Eight less than a number is six more than twice the same number. I need the number.

1 answer:

6 0

The answer is -14

Explanation:

x - 8 = 2x + 6

We move all term to the left

x - 8 - ( 2x + 6 ) = 0

We get rid of parentheses

x - 2x - 6 - 8 = 0

We add all the numbers together, and all the variables

-1x - 14 = 0

We move all terms containing x to the left, all other term to the right

-x = 14
x = 14/-1
x = -14

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Given that cos(theta) = 8/17 and that theta lies in Quadrant IV, what is the exact value of sin 2(theta)?

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Answer: $-\frac{240}{289}$

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Explanation:

Use the pythagorean trig identity $\sin^2(\theta)+\cos^2(\theta) = 1$ and plug in the fact that $\cos(\theta) = \frac{8}{17}\\\\$

Isolating sine leads to $\sin(\theta) = -\frac{15}{17}\\\\$ . I'm skipping the steps here, but let me know if you need to see them.

The result is negative because we're in quadrant 4, when y < 0 so it's when sine is negative.

Therefore,

$\sin(2\theta) = 2\sin(\theta)\cos(\theta)\\\\\sin(2\theta) = 2*\left(-\frac{15}{17}\right)*\left(\frac{8}{17}\right)\\\\\sin(2\theta) = -\frac{240}{289}\\\\$

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Which expressions are equivalent to the one below? Check all that apply. 53 • 5x

weeeeeb [17]

Calculate 3 x 5, which is 15.Since 15 is two-digit, we carry the first digit 1 to the next column.

Calculate 5 x 5, which is 25. Now add the carry digit of 1, which is 26.Since 26 is two-digit, we carry the first digit 2 to the next column.

Bring down the carry digit of 2.

Therefore, 53 x 5 = 265.