The cost of a jacket increased from $85.00 to $94.35. What is the percentage increase of the cost of the jacket?

1 answer:

8 0

It's an 11% increase. To find this, you have to subtract 85 from 94.35 and then you divide that difference by the original amount. In this case it's 85. After that, you get .11. Then you just turn it into a percent.

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The diameter of a circle has endpoints (-10,5) and (-4,11)

Marta_Voda [28]

well, since we know the endpoints for the diameter, its midpoint will be where the center of the circle is located, so

$~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{-10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{11}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left(\cfrac{ -4 -10}{2}~~~ ,~~~ \cfrac{ 11 + 5}{2} \right)\implies \left(\cfrac{-14}{2}~~,~~\cfrac{16}{2} \right)\implies \stackrel{center}{(-7~~,~~8)}$

and if we get the distance between those endpoints, and take half of that, that'd be the radius of it.

$~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{-4}~,~\stackrel{y_2}{11})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{[-4 - (-10)]^2 + [11 - 5]^2}\implies d=\sqrt{(-4+10)^2+6^2} \\\\\\ d=\sqrt{6^2+6^2}\implies d=\sqrt{72}~\hfill \stackrel{radius=half~that}{\cfrac{\sqrt{72}}{2}} \\\\[-0.35em] ~\dotfill$

$\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-7}{ h},\stackrel{8}{ k})\qquad \qquad radius=\stackrel{\frac{\sqrt{72}}{2}}{ r} \\\\\\\ [x-(-7)]^2~~ + ~~[y-8]^2~~ = ~~\left( \frac{\sqrt{72}}{2} \right)^2\implies (x+7)^2~~ + ~~(y-8)^2~~ = ~~18$