3/4 of a number minus -16 equals 28. What is the number ?

Mathematics

1 answer:

Zigmanuir [339]3 years ago

6 0

Answer:

The number is 16

Step-by-step explanation:

3/4 n- (-16) = 28

3/4 n + 16 = 28

Subtract 16 from each side

3/4 n +16-16 = 28-16

3/4 n =12

Multiply by 4/3 to isolate n

4/3 * 3/4 n = 12 * 4/3

n = 16

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Given sin(−θ)=−1/6 and tanθ=−√35/35 What is the value of cosθ?

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Answer:

$cos(\theta)=-\frac{\sqrt{35} }{6}$

Step-by-step explanation:

Recall the negative angle identity for the sine function:

$sin(- \theta)=-sin(\theta)$

Then, we can find the value of $sin(\theta)$ :

$sin(\theta)=-sin(-\theta)\\sin(\theta) =-(-\frac{1}{6} )\\sin(\theta)= \frac{1}{6}$

Now recall the definition of the tangent function:

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}$

Therefore, now that we know the value of $sin(\theta)$ , we can solve in this equation for $cos(\theta)$

$tan(\theta)=\frac{sin(\theta)}{cos(\theta)}\\-\frac{\sqrt{35} }{35} =\frac{1/6}{cos(\theta)} \\cos(\theta)=-\frac{\frac{1}{6} }{\frac{\sqrt{35} }{35} } \\cos(\theta)=-\frac{35}{6\,\sqrt{35} } \\cos(\theta)=-\frac{\sqrt{35} }{6}$