It’s c. 55
Message me if you want to know why
Answer:
(x - 2)² + (y - 9)² = 9
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
The radius is the distance from the centre to a point on the circle.
Calculate r using the distance formula
r = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (2, 9) and (x₂, y₂ ) = (2, 6)
r = ![\sqrt{(2-2)^2+(6-9)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B%282-2%29%5E2%2B%286-9%29%5E2%7D)
= ![\sqrt{0^2+(-3)^2}](https://tex.z-dn.net/?f=%5Csqrt%7B0%5E2%2B%28-3%29%5E2%7D)
=
=
= 3
Centre = (h, k) = (2, 9) and r = 3, thus equation of circle is
(x - 2)² + (y - 9)² = 9
13. An exponent in the form of
![a^{\frac{2}{3}}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D)
is equivalent in saying
![\sqrt[3]{a^{2}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7Ba%5E%7B2%7D%7D)
So, we can apply that to our fraction:
![(\frac{64m^{6}}{27n^{9}})^{\frac{2}{3}} = \sqrt[3]{(\frac{64m^{6}}{27n^{9}})^{2}}](https://tex.z-dn.net/?f=%28%5Cfrac%7B64m%5E%7B6%7D%7D%7B27n%5E%7B9%7D%7D%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B%28%5Cfrac%7B64m%5E%7B6%7D%7D%7B27n%5E%7B9%7D%7D%29%5E%7B2%7D%7D)
![=\sqrt[3]{\frac{4096m^{12}}{729n^{18}}}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B4096m%5E%7B12%7D%7D%7B729n%5E%7B18%7D%7D%7D)
![=\frac{16m^{4}}{9n^{6}}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B16m%5E%7B4%7D%7D%7B9n%5E%7B6%7D%7D%7D)
14. Using the properties from the previous question, you should be able to complete this question. If you're having troubles, let me know and I'll walk you through it.
17. (x^2-x+3)(4x+1)
18.(x+2)(x) - (7)(3)