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Genrish500 [490]
3 years ago
8

Find the points of intersection of the graphs of the equations.

Mathematics
1 answer:
AURORKA [14]3 years ago
4 0

Answer:

To find the point of intersection, just solve for x and y in the equations

so since x - y = -5

x = y - 5

now that we have a value of x, we will substitute x with in in the other equation

<em>5x + 3y = -9</em>

<em>5(y-5) + 3y = -9</em>

<em>5y - 25 + 3y = -9</em>

<em>8y = 16 </em>

y = 2

now use this value of y in the equation we made for x

<em>x = y - 5</em>

<em>x = 2 - 5</em>

x = -3

Hence, the point of contact is (-3 , 2)

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Check the picture below.  so, that'd be the triangle's sides hmmm so let's use Heron's Area formula for it.

~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ (\stackrel{x_1}{10}~,~\stackrel{y_1}{5})\qquad (\stackrel{x_2}{15}~,~\stackrel{y_2}{15}) ~\hfill a=\sqrt{[ 15- 10]^2 + [ 15- 5]^2} \\\\\\ ~\hfill \boxed{a=\sqrt{125}} \\\\\\ (\stackrel{x_1}{15}~,~\stackrel{y_1}{15})\qquad (\stackrel{x_2}{30}~,~\stackrel{y_2}{9}) ~\hfill b=\sqrt{[ 30- 15]^2 + [ 9- 15]^2} \\\\\\ ~\hfill \boxed{b=\sqrt{261}}

(\stackrel{x_1}{30}~,~\stackrel{y_1}{9})\qquad (\stackrel{x_2}{10}~,~\stackrel{y_2}{5}) ~\hfill c=\sqrt{[ 10- 30]^2 + [ 5- 9]^2} \\\\\\ ~\hfill \boxed{c=\sqrt{416}} \\\\[-0.35em] ~\dotfill

\qquad \textit{Heron's area formula} \\\\ A=\sqrt{s(s-a)(s-b)(s-c)}\qquad \begin{cases} s=\frac{a+b+c}{2}\\[-0.5em] \hrulefill\\ a=\sqrt{125}\\ b=\sqrt{261}\\ c=\sqrt{416}\\ s\approx 23.87 \end{cases} \\\\\\ A\approx\sqrt{23.87(23.87-\sqrt{125})(23.87-\sqrt{261})(23.87-\sqrt{416})}\implies \boxed{A\approx 90}

6 0
2 years ago
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Hey there!
I think that it safe to say that this room is a rectangular prism. Therefore, the top and bottom (floor and ceiling) have the same area. We see that our floor dimensions are 12 cm long and 7 cm wide. This also applies to the ceiling. Let’s take our two sides and multiply then to find our area.

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Therefore, the area is 84 square centimeters.

I hope that this helps!
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