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Aleksandr [31]
3 years ago
13

Children 4 years old or younger can ride the train for free. Write an inequality that expresses who can ride the train for free.

Mathematics
1 answer:
viktelen [127]3 years ago
3 0

x<=4

x is less than or equal to four

children less than or equal to four can ride the train for free

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44 %

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What is the product? 8(–1) A. –1.4 B. –8 C. 8 D. 11.2
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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}

3 0
3 years ago
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