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3 years ago

Absolute value equation|3x] = 9

Mathematics

1 answer:

avanturin [10]3 years ago

7 0

Answer:

Step-by-step explanation:

3x = 9

9 ÷ 3 = 3

3x ÷ 3 = x

x = 3

|3| = 3

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In the right triangle shown, \angle B = 60^\circ∠B=60

Liono4ka [1.6K]

Answer:

Part 1) $AC=6\sqrt{3}\ units$

Part 2) $AC=12\sqrt{3}\ units$

Step-by-step explanation:

I will analyze two problems

see the attached figure to better understand the problem

Problem 1

The hypotenuse is the segment AB and the right angle is C

we know that

In the right triangle ABC

$sin(B)=\frac{AC}{AB}$ ---> by SOH (opposite side divided by the hypotenuse)

substitute the given values

$sin(60^o)=\frac{AC}{12}$

Remember that

$sin(60^o)=\frac{\sqrt{3}}{2}$

substitute

$\frac{\sqrt{3}}{2}=\frac{AC}{12}$

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Problem 2

The hypotenuse is the segment BC and the right angle is A

we know that

In the right triangle ABC

$tan(B)=\frac{AC}{AB}$ ---> by TOA (opposite side divided by the adjacent side)

substitute the given values

$tan(60^o)=\frac{AC}{12}$

Remember that

$tan(60^o)=\sqrt{3}$

substitute

$\sqrt{3}=\frac{AC}{12}$

$AC=12\sqrt{3}\ units$

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Absolute value equation|3x] = 9​

Absolute value equation|3x] = 9