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IrinaK [193]
3 years ago
7

In the diagram, line x|| line y. Find the angle measures below.

Mathematics
1 answer:
Yanka [14]3 years ago
5 0

Answer:

<1 = 95

<2 =85

Step-by-step explanation:

<1 = 95

They are alternate exterior angles and alternate exterior angles are equal when the lines are parallel

<1 + <2 = 180  since they form a straight line

95+ <2 =190

Subtract 95 from each side

95-95+<2 =180-95

<2 =85

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PLEASE HELP ME I'M GIVING 20PTS AND MARKING BRAINLIEST!!!!
pishuonlain [190]

Using a trigonometric identity, it is found that the values of the cosine and the tangent of the angle are given by:

  • \cos{\theta} = \pm \frac{2\sqrt{2}}{3}
  • \tan{\theta} = \pm \frac{\sqrt{2}}{4}

<h3>What is the trigonometric identity using in this problem?</h3>

The identity that relates the sine squared and the cosine squared of the angle, as follows:

\sin^{2}{\theta} + \cos^{2}{\theta} = 1

In this problem, we have that the sine is given by:

\sin{\theta} = \frac{1}{3}

Hence, applying the identity, the cosine is given as follows:

\cos^2{\theta} = 1 - \sin^2{\theta}

\cos^2{\theta} = 1 - \left(\frac{1}{3}\right)^2

\cos^2{\theta} = 1 - \frac{1}{9}

\cos^2{\theta} = \frac{8}{9}

\cos{\theta} = \pm \sqrt{\frac{8}{9}}

\cos{\theta} = \pm \frac{2\sqrt{2}}{3}

The tangent is given by the sine divided by the cosine, hence:

\tan{\theta} = \frac{\sin{\theta}}{\cos{\theta}}

\tan{\theta} = \frac{\frac{1}{3}}{\pm \frac{2\sqrt{2}}{3}}

\tan{\theta} = \pm \frac{1}{2\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}

\tan{\theta} = \pm \frac{\sqrt{2}}{4}

More can be learned about trigonometric identities at brainly.com/question/24496175

#SPJ1

5 0
2 years ago
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Nataly [62]

The formula of a midpoint of AB:

M_{AB}\left(\dfrac{x_A+x_B}{2};\ \dfrac{y_A+y_B}{2}\right)

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G(b; 0); F(3b; 2b)

substitute:

M_{GF}\left(\dfrac{b+3b}{2};\ \dfrac{0+2b}{2}\right)\to M_{GF}(2b;\ b)

Answer: (2b, b)

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3 years ago
Carlos just took a 40 question math test. He scored a 75%. How many questions did he get correct?
sergiy2304 [10]

Answer:

He missed 10 questions and got 30 right

Step-by-step explanation:

So we could do 0.75 times 40 and we would get 30

So he got 30 questions right which isn't too bad

8 0
2 years ago
How many of these pitchers can a cylinder with height 9 inches and 2r fill? Explain how you know.
irakobra [83]

Answer:

4 pitches

Step-by-step explanation:

if a cylinder with height 9 inches and radius r is filled with water, it can fill a certain pitcher. how many of these pitchers can a cylinder with height 9 inches and radius 2r fill? explain how you know.

Solution:

The volume of a cylinder is given by:

V = πr²h;

where V is the volume, r is the radius of the cylinder and h is the height of the cylinder.

A cylinder with height 9 inches and radius r can fill a certain pitcher. Therefore the volume of the cylinder is:

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For a cylinder with height 9 inches and radius 2r its volume is:

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Therefore, the number of pitchers a cylinder with height 9 inches and radius 2r can fill is:

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Therefore a cylinder with height 9 inches and radius 2r can fill 4 pitches.

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Answer: The correct answer is (B)

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