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2 years ago

Find the slope of y+2=−2(x−3) Options A) -1/2 B) 1 C) -2 D) -1

Mathematics

1 answer:

djyliett [7]2 years ago

5 0

Answer:

C) -2

Step-by-step explanation:

y+2=-2(x-3)

y+2=-2x+6

-2 -2

y=-2x+4

y=mx+b

m is slope

the slope is -2

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Prove that sin(Π÷14)sin(3Π÷14)sin(5Π÷14)=2

Oxana [17]

Answer:

The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Step-by-step explanation:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$

Multiply and Divide by $2cos(\frac{\pi }{14})$

= $\frac{2sin(\frac{\pi }{14})cos(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})}{2cos(\frac{\pi }{14})}$

⇒ Let $\frac{\pi }{14}$ = Ф and 7Ф = $\frac{\pi }{2}$

= sin2Ф sin3Ф sin5Ф ÷ 2cosФ

= 1/2(2sin2Фsin5Ф)sin3Ф ÷ 2cosФ

= (cos3Ф - cos7Ф) sin3Ф ÷ 4cosФ

= 1/2(2cos3Ф sin3Ф) ÷ 4cosФ ∵cos7Ф = 0

= sin6Ф ÷ 8cosФ

= sin(7Ф - Ф) ÷ 8cosФ

= (sin7ФcosФ - cos7ФsinФ) ÷ 8cosФ ∵sin7Ф = 1

= cosФ ÷ 8cosФ

= 1/8

Hence, The correct prove will be:

$sin(\frac{\pi }{14})sin(\frac{3\pi }{14})sin(\frac{5\pi }{14})$ $= \frac{1}{8}$

Keywords: prove, sinФ, cosФ

Learn more about trigonometric functions from brainly.com/question/7331447

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4 0

2 years ago

A regular room at the Great Wolf Lodge is $229.99. You have a discount code to get 20% off of the room rate. The sales tax on th

vovangra [49]

229.99*.20 = $46 off
229.99-46 = $183.99
$183.99*.13 =$23.92 sales tax added
183.99+23.92 = $207.91

6 0

3 years ago

Read 2 more answers

Help solve equations by completing the square

Allushta [10]

$x^2+10x+22=13\\x^2+10x+22-13=0\\x^2+10x+9=0\\$

Now completing the square.

$(x^2+10x)+9=0\\(x^2+10x+25)+9-25=0\\(x+5)^2-16=0\\(x+5)^2=16$

(x+5)² = 16 is the rewritten equation... For first question btw.

For the solutions to the equation -

$x+5=\sqrt{16},-\sqrt{16} \\x+5=4,-4\\x=4-5,-4-5\\x=-1,-9$

x = -1,-9 is the solution, for the second question.

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2 years ago

Y = 2x + 3 find the 151st term

harkovskaia [24]

Y=2(151)+3

y=302+3

y=305

So the 151st term is 305

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2 years ago

What will be 66 2/3 as a percent explanation

VashaNatasha [74]

66.666666 repeated decimal
You would keep the 66 as is, and divide 2 by 3. That equals 0.66666666666 repeated, so the answer would be 66.666666 (rounded: 66.67)

6 0

3 years ago