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3 years ago

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A movie theater is located on a map of a city represented by a coordinate plane. The location of the movie theater is at (−4, 2)

. Which map shows the correct location of the movie theater? (3 points)
Group of answer choices

1 answer:

Rom4ik [11]3 years ago

4 0

Answer:

A. 11/5

Step-by-step explanation:

48/40 = 1 8/40

1 8/40 Simplify to 1 1/5

Hope this helps!

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How many different ordered pairs satisfy both x^{2} + y^{2} = 100 and x^{2} + 2y^{2} = 108?

Dominik [7]

$\begin{cases}x^2+y^2=100\\x^2+2y^2=108\end{cases}\\\\\\
\begin{cases}x^2+y^2=100\\x^2+y^2+y^2=108\end{cases}\\\\\\100+y^2=108\\\\y^2=108-100\\\\y^2=8\qquad|\sqrt{(\ldots)}\\\\y=-\sqrt{8}\qquad\vee\qquad y=\sqrt{8}\\\\\boxed{y=-2\sqrt{2}\qquad\vee\qquad y=2\sqrt{2}}$

We know that $y^2=8$ so:

$x^2+y^2=100\\\\x^2+8=100\\\\x^2=100-8\\\\x^2=92\qquad|\sqrt{(\ldots)}\\\\
x=-\sqrt{92}\qquad\vee\qquad x=\sqrt{92}\\\\x=-\sqrt{4\cdot23}\qquad\vee\qquad x=\sqrt{4\cdot23}\\\\\boxed{x=-2\sqrt{23}\qquad\vee\qquad x=2\sqrt{23}}$

As we see there are 4 such pairs:

$x=-2\sqrt{23}\qquad y=-2\sqrt{2}\\\\x=2\sqrt{23}\qquad y=-2\sqrt{2}\\\\
x=-2\sqrt{23}\qquad y=2\sqrt{2}\\\\x=2\sqrt{23}\qquad y=2\sqrt{2}$

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m = (7-6)/(8-4)

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Choice C

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