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3 years ago

The mean of the data set is 10. What is the 5th number in the data set? 12,9,8,13,?

1 answer:

8 0

What number divided by five is ten? 50.
If you add together 12, 9,8, and 13 you will get 42. The fifth number is 8 because 42+8= 50

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Find the length of WY

DENIUS [597]

Answer:

WY = 180

Step-by-step explanation:

the diagonals of an isosceles trapezoid are congruent , so

ZX = WY , that is

8y - 4 = 7y + 19 ( subtract 7y from both sides )

y - 4 = 19 ( add 4 to both sides )

y = 23

Then

WY = 7y + 19 = 7(23) + 19 = 161 + 19 = 180

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Step-by-step explanation:

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True or false. Tan^2 x = 1 - cos2x/ 1 + cos 2x

koban [17]

<u>ANSWER</u>

True

<u>EXPLANATION</u>

The given trigonometric equation is

$\tan^{2} (x) = \frac{1 - \cos(2x) }{1 + \cos(2x) }$

Recall the double angle identity:

$\cos(2x) = \cos^{2} x - \sin^{2}x$

We apply this identity to obtain:

$\tan^{2} (x) = \frac{1 - (\cos^{2} x - \sin^{2}x) }{1 + (\cos^{2} x - \sin^{2}x) }$

We maintain the LHS and simplify the RHS to see whether they are equal.

Expand the parenthesis

$\tan^{2} (x) = \frac{1 - \cos^{2} x + \sin^{2}x }{1 + \cos^{2} x - \sin^{2}x}$

$\implies\tan^{2} (x) = \frac{1 - \cos^{2} x + \sin^{2}x }{1 - \sin^{2}x + \cos^{2} x }$

Recall that:

$1 - \sin^{2}x = \cos^{2}x$

$1 - \cos^{2}x = \sin^{2}x$

We apply these identities to get:

$\implies\tan^{2} (x) = \frac{\sin^{2}x + \sin^{2}x }{\cos^{2} x + \cos^{2} x }$

$\implies\tan^{2} (x) = \frac{2\sin^{2}x }{ 2\cos^{2} x }$

$\implies\tan^{2} (x) = \frac{\sin^{2}x }{ \cos^{2} x }$

$\implies \tan^{2} (x) =( \frac{\sin x }{ \cos x })^{2}$

Also

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

$\implies \tan^{2} (x) =( \tan x )^{2}$

$\implies \tan^{2} (x) =\tan^{2} (x)$

Therefore the correct answer is True

5 0

3 years ago