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3 years ago

D 3. Which side in the smallest triangle would correspond with RS in the largest triangle?

Mathematics

1 answer:

Morgarella [4.7K]3 years ago

8 0

P I hope this helps sorry if it didn’t

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What is the interquartile range for the data set?<br><br> 8 1 7 3 7 2 6 7 9

kiruha [24]

Answer:

the interquartile range is 7

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3 years ago

How can you prove that csc^2(θ)tan^2(θ)-1=tan^2(θ)

Oxana [17]

Answer:

Make use of the fact that as long as $\sin(\theta) \ne 0$ and $\cos(\theta) \ne 0$ :

$\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ .

$\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}$ .

$\sin^{2}(\theta) + \cos^{2}(\theta) = 1$ .

Step-by-step explanation:

Assume that $\sin(\theta) \ne 0$ and $\cos(\theta) \ne 0$ .

Make use of the fact that $\tan(\theta) = (\sin(\theta)) / (\cos(\theta))$ and $\csc(\theta) = (1) / (\sin(\theta))$ to rewrite the given expression as a combination of $\sin(\theta)$ and $\cos(\theta)$ .

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}$ .

Since $\cos(\theta) \ne 0$ :

$\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}$ .

Substitute this equality into the expression:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}$ .

By the Pythagorean identity, $\sin^{2}(\theta) + \cos^{2}(\theta) = 1$ . Rearrange this identity to obtain:

$\sin^{2}(\theta) = 1 - \cos^{2}(\theta)$ .

Substitute this equality into the expression:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}$ .

Again, make use of the fact that $\tan(\theta) = (\sin(\theta)) / (\cos(\theta))$ to obtain the desired result:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}$ .

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2 years ago

Out of these numbers which ones are multiples of 7 {−7, −4, 2, 14, 21, 34, 42}

xxMikexx [17]

Answer:

-7, 14, 21, and 42

Step-by-step explanation:

7•-1=-7

7•2=14

7•3=21

7•6=42

7 0

3 years ago

7. What type of angle pair are LMS and SMN? 1.adjacent angles 2.linear pair 3.complementary angles 4.vertical angles

steposvetlana [31]

In this question we have a diagram given. ANd on the basis of that diagram, we have to find the relationship between angles LMS and SMN.

As we see in the diagram, that these angles are one after another. ANd such angles are known as adjacent angles . So these two angles are adjacent angles .

So out of the four options, the correct option is the first option .

4 0

3 years ago

99 POINTS

defon

Answer:

C.) -a^2 - a + 12

Step-by-step explanation:

(-a + 3) (a + 4)

FOIL (First, Outer, Inner, Last)

-a * a = -a^2

-a * 4 = -4a

3 * a = 3a

3 * 4 = 12

-4a + 3a = -a

Answer:

-a^2 - a + 12

5 0

4 years ago

Read 2 more answers