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3 years ago

The difference of three times a number and six is nine

Mathematics

2 answers:

Artyom0805 [142]3 years ago

6 0

Answer:

3x-6=9 is your equation x=5

Step-by-step explanation:

Step 1: Add 6 to both sides

Step 2: Divide both sides by 3

3241004551 [841]3 years ago

4 0

Answer:

n=5

Step-by-step explanation:

Write an equation

The difference of 3 times a number and six

Difference means subtract. Times means multiply. And means add.

So, 3 times a number, n minus 6

3n-6

Is nine

Is means equal

= 9

3n-6=9

Solve

3n-6=9

Add 6 to both sides

3n-6+6=9+6

3n=15

Divide both sides by 3

3n/3=15/3

n=5

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3 years ago

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Answer:

Step-by-step explanation:

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3 years ago

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3 years ago

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eduard

If you're using the app, try seeing this answer through your browser: brainly.com/question/2787701

_______________

$\mathsf{tan\,\theta=\dfrac{1}{4}\qquad\qquad(sin\,\theta\ \textgreater \ 0)}\\\\\\
\mathsf{\dfrac{sin\,\theta}{cos\,\theta}=\dfrac{1}{4}}\\\\\\
\mathsf{4\,sin\,\theta=cos\,\theta\qquad\quad(i)}$

Square both sides:

$\mathsf{(4\,sin\,\theta)^2=(cos\,\theta)^2}\\\\
\mathsf{4^2\,sin^2\,\theta=cos^2\,\theta}\\\\
\mathsf{16\,sin^2\,\theta=cos^2\,\theta\qquad\qquad(but,~cos^2\,\theta=1-sin^2\,\theta)}\\\\
\mathsf{16\,sin^2\,\theta=1-sin^2\,\theta}$

$\mathsf{16\,sin^2\,\theta+sin^2\,\theta=1}\\\\
\mathsf{17\,sin^2\,\theta=1}\\\\
\mathsf{sin^2\,\theta=\dfrac{1}{17}}\\\\\\
\mathsf{sin\,\theta=\pm\,\sqrt{\dfrac{1}{17}}}\\\\\\
\mathsf{sin\,\theta=\pm\,\dfrac{1}{\sqrt{17}}}$

Since $\mathsf{sin\,\theta}$ is positive, you can discard the negative sign. So,

$\mathsf{sin\,\theta=\dfrac{1}{\sqrt{17}}\qquad\quad\checkmark}$

Substitute this value back into $\mathsf{(i)}$ to find $\mathsf{cos\,\theta:}$

$\mathsf{4\cdot \dfrac{1}{\sqrt{17}}=cos\,\theta}\\\\\\
\mathsf{cos\,\theta=\dfrac{4}{\sqrt{17}}\qquad\quad\checkmark}$

I hope this helps. =)

Tags: trigonometric identity relation trig sine cosine tangent sin cos tan trigonometry precalculus

7 0

3 years ago