Answer:
All four
Step-by-step explanation:
SSS, SAS, ASA, and HL
You start by distributing: 8s-4=7s+12
Combine like terms: 8s-7s=12+4
Solve and get your answer: s=16
9514 1404 393
Answer:
{Segments, Geometric mean}
{PS and QS, RS}
{PS and PQ, PR}
{PQ and QS, QR}
Step-by-step explanation:
The three geometric mean relationships are derived from the similarity of the triangles the similarity proportions can be written 3 ways, each giving rise to one of the geometric mean relations.
short leg : long leg = SP/RS = RS/SQ ⇒ RS² = SP·SQ
short leg : hypotenuse = RP/PQ = PS/RP ⇒ RP² = PS·PQ
long leg : hypotenuse = RQ/QP = QS/RQ ⇒ RQ² = QS·QP
I find it easier to remember when I think of it as <em>the segment from R is equal to the geometric mean of the two segments the other end is connected to</em>.
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segments PS and QS, gm RS
segments PS and PQ, gm PR
segments PQ and QS, gm QR
The answer for this question is choice c. Memorization is not a good way to truly understand math. You want to understand the reasoning behind your answers always.
A math expert is what you should strive to be! The first two choices are great ways to become this.
well, first off let's check those two points, we know it's centerd at (-26 , 120) and we also know it passes through (0 , 0), so the distance between those two points is its radius
![~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{-26}~,~\stackrel{y_2}{120})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{radius}{r}=\sqrt{(~~-26 - 0~~)^2 + (~~120 - 0~~)^2} \implies r=\sqrt{(-26)^2 + (120 )^2} \\\\\\ r=\sqrt{( -26 )^2 + ( 120 )^2} \implies r=\sqrt{ 676 + 14400 } \implies r=\sqrt{ 15076 } \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=~~~~~~~~~~~~%5Ctextit%7Bdistance%20between%202%20points%7D%20%5C%5C%5C%5C%20%28%5Cstackrel%7Bx_1%7D%7B0%7D~%2C~%5Cstackrel%7By_1%7D%7B0%7D%29%5Cqquad%20%28%5Cstackrel%7Bx_2%7D%7B-26%7D~%2C~%5Cstackrel%7By_2%7D%7B120%7D%29%5Cqquad%20%5Cqquad%20d%20%3D%20%5Csqrt%7B%28%20x_2-%20x_1%29%5E2%20%2B%20%28%20y_2-%20y_1%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20%5Cstackrel%7Bradius%7D%7Br%7D%3D%5Csqrt%7B%28~~-26%20-%200~~%29%5E2%20%2B%20%28~~120%20-%200~~%29%5E2%7D%20%5Cimplies%20r%3D%5Csqrt%7B%28-26%29%5E2%20%2B%20%28120%20%29%5E2%7D%20%5C%5C%5C%5C%5C%5C%20r%3D%5Csqrt%7B%28%20-26%20%29%5E2%20%2B%20%28%20120%20%29%5E2%7D%20%5Cimplies%20r%3D%5Csqrt%7B%20676%20%2B%2014400%20%7D%20%5Cimplies%20r%3D%5Csqrt%7B%2015076%20%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \hspace{5em}\stackrel{center}{(\underset{-26}{h}~~,~~\underset{120}{k})}\qquad \stackrel{radius}{\underset{\sqrt{15076}}{r}} \\\\[-0.35em] ~\dotfill\\\\ ( ~~ x - (-26) ~~ )^2 ~~ + ~~ ( ~~ y-120 ~~ )^2~~ = ~~(\sqrt{15076})^2 \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (x+26)^2+(y-120)^2 = 15076~\hfill](https://tex.z-dn.net/?f=%5Ctextit%7Bequation%20of%20a%20circle%7D%5C%5C%5C%5C%20%28x-%20h%29%5E2%2B%28y-%20k%29%5E2%3D%20r%5E2%20%5Chspace%7B5em%7D%5Cstackrel%7Bcenter%7D%7B%28%5Cunderset%7B-26%7D%7Bh%7D~~%2C~~%5Cunderset%7B120%7D%7Bk%7D%29%7D%5Cqquad%20%5Cstackrel%7Bradius%7D%7B%5Cunderset%7B%5Csqrt%7B15076%7D%7D%7Br%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%28%20~~%20x%20-%20%28-26%29%20~~%20%29%5E2%20~~%20%2B%20~~%20%28%20~~%20y-120%20~~%20%29%5E2~~%20%3D%20~~%28%5Csqrt%7B15076%7D%29%5E2%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20~%5Chfill%20%28x%2B26%29%5E2%2B%28y-120%29%5E2%20%3D%2015076~%5Chfill)
