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3 years ago

Which best describes the solution set for the inequality below?

Mathematics

1 answer:

swat323 years ago

8 0

3x + 7 <_ 4x -8

Subtract 3x from both sides.

3x - 3x = 0x

4x - 3x = 1x (or just x)

7 <_ x -8

Add 8 to both sides.

7 + 8 = 15

-8 + 8 = 0

x _> 15 is the solution for the first inequality.

Although A.) is the only one with x_>15, let's continue to ensure our answer.

-2x + 3 _> 1

Subtract 3 from both sides.

3 - 3 = 0

1 - 3 = -2

-2x _> -2

Divide both sides by -2 to solve for x.

-2x / -2 = x

-2 / -2 = 1

Remember to flip the inequality when dividing or multiplying by a negative.

x <_ 1 is our other inequality.

Our answers are:

x_> 15 and x<_1

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Use the triangle below to find cos V.

Semenov [28]

Answer:

$cos\ V = \frac{2\sqrt{29}}{29}$

Step-by-step explanation:

Given

The attached triangle

Required

Find cos V

In trigonometry:

$cos\theta = \frac{Adjacent}{Hypotenuse}$

In this case:

$cos V= \frac{TV}{UV}$

Where

$TV = 6$

and

$UV^2 = TV^2 + TU^2$ -- Pythagoras

$UV^2 = 6^2 + 15^2$

$UV^2 = 261$

Take square roots

$UV = \sqrt{261$

$UV = \sqrt{9*29$

$UV = \sqrt{9} *\sqrt{29$

$UV = 3\sqrt{29$

So:

$cos V= \frac{TV}{UV}$

$cos\ V = \frac{6}{3\sqrt{29}}$

$cos\ V = \frac{2}{\sqrt{29}}$

Rationalize:

$cos\ V = \frac{2}{\sqrt{29}}*\frac{\sqrt{29}}{\sqrt{29}}$

$cos\ V = \frac{2\sqrt{29}}{29}$

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3 years ago

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jolli1 [7]

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The base of a rectangular prism is a square. The height of the prism is half the length of one edge of the base. The volume of t

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Answer:

The prism is 3 by 3 by 1.5.

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4 years ago