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3 years ago

14

-6(x+6)-10=-2(5+4x)

1 answer:

dimaraw [331]3 years ago

3 0

Assuming you need to solve for x:

-6(x + 6) - 10 = -2(5 + 4x)

start by distributing your numbers outside the front of your parentheses:

-6x - 36 - 10 = -10 - 8x

then combine like terms:

-6x - 46 = -10 - 8x ... add 10 to both sides (which technically could have cancelled out in the step prior, but regardless)
-6x - 36 = -8x ... add 6x to both sides
-36 = -2x ... divide both sides by -2
x = 18

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Find the missing side lengths. Leave your answers as radicals in simplest form.

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Answer:

A.

$x = \frac{7\sqrt{6}{3}$

$y = \frac{7\sqrt{6}}{3}$

Step-by-step explanation:

Reference angle = 60°

Opposite = $\frac{7\sqrt{2}}{2}$

Hypotenuse = x

Adjacent = y

✔️To find x, apply the trigonometric function SOH:

Sin 60° = Opp/Hyp

$sin 60° = \frac{\frac{7\sqrt{2}}{2}}{x}$

$\frac{\sqrt{3}}{2} = \frac{\frac{7\sqrt{2}}{2}}{x}$ (sin 60 = √3/2)

$\frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2}*\frac{1}{x}$

$\frac{\sqrt{3}}{2} = \frac{7\sqrt{2}}{2x}$

Cross multiply

$\sqrt{3}*2x = 7\sqrt{2}*2$

$2\sqrt{3}*x = 14\sqrt{2}$

Divide both sides by 2

$\sqrt{3}*x = 7\sqrt{2}$

Divide both sides by √3

$x = \frac{7\sqrt{2}}{\sqrt{3}}$

Rationalize

$x = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$x = \frac{7\sqrt{6}{3}$

✔️To find y, apply the trigonometric function TOA:

Tan 60° = Opp/Adjacent

$Tan 60° = \frac{\frac{7\sqrt{2}}{2}}{y}$

$\sqrt{3} = \frac{\frac{7\sqrt{2}}{2}}{y}$ (tan 60 = √3)

$\sqrt{3} = \frac{7\sqrt{2}}{2}*\frac{1}{y}$

$\sqrt{3} = \frac{7\sqrt{2}}{2y}$

Cross multiply

$\sqrt{3}*2y = 7\sqrt{2}$

$2\sqrt{3}*y = 7\sqrt{2}$

Divide both sides by √3

$y = \frac{7\sqrt{2}}{\sqrt{3}}$

Rationalize

$y = \frac{7\sqrt{2}*\sqrt{3}}{\sqrt{3}*\sqrt{3}}$

$y = \frac{7\sqrt{6}}{3}$

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Answer:

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In the end, the number of times each prime divides the original integer becomes its exponent.

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Prime number 3 to the power of 1 equals 3 .

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<u> OAmalOHopeO</u>

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