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olga_2 [115]
3 years ago
8

Y = 5x + 15 y = -5x - 15

Mathematics
1 answer:
algol [13]3 years ago
3 0

Answer:

5x + 15 = -5x - 15

10x = -30

x = -3

y = 5(-3) + 15 = -15 + 15 = 0

(-3,0)

Step-by-step explanation:

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The <em>trigonometric</em> expression \frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1} is equivalent to the <em>trigonometric</em> expression \sec \alpha \cdot \csc \alpha + 1.

<h3>How to prove a trigonometric equivalence</h3>

In this problem we must prove that <em>one</em> side of the equality is equal to the expression of the <em>other</em> side, requiring the use of <em>algebraic</em> and <em>trigonometric</em> properties. Now we proceed to present the corresponding procedure:

\frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1}

\frac{\tan^{2}\alpha}{\tan \alpha - 1} + \frac{\frac{1}{\tan^{2}\alpha} }{\frac{1}{\tan \alpha} - 1 }

\frac{\tan^{2}\alpha}{\tan \alpha - 1} - \frac{\frac{1 }{\tan \alpha} }{\tan \alpha - 1}

\frac{\frac{\tan^{3}\alpha - 1}{\tan \alpha} }{\tan \alpha - 1}

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\frac{(\tan \alpha - 1)\cdot (\tan^{2} \alpha + \tan \alpha + 1)}{\tan \alpha\cdot (\tan \alpha - 1)}

\frac{\tan^{2}\alpha + \tan \alpha + 1}{\tan \alpha}

\tan \alpha + 1 + \cot \alpha

\frac{\sin \alpha}{\cos \alpha} + \frac{\cos \alpha}{\sin \alpha} + 1

\frac{\sin^{2}\alpha + \cos^{2}\alpha}{\cos \alpha \cdot \sin \alpha} + 1

\frac{1}{\cos \alpha \cdot \sin \alpha} + 1

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The <em>trigonometric</em> expression \frac{\tan^{2} \alpha}{\tan \alpha - 1} + \frac{\cot^{2} \alpha}{\cot \alpha - 1} is equivalent to the <em>trigonometric</em> expression \sec \alpha \cdot \csc \alpha + 1.

To learn more on trigonometric expressions: brainly.com/question/10083069

#SPJ1

6 0
2 years ago
If a survey of a movie shows that 50% of all people who like the movie, enjoyed the official movie soundtrack too. If a total of
Murljashka [212]

Answer:

For the first question the sample size is n= 3850

ME= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

\hat p \pm ME

And replacing we got:

0.5- 0.016 = 0.484

0.5+ 0.016 = 0.516

We are confident at 95% that the true proportion of all people who like the movie is between 0.484 and 0.516.

Step-by-step explanation:

We have the following info given:

\hat p = 0.5 represent the estimated proportion of all people who like the movie

n = 3850 represent the sample size selected

For the first question the sample size is n= 3850

For the second part they gives to us the margin of error:

ME = 0.016

We know that the confidence interval for a population proportion p of interest is given by:

\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

And the margin of error is given by:

ME= z_{\alpha/2}\sqrt{\frac{\hat p(1-\hat p)}{n}}

So then the confidence interval can be found with this formula:

\hat p \pm ME

And replacing we got:

0.5- 0.016 = 0.484

0.5+ 0.016 = 0.516

We are confident at 95% that the true proportion of all people who like the movie is between 0.484 and 0.516.

5 0
3 years ago
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