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2 years ago

From the following figure, how can you conclude that lines l and m are parallel?

Mathematics

2 answers:

loris [4]2 years ago

4 0

C. Alternate interior angles theorem

The angles labeled are on the inside of lines l and m and they are also on alternate sides of the unnamed line

:)))

lianna [129]2 years ago

4 0

Answer:

C) Alternate interior angles theorem.

Step-by-step explanation:

Given : Figure with two line l and m ans alternates interior angle 70°

To find : how can you conclude that lines l and m are parallel.

Solution : We have given that two line l and m ans alternates interior angle 70°.

Two angle are alternate and interior to the line l and m .

Hence they are congruent to each other .

By the alternates interior angle theorem : if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Therefore, C) Alternate interior angles theorem.

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Answer:

Bill launched a model rocket, and estimated its height h, In feet, after 1 seconds. His results are shown in the table

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Height, h 0 110 190 240 255

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A 150 ft

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2 years ago

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Answer:

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Step-by-step explanation:

Let's start assuming that men and women come in at the same rate.

Let's define the following random variables :

X : ''Number of people that enter a drugstore''

M : ''Number of men that enter a drugstore''

W : ''Number of women that enter a drugstore''

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⇒

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We are also assuming that M and W are independent random variables.

X ~ Po (10)

M ~ Po (λ1)

W ~ Po (λ2)

λ1 = λ2 because we assumed that men and women come in at the same rate.

λ1 = λ2 = λ

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W ~ Po (5)

Because X is the sum of two independent Poisson random variables.

We are looking for :

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Because we assume independence.

$P(M\leq 3)= P(M=0)+P(M=1)+P(M=2)+P(M=3)$

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$P(M\leq 3)=\frac{5^{0}}{0!}e^{-5}+\frac{5^{1}}{1!}e^{-5}+\frac{5^{2}}{2!}e^{-5}}+\frac{5^{3}}{3!}e^{-5}$

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$P(M\leq 3)=0.2650$

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2 years ago

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

see the attached figure to better understand the problem

we know that

∠QSR≅∠XZY ---> given problem

∠QRS≅∠XYZ ---> given problem

△QRS ~ △XYZ ----> by AA Similarity theorem

Remember that, if two triangles are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

That means

$\frac{QS}{XZ}=\frac{QR}{XY}=\frac{RS}{YZ}$

∠Q≅∠X

∠R≅∠Y

∠S≅∠Z

<em>In the right triangle XYZ</em>

Find the tangent of angle X

$tan(X)=\frac{YZ}{XZ}$ ---> opposite side angle X divided by adjacent side angle X

substitute the given values

$tan(X)=\frac{9}{12}$

Simplify

$tan(X)=\frac{3}{4}$

Remember that

∠Q≅∠X

$tan(Q)=tan(X)$

therefore

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2 years ago

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