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nlexa [21]
3 years ago
8

Y-8= - * - 4 y=-* 4 (3,-5) no solution an infinite number of solutions

Mathematics
1 answer:
muminat3 years ago
3 0

Given:

The system of equation is

y-8=-\dfrac{1}{3}x-4

y=-\dfrac{1}{3}x-4

To find:

The solution of given system of equations.

Solution:

The slope intercept form of a line is

y=mx+b

Where, m is slope and b is y-intercept.

Write the given equation in slope intercept form.

The first equation is

y-8=-\dfrac{1}{3}x-4

y=-\dfrac{1}{3}x-4+8

y=-\dfrac{1}{3}x+4              ...(i)

Here, slope is -\dfrac{1}{3} and y-intercept is 4.

The second equation is

y=-\dfrac{1}{3}x-4              ...(i)

Here, slope is -\dfrac{1}{3} and y-intercept is -4.

Since the slopes of both lines are same but the y-intercepts are different, therefore the given equations represent parallel lines.

Parallel lines never intersect each other. So, the given system of equation has no solution.

Hence, the correct option is B.

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Find the area of the shaded region ​
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so hmmm let's get the area of the whole hexagon, and then get the area of the circle inside it, then <u>subtract the area of the circle from that of the hexagon's</u>, what's leftover is what we didn't subtract, namely the shaded part.

\textit{area of a regular polygon}\\\\ A=\cfrac{1}{4}ns^2\cot\stackrel{\stackrel{degrees}{\downarrow }}{\left( \frac{180}{n} \right)}~ \begin{cases} n=\textit{number of sides}\\ s=\textit{length of a side}\\[-0.5em] \hrulefill\\ n=\stackrel{hexagon}{6}\\ s=\frac{9}{2} \end{cases}\implies A=\cfrac{1}{4}(6)\left( \cfrac{9}{2} \right)^2 \cot\left( \cfrac{180}{6} \right)

A=\cfrac{1}{4}(6)\cfrac{9^2}{2^2} \cot(30^o)\implies A=\cfrac{243}{8}\cot(30^o)\implies A=\cfrac{243\sqrt{3}}{8} \\\\[-0.35em] ~\dotfill\\\\ \textit{area of circle}\\\\ A=\pi r^2~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=\frac{4}{5} \end{cases}\implies A=\pi \left( \cfrac{4}{5} \right)^2\implies A=\cfrac{16\pi }{25} \\\\[-0.35em] ~\dotfill

\stackrel{\textit{area of the hexagon}}{\cfrac{243\sqrt{3}}{8}}~~ - ~~\stackrel{\textit{area of the circle}}{\cfrac{16\pi }{25}}\implies \cfrac{6075\sqrt{3}-128\pi }{200}

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2 years ago
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