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3 years ago

Solve the inequality. Negative 3 x + 6 greater-than negative 2

Mathematics

1 answer:

slavikrds [6]3 years ago

7 0

Answer:

$x < 2 \frac{2}{3}$

Step-by-step explanation:

The symbol for greater than is '>'.

-3x +6 > -2

Bring constants to one side:

-3x > -6 -2

Simplify:

-3x > -8

Divide both sides by -1, change sign:

3x < 8

Divide by 3 on both sides:

$x < \frac{8}{3} \\ x < 2 \frac{2}{3}$

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In ∆XYZ, m∠X = 152, y = 15, and z = 19. Find side x and the measure of angle Y to the nearest tenth

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The measure of the side $x$ is approximately 33 and the measure of angle $Y$ is approximately 12.321°.

<h3>How to find a missing angle in a triangle by law of sine and law of cosine</h3>

In this problem we must apply the law of cosine and the law of sine to determine the angle Y:

<h3>Law of cosine</h3>

$x = \sqrt{y^{2}+z^{2}-2\cdot y\cdot z\cdot \cos X}$

$x = \sqrt{15^{2}+19^{2}-2\cdot (15)\cdot (19)\cdot \cos 152^{\circ}}$

$x \approx 33$

$\frac{\sin Y}{y} = \frac{\sin X}{x}$

$Y = \sin^{-1}\left(\frac{y}{x}\cdot \sin X \right)$

$Y = \sin^{-1}\left(\frac{15}{33}\cdot \sin 152^{\circ} \right)$

$Y \approx 12.321^{\circ}$

The measure of the side $x$ is approximately 33 and the measure of angle $Y$ is approximately 12.321°. $\blacksquare$

To learn more on triangles, we kindly invite to check this verified question: brainly.com/question/25813512

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