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2 years ago

If the angle of R and the angle of S are vertical angles and the measure of Angle R = 39 degrees, what is the measure of angle S

Mathematics

1 answer:

Marat540 [252]2 years ago

3 0

Answer:

Step-by-step explanation:

Verticle angles are formed when two lines intersect each other, the angles opposite each other are called verticle angles. Verticle angles are congruent, meaning their angle measures are the same. One can apply this knowledge here by stating the following,

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How do I get (tan^2(x)-sin^2(x))/tan(x) equal to (sin^2(x))/cot(x)

shepuryov [24]

$LHS\\ \\ =\frac { \tan ^{ 2 }{ x-\sin ^{ 2 }{ x } } }{ \tan { x } } \\ \\ =\frac { 1 }{ \tan { x } } \left( \tan ^{ 2 }{ x-\sin ^{ 2 }{ x } } \right)$

$\\ \\ =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^{ 2 }{ x } }{ \cos ^{ 2 }{ x } } -\frac { \sin ^{ 2 }{ x\cos ^{ 2 }{ x } } }{ \cos ^{ 2 }{ x } } \right) \\ \\ =\frac { \cos { x } }{ \sin { x } } \left( \frac { \sin ^{ 2 }{ x-\sin ^{ 2 }{ x\cos ^{ 2 }{ x } } } }{ \cos ^{ 2 }{ x } } \right)$

$\\ \\ =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^{ 2 }{ x\left( 1-\cos ^{ 2 }{ x } \right) } }{ \cos ^{ 2 }{ x } } \\ \\ =\frac { \cos { x } }{ \sin { x } } \cdot \frac { \sin ^{ 2 }{ x\cdot \sin ^{ 2 }{ x } } }{ \cos ^{ 2 }{ x } } \\ \\ =\frac { \cos { x } \sin ^{ 4 }{ x } }{ \sin { x\cos ^{ 2 }{ x } } } \\ \\ =\frac { \sin ^{ 3 }{ x } }{ \cos { x } }$

$\\ \\ =\sin ^{ 2 }{ x } \cdot \frac { \sin { x } }{ \cos { x } } \\ \\ =\sin ^{ 2 }{ x } \cdot \frac { 1 }{ \frac { \cos { x } }{ \sin { x } } } \\ \\ =\sin ^{ 2 }{ x } \cdot \frac { 1 }{ \cot { x } } \\ \\ =\frac { \sin ^{ 2 }{ x } }{ \cot { x } } \\ \\ =RHS$

8 0

2 years ago

What is the rate of return when 35 shares of Stock A, purchased for $20/share, are sold for $815? The commission on the sale is

wariber [46]

Cost price:-

$\\ \sf\longmapsto 35\times 20$

$\\ \sf\longmapsto 700$

Commision=$6
Total sold price=815+6=823$

Now

Return=823-700=123

Rate of return

$\\ \sf\longmapsto \dfrac{123}{700}\times 100$

$\\ \sf\longmapsto \dfrac{123}{7}$

$\\ \sf\longmapsto 17.5\%$

7 0

2 years ago

Read 2 more answers

Which of the following is equivalent to 0 equals 3 x squared minus 12 x minus 15 when completing the square?

skad [1K]

Answer:

x = 5, -1

Step-by-step explanation:

0 = 3x^2 - 12x - 15 or

3x^2 - 12x - 15 = 0

By solving for x, use the Quadratic Formula.

… x = 5 and/or -1

8 0

2 years ago

• Chandra bought a 2-liter bottle of

frosja888 [35]

Answer:

Step-by-step explanation:

1 liter = 33.8 fl oz

Hence

2 liter = 33.8 * 2 = 67.6 fl oz

Now, we need to determine, how many 8 fl oz glasses can be filled with 67.6 fl oz of juice. For that, we need to divide total amount of juice (in fl oz) by 8. We will get:

$\frac{67.6}{8}=8.45$

So there is enough juice to fill around 8.5 glasses, but we need to know how many FULL GLASSES can be filled, NOT PARTIAL.

Thus, we can say:

8 glasses max can be filled with 2 Liters of juice

Answer choice D is right

3 0

2 years ago

The dwarves of the Grey Mountains wish to conduct a survey of their pick-axes in order to construct a 99% confidence interval ab

Dmitry_Shevchenko [17]

Answer:

The minimum sample size needed is 125.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of $\pi$ , and a confidence level of $1-\alpha$ , we have the following confidence interval of proportions.

$\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}$

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$ .

The margin of error is:

$M = z\sqrt{\frac{\pi(1-\pi)}{n}}$

For this problem, we have that:

$\pi = 0.25$

99% confidence level

So $\alpha = 0.01$ , z is the value of Z that has a pvalue of $1 - \frac{0.01}{2} = 0.995$ , so $Z = 2.575$ .

What minimum sample size would be necessary in order ensure a margin of error of 10 percentage points (or less) if they use the prior estimate that 25 percent of the pick-axes are in need of repair?

This minimum sample size is n.

n is found when $M = 0.1$