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3 years ago

Find the value of x for which r || S. A) 44 B) 10 C) Can't be determined. D) 14

Mathematics

2 answers:

nlexa [21]3 years ago

5 0

The answer is A because 10 and 14 don’t fit the question at all.

Elodia [21]3 years ago

4 0

Answer:

x=44

Step-by-step explanation:

For the two lines to be parallel, the two angles have to add to 180 degrees

45+3x+3 =180

Combine like terms

3x+48 = 180

Subtract 48 from each side

3x+48-48=180-48

3x=132

Divide each side by 3

3x/3 = 132/3

x =44

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3 years ago

In the pulley system shown in this figure, MQ = 30 mm, NP = 10 mm, and QP = 21 mm. Find MN.

ankoles [38]

<h2>Answer:</h2>

$\boxed{\overline{MN}=37.96}$

<h2>Step-by-step explanation:</h2>

For a better understanding of this problem, see the figure below. Our goal is to find $\overline{MN}$ . Since:

$\angle MRS=\angle MQP=90^{\circ} \\ \\ \overline{MQ}=\overline{MR}=30mm$

and $\overline{MN}$ is a common side both for ΔMRN and ΔMQN, then by SAS postulate, these two triangles are congruent and:

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By Pythagorean theorem, for triangle NQP:

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Applying Pythagorean theorem again, but for triangle MQN:

$\overline{MN}=\sqrt{\overline{MQ}^2+\overline{QN}^2} \\ \\ \overline{MN}=\sqrt{30^2+(\sqrt{541})^2} \\ \\ \boxed{\overline{MN}=37.96}$

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