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3 years ago

{3} is a subset of {1, 2, 4, 5, 6} ?

1 answer:

5 0

No, a set is only a subset of another set if it only contains elements contained in the original set.
3 isn't an element of {1,2,4,5,6}, so {3} isn't a subset of {1,2,4,5,6}.

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11 divided by 1/3 (fraction form)

Montano1993 [528]

11 / 1/3
11 * 3/1
33/1

Fraction Form: 33/1
Simplified Form: 33

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3 years ago

Read 2 more answers

Solve each system by elimination.

max2010maxim [7]

Answer:

Step-by-step explanation:

-x-2y+4z=-14

x=-2y+4z+14

2x+2y+2z=-6

2x=-2y-2z-6

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x=3-6z

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3 years ago

What is the surface area of the triangular prism whose net is shown below?

densk [106]

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3 years ago

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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:

$\overline{RN}=\overline{QN}$

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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3 years ago