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3 years ago

What is the solution of this equation 4(x-8)+10=-10

Mathematics

2 answers:

Maru [420]3 years ago

6 0

-10 to other side
4(x-8) = -20
divide 4
x-8 = -5
plus 8
x=3

Rom4ik [11]3 years ago

5 0

Start by subtracting 10 from both sides.

This gives us 4x - 32 = -20.

Now add 32 to both sides to get 4x = 12.

Now divide both sides by 3 to get <em>x = 3</em>.

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Read 2 more answers

If the terminal ray of β lies in the third quadrant and the value of sin(β) is shown below. Determine cos(β) in the simplest for

Brut [27]

Answer:

$cos \beta = -\sqrt\dfrac{2}{3}$

Step-by-step explanation:

It is given that $\angle \beta$ lies in the third quadrant.

In 3rd quadrant, sine and cosine both are negative.

Also given that:

$sin \beta =-\dfrac{\sqrt3}{3}$

We know that identity between sine and cosine as:

$sin^2\theta + cos^2\theta = 1$

Here, $\angle \theta\ is\ \angle \beta$

Therefore, the identity can be written as:

$sin^2\beta + cos^2\beta= 1$

Putting the value of $sin\beta$ :

$(-\dfrac{\sqrt3}{3})^2+ cos^2\beta= 1\\\Rightarrow cos^2\beta = 1 -\dfrac{3}{9}\\\Rightarrow cos^2\beta = \dfrac{9-3}{9}\\\Rightarrow cos^2\beta = \dfrac{6}{9}\\\Rightarrow cos\beta = \pm \sqrt{\dfrac{6}{9}}\\\Rightarrow cos\beta = \pm \sqrt{\dfrac{2}{3}}$

But, it is given that $\beta$ is in <em>3rd quadrant</em>. That means, value of cos $\beta$ will be <em>negative</em>.

Therefore, the correct answer is:

$cos \beta = -\sqrt\dfrac{2}{3}$

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3 years ago