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4 years ago

If &A and B are a linear pair and m&A = 2x + 8 and m&B = 3x + 2, what is the

Mathematics

1 answer:

Alinara [238K]4 years ago

3 0

Answer:

34;

Step-by-step explanation:

1. m<A = 2x + 8 (given)

m<B = 3x + 2 (given)

Since <A and <B are a linear pair, therefore:

m<A + m<B = 180° (angles in a linear pair add up to 180°)

(2x + 8) + (3x + 2) = 180 (substitution)

Solve for x

2x + 8 + 3x + 2 = 180

Collect like terms

5x + 10 = 180

Subtract 10 from each side of the equation

5x = 180 - 10

5x = 170

Divide both sides by 5

x = 34

2. m<A = 7x - 5 (given)

m<B = 4x + 10 (given),

Since m<A and m<B are vertical angles, therefore:

m<A = m<B (vertical angles are congruent)

7x - 5 = 4x + 10 (substitution)

Subtract 4x from both sides

7x - 5 - 4x = 4x + 10 - 4x

3x - 5 = 10

Add 5 to both sides

3x - 5 + 5 = 10 + 5

3x = 15

Divide both sides by 3

3x/3 = 15/3

x = 5

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Alternative hypothesis : $H_a: p>0.5$

Since $H_a$ is right-tailed , so the hypothesis test is a right-tailed z-test.

Also, it is given that , the sample size : n= 291

Sample proportion: $\hat{p}=\dfrac{239}{291}\approx0.82$

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