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2 years ago

Find the measure of angle F

Mathematics

1 answer:

Tema [17]2 years ago

3 0

Answer:

∠ F = 80°

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here n = 6 , then

sum = 180° × 4 = 720°

Sum the interior angles and equate to 720

7x + 7x + 4x + 7x + 7x + 4x = 720

36x = 720 ( divide both sides by 36 )

x = 20

Then

∠ F = 4x = 4 × 20° = 80°

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If Amelia wanted to know if the percentage was less than 81%, then the alternative would be p < 0.81

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However, she wants to know if the percentage is 81%.

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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raketka [301]

Answer:

$\displaystyle x=\left \{\frac{2\pi}{3}+2\pi k,\frac{4\pi}{3}+2\pi k, \frac{8\pi}{3}+2\pi k, \frac{10\pi}{3}+2\pi k\right \}k\in \mathbb{Z}$

Step-by-step explanation:

Hi there!

We want to solve for $x$ in:

$4\sin^2(\frac{x}{2})=3$

Since $x$ is in the argument of $\sin^2$ , let's first isolate $\sin^2$ by dividing both sides by 4:

$\displaystyle \sin^2\left(\frac{x}{2}\right)=\frac{3}{4}$

Next, recall that $\sin^2x$ is just shorthand notation for $(\sin x)^2$ . Therefore, take the square root of both sides:

$\displaystyle \sqrt{\sin^2\left(\frac{x}{2}\right)}=\sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}}$

Simplify using $\displaystyle \sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$ :

$\displaystyle \sin\left(\frac{x}{2}\right)=\pm \sqrt{\frac{3}{4}},\\\sin\left(\frac{x}{2}\right)=\pm \frac{\sqrt{3}}{\sqrt{4}}=\pm \frac{\sqrt{3}}{2}$

Let $\phi = \frac{x}{2}$ .

<h3><u>Case 1 (positive root):</u></h3>

$\displaystyle \sin(\phi)=\frac{\sqrt{3}}{2},\\\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}$

Therefore, we have:

$\displaystyle \frac{x}{2}=\phi = \frac{\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\frac{x}{2}=\phi =\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z},\\\\\begin{cases}x=\boxed{\frac{2\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{4\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

<h3><u>Case 2 (negative root):</u></h3>

$\displaystyle \sin(\phi)=-\frac{\sqrt{3}}{2},\\\phi = \frac{4\pi}{3}+2\pi k, k\in \mathbb{Z}, \\\\\phi =\frac{5\pi}{3}+2\pi k, k\in \mathbb{Z},\\\begin{cases}x=\boxed{\frac{8\pi}{3}+2\pi k, k\in \mathbb{Z}},\\x=\boxed{\frac{10\pi}{3}+2\pi k , k \in \mathbb{Z}}\end{cases}$

8 0

2 years ago

Nina saves 40% of her summer job earnings for college. This summer, she earned $200 more than last summer, and she saved $900. W

beks73 [17]

Answer:

(900 ÷ 4) x 10 -200 = 2050 And this will equal last Summer's earnings

Step-by-step explanation:

So we know that 900$ is equal to 40% and that we can simplify this

900 ÷ 4 = 225

40% ÷ 4 = 10%

Therefore:

225 = 10% and

2250 = 100% of earnings

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3 years ago

1. 3x + x - 2x + 8 = 3x + x

FinnZ [79.3K]

Step-by-step explanation:

1. 3x+x-2x+8=3x+x

x-2x+8=x

x+8=x+2x

8=2x

8÷2=4

x=4

2. 2(2x+4)-2x=x+18

8+4x-2x=x+18

8+2x=x+18

2x=x+10

x=10

3. 2(x+3)+3x

2(5+3)+15

16+15

4. 3(2x)-3x+4=2x+5

6x-3x+4=2x+5

3x+4=2x+5

3x-2x+4=5

x=1

5. 3x+2x+x=x+6

6x=x+6

5x=6

x=6/5

6. 2(x+4)+x=16

2x+8+x=16

3x+8=16

3x=8

x=8/3

Hope I calculated it right you can check it in calculator

3 0

2 years ago