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)
Answer:
90percent to my money can be gone by today ortommorow
The result of the log function
is 60
According to the law of logarithm if
then ![b=a^y](https://tex.z-dn.net/?f=b%3Da%5Ey)
Given the following expressions
![log_am=10\\log_an=25](https://tex.z-dn.net/?f=log_am%3D10%5C%5Clog_an%3D25)
This can be expressed as
![m =a^{10} \ and \ n = a^{25}](https://tex.z-dn.net/?f=m%20%3Da%5E%7B10%7D%20%5C%20and%20%5C%20n%20%3D%20a%5E%7B25%7D)
Substitute the value of m and n into the expression
to have:
![log_a (m * n ^ 2) = log_a(a^{10}\times a^{50})\\=log_aa^{60}\\=60log_aa\\=60(1) \\= 60](https://tex.z-dn.net/?f=log_a%20%28m%20%2A%20n%20%5E%202%29%20%3D%20log_a%28a%5E%7B10%7D%5Ctimes%20a%5E%7B50%7D%29%5C%5C%3Dlog_aa%5E%7B60%7D%5C%5C%3D60log_aa%5C%5C%3D60%281%29%20%5C%5C%3D%2060)
This shows that the result of the log function
is 60
Learn more here: brainly.com/question/12049968
You must multiply first the first two terms and then, once you have that result, you mutliply what you've got times the other number (14). Then you'll get the final result :)
Answer: 7 wholes and 63/81
Answer:
ohhhhhhhh
Step-by-step explanation:
weird flex but ok