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aalyn [17]
3 years ago
6

How to write a linear equation for this problem

Mathematics
1 answer:
Minchanka [31]3 years ago
6 0
I just found out my answer was 40.3 idk if that it just check it
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find the equation of the circle where (-9,4),(-2,5),(-8,-3),(-1,-2) are the vertices of an inscribed square.
solniwko [45]
Check the picture below, so, that'd be the square inscribed in the circle.

so... hmm the diagonals for the square are the diameter of the circle, and keep in mind that the radius of a circle is half the diameter, so let's find the diameter.

\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -2}}\quad ,&{{ 5}})\quad 
%  (c,d)
&({{ -8}}\quad ,&{{ -3}})
\end{array}\qquad 
%  distance value
d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}
\\\\\\
\stackrel{diameter}{d}=\sqrt{[-8-(-2)]^2+[-3-5]^2}
\\\\\\
d=\sqrt{(-8+2)^2+(-3-5)^2}\implies d=\sqrt{(-6)^2+(-8)^2}
\\\\\\
d=\sqrt{36+64}\implies d=\sqrt{100}\implies d=10

that means the radius r = 5.

now, what's the center?  well, the Midpoint of the diagonals, is really the center of the circle, let's check,

\bf \textit{middle point of 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
%  (a,b)
&({{ -2}}\quad ,&{{ 5}})\quad 
%  (c,d)
&({{ -8}}\quad ,&{{ -3}})
\end{array}\qquad 
\left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right)
\\\\\\
\left( \cfrac{-8-2}{2}~,~\cfrac{-3+5}{2} \right)\implies (-5~,~1)

so, now we know the center coordinates and the radius, let's plug them in,

\bf \textit{equation of a circle}\\\\ 
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad 
\begin{array}{lllll}
center\ (&{{ h}},&{{ k}})\qquad 
radius=&{{ r}}\\
&-5&1&5
\end{array}
\\\\\\\
[x-(-5)]^2-[y-1]^2=5^2\implies (x+5)^2-(y-1)^2=25

8 0
3 years ago
Kevin drove 693 miles in 11 hours. At the same rate, how many miles would he drive in 9 hours
rodikova [14]

Answer:

567 Miles

Step-by-step explanation:

5 0
3 years ago
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Suppose an oligopoly consists of two firms. Firm A lowers price and Firm B responds by lowering its price by the same amount. If
VMariaS [17]

Answer:

The profits for firma A and B will decrease.

Step-by-step explanation:

Oligopoly by definition "is a market structure with a small number of firms, none of which can keep the others from having significant influence. The concentration ratio measures the market share of the largest firms".

If the costs remain the same for both companies and both firms decrease the prices then we will have a decrease of profits, we can see this on the figure attached.

We have an equilibrium price (let's assume X) and when we decrease a price and we have the same level of output the area below the curve would be lower and then we will have less profits for both companies.

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3 years ago
What is the measure of angle DEG on circle O? Please help! 50 points!
SIZIF [17.4K]

Answer:

50 degrees

Step-by-step explanation:

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Look at Jerry's monthly budget below. What percentage of Jerry's net income is spent on food?
Mila [183]
450/2,970*100
450*10/297=15.2
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3 years ago
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