Answer:
It has to be the middle one. The 27...
Step-by-step explanation:
recall that the radius is the distance from the center of a circle to any point on the circle.
we know the center is at -16,-14, and we know that -8,-8 is a point on the circle, so the distance between both must be the radius.
![\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-16}~,~\stackrel{y_1}{-14})\qquad (\stackrel{x_2}{-8}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{[-8-(-16)]^2+[-8-(-14)]^2} \\\\\\ r=\sqrt{(-8+16)^2+(-8+14)^2}\implies r=\sqrt{8^2+6^2} \\\\\\ r=\sqrt{100}\implies \boxed{r=10} \\\\[-0.35em] \rule{34em}{0.25pt}](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%0A%5C%5C%5C%5C%0A%28%5Cstackrel%7Bx_1%7D%7B-16%7D~%2C~%5Cstackrel%7By_1%7D%7B-14%7D%29%5Cqquad%0A%28%5Cstackrel%7Bx_2%7D%7B-8%7D~%2C~%5Cstackrel%7By_2%7D%7B-8%7D%29%5Cqquad%20%5Cqquad%0Ad%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cstackrel%7Bradius%7D%7Br%7D%3D%5Csqrt%7B%5B-8-%28-16%29%5D%5E2%2B%5B-8-%28-14%29%5D%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ar%3D%5Csqrt%7B%28-8%2B16%29%5E2%2B%28-8%2B14%29%5E2%7D%5Cimplies%20r%3D%5Csqrt%7B8%5E2%2B6%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ar%3D%5Csqrt%7B100%7D%5Cimplies%20%5Cboxed%7Br%3D10%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D)
![\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-16}{ h},\stackrel{-14}{ k})\qquad \qquad radius=\stackrel{10}{ r} \\\\\\\ [x-(-16)]^2+[y-(-14)]^2=10^2\implies \blacktriangleright (x+16)^2+(y+14)^2=100 \blacktriangleleft](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bequation%20of%20a%20circle%7D%5C%5C%5C%5C%0A%28x-%20h%29%5E2%2B%28y-%20k%29%5E2%3D%20r%5E2%0A%5Cqquad%0Acenter~~%28%5Cstackrel%7B-16%7D%7B%20h%7D%2C%5Cstackrel%7B-14%7D%7B%20k%7D%29%5Cqquad%20%5Cqquad%0Aradius%3D%5Cstackrel%7B10%7D%7B%20r%7D%0A%5C%5C%5C%5C%5C%5C%5C%0A%5Bx-%28-16%29%5D%5E2%2B%5By-%28-14%29%5D%5E2%3D10%5E2%5Cimplies%20%5Cblacktriangleright%20%28x%2B16%29%5E2%2B%28y%2B14%29%5E2%3D100%20%5Cblacktriangleleft)
Prime factorization means to factor the composite number into only prime numbers.
So, 45=9x5=3x3x5...which are all prime.
So your answer is 3, 3, 5
Hi!
<h3>Expanded form is when we multiply each of the digits by how many 0s they have. </h3>
So 253 is (2 x 100) + (5 x 10) + (3 x 1).
17,000
400
9
(<u>17 x 10,000) + (4 x 100) + (9 x 1)</u>
<h2>The answer is C) (<u>17 x 10,000) + (4 x 100) + (9 x 1)</u> (which equals 17,409)</h2>
Hope this helps! :)
-Peredhel
