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joja [24]
2 years ago
9

What is the slope of the line shown?

Mathematics
1 answer:
Sever21 [200]2 years ago
5 0

Answer:

Slope = -3

Step-by-step explanation:

<u>Slope formula:</u>

\frac{y2}{x2}  -  \frac{y1}{x1}  = m

m = slope.

<u>Substitute the </u><u>point</u><u> </u><u>values</u><u> </u><u>given</u><u> </u><u>into the formula</u><u>:</u>

\frac{2}{2}  -  \frac{8}{0}  = ?

<u>Solve:</u>

\frac{2}{2}  -  \frac{8}{0}  =  \frac{ - 6}{2}  =  - 3

The slope of your line is -3.

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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:

\overline{RN}=\overline{QN}

By Pythagorean theorem, for triangle NQP:

\overline{QN}=\sqrt{\overline{NP}^2+\overline{QP}^2} \\ \\ \overline{QN}=\sqrt{10^2+21^2} \\ \\ \overline{QN}=\sqrt{541}

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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