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Fudgin [204]
3 years ago
7

Question:

Mathematics
1 answer:
aivan3 [116]3 years ago
4 0

Answer:

part A) The scale factor of the sides (small to large) is 1/2

part B) Te ratio of the areas (small to large) is 1/4

part C) see the explanation

Step-by-step explanation:

Part A) Determine the scale factor of the sides (small to large).

we know that

The dilation is a non rigid transformation that produce similar figures

If two figures are similar, then the ratio of its corresponding sides is proportional

so

Let

z ----> the scale factor

\frac{CB}{C'B'}=\frac{CD}{C'D'}=\frac{BD}{B'D'}

The scale factor is equal to

z=\frac{CB}{C'B'}

substitute

z=\frac{4}{8}

simplify

z=\frac{1}{2}

Part B) What is the ratio of the areas (small to large)?

<em>Area of the small triangle</em>

A=\frac{1}{2}(2)(4)=4\ units^2

<em>Area of the large triangle</em>

A=\frac{1}{2}(4)(8)=16\ units^2

ratio of the areas (small to large)

ratio=\frac{4}{16}=\frac{1}{4}

Part C) Write a generalization about the ratio of the sides and the ratio of the areas of similar figures

In similar figures the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In similar figures the ratio of its areas is equal to the scale factor squared

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Ivan
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Answer:

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Step-by-step explanation:

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Screenshot of the question attatched. please help me
Law Incorporation [45]
<h2>Rules of Exponents</h2>

There are many rules that apply to operations involving exponents. In this question, we'll need the following:

<h3>The division rule</h3>
  • ⇒ \dfrac{a^n}{a^m}=a^{n-m}

<h2>Solving the Question</h2>

We're given:

z^{21}\div z^7=z^k (solve for k.)

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<h2>Answer</h2>

<em>k</em> = 14

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