-2%284%29y%2B4%5E%7B2%7D%3Dy%5E%7B2%7D-8y%2B16%3D%28y-4%29%5E%7B2%7D)
Then, equation (5) is rewritten as follows:
(6)
<u>Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.</u>
Rearranging:
(7)
At this point we have the circle equation in the center radius form ![(x-h)^{2} +(y-k)^{2}=r^{2}](https://tex.z-dn.net/?f=%28x-h%29%5E%7B2%7D%20%2B%28y-k%29%5E%7B2%7D%3Dr%5E%7B2%7D)
Hence:
![h=-3](https://tex.z-dn.net/?f=h%3D-3)
![k=4](https://tex.z-dn.net/?f=k%3D4)
![r=\sqrt{100}=10](https://tex.z-dn.net/?f=r%3D%5Csqrt%7B100%7D%3D10)
Anna has 100 quarters and jazmin has 100 dimes 100 dimes are equal to 10.00 and 100 quarters are equal to 25.00 Anna has more