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2 years ago

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Prove that the two circles shown below are similar. (10 points) Circle B Has A Center Of (-1, 5) And A Radius Of 4. Circle D Has

A Center Of (7, 4) And A Radius Of 2.
PLEASE HELP ASAP!

1 answer:

nexus9112 [7]2 years ago

8 0

All circles are similar shapes.

However, we can prove that these circles are similar by finding their radius-circumference ratios.

<h2>Circle B</h2>

Radius:

4 units

Circumference:

$C=2\pi r\\C=2\pi (4)\\C=8\pi$

Radius/circumference ratio:

$\dfrac{4}{8\pi}\\\\\dfrac{1}{2\pi}$

<h2>Circle D</h2>

Radius:

2 units

Circumference:

$C=2\pi r\\C=2\pi (2)\\C=4\pi$

Radius/circumference ratio:

$\dfrac{2}{4\pi}\\\\\dfrac{1}{2\pi}$

The radius/circumference ratio for both the circles is $\dfrac{1}{2\pi}$ , thus making the two circles similar.

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Answer:

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}=-12$

Step-by-step explanation:

Considering the expression

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}$

Solution Steps:

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}$

as

$\mathrm{Combine\:the\:fractions\:}\frac{1}{5}-\frac{3}{5}:\quad -\frac{2}{5}$

so

$=\frac{\frac{4}{5}}{\frac{1}{3}-\frac{2}{5}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{\frac{b}{c}}{a}=\frac{b}{c\:\cdot \:a}$

$=\frac{4}{5\left(\frac{1}{3}-\frac{2}{5}\right)}$

join $\frac{1}{3}-\frac{2}{5}:\quad -\frac{1}{15}$

so

$=\frac{4}{5\left(-\frac{1}{15}\right)}$

$\mathrm{Remove\:parentheses}:\quad \left(-a\right)=-a$

$=\frac{4}{-5\cdot \frac{1}{15}}$

$\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{a}{-b}=-\frac{a}{b}$

$=-\frac{4}{5\cdot \frac{1}{15}}$

$\mathrm{Multiply\:}5\cdot \frac{1}{15}\::\quad \frac{1}{3}$

so

$=-\frac{4}{\frac{1}{3}}$

$\mathrm{Simplify}\:\frac{4}{\frac{1}{3}}:\quad \frac{12}{1}$

so

$=-\frac{12}{1}$

$\mathrm{Apply\:rule}\:\frac{a}{1}=a$

$=-12$

Therefore

$\frac{\frac{4}{5}}{\frac{1}{3}+\frac{1}{5}-\frac{3}{5}}=-12$

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Given :

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The Length and width of the rectangle .

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Solution :

We know that,

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Let's assume the length of the rectangle as 3x inches. and the width is 2x inches.

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Now, Substituting the given values in the formula :

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$\qquad { \pmb{ \bf{ Width _{(rectangle)} = 2x = 2(5) = 10 \: inches}}}\:$

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