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svet-max [94.6K]

4 years ago

13

Look at the following numbers: −3, −1, 0, 3 Which pair of numbers has a sum of 0? (5 points) 0, −1 −3, 3 −1, 3 −1, 0

1 answer:

Zielflug [23.3K]4 years ago

5 0

Summing to zero means the two numbers are additive inverses, i.e. negatives of each other. We choose the pair of negations:

Answer: -3, 3

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Please help me for the love of God if i fail I have to repeat the class

Elena-2011 [213]

$\theta$ is in quadrant I, so $\cos\theta>0$ .

$x$ is in quadrant II, so $\sin x>0$ .

Recall that for any angle $\alpha$ ,

$\sin^2\alpha+\cos^2\alpha=1$

Then with the conditions determined above, we get

$\cos\theta=\sqrt{1-\left(\dfrac45\right)^2}=\dfrac35$

and

$\sin x=\sqrt{1-\left(-\dfrac5{13}\right)^2}=\dfrac{12}{13}$

Now recall the compound angle formulas:

$\sin(\alpha\pm\beta)=\sin\alpha\cos\beta\pm\cos\alpha\sin\beta$

$\cos(\alpha\pm\beta)=\cos\alpha\cos\beta\mp\sin\alpha\sin\beta$

$\sin2\alpha=2\sin\alpha\cos\alpha$

$\cos2\alpha=\cos^2\alpha-\sin^2\alpha$

as well as the definition of tangent:

$\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}$

Then

1. $\sin(\theta+x)=\sin\theta\cos x+\cos\theta\sin x=\dfrac{16}{65}$

2. $\cos(\theta-x)=\cos\theta\cos x+\sin\theta\sin x=\dfrac{33}{65}$

3. $\tan(\theta+x)=\dfrac{\sin(\theta+x)}{\cos(\theta+x)}=-\dfrac{16}{63}$

4. $\sin2\theta=2\sin\theta\cos\theta=\dfrac{24}{25}$

5. $\cos2x=\cos^2x-\sin^2x=-\dfrac{119}{169}$

6. $\tan2\theta=\dfrac{\sin2\theta}{\cos2\theta}=-\dfrac{24}7$

7. A bit more work required here. Recall the half-angle identities:

$\cos^2\dfrac\alpha2=\dfrac{1+\cos\alpha}2$

$\sin^2\dfrac\alpha2=\dfrac{1-\cos\alpha}2$

$\implies\tan^2\dfrac\alpha2=\dfrac{1-\cos\alpha}{1+\cos\alpha}$

Because $x$ is in quadrant II, we know that $\dfrac x2$ is in quadrant I. Specifically, we know $\dfrac\pi2$ , so $\dfrac\pi4$ . In this quadrant, we have $\tan\dfrac x2>0$ , so

$\tan\dfrac x2=\sqrt{\dfrac{1-\cos x}{1+\cos x}}=\dfrac32$

8. $\sin3\theta=\sin(\theta+2\theta)=\dfrac{44}{125}$

6 0

4 years ago

Amanda can jog 18 miles in 5 hours.<br> At this rate, how many miles can Amanda jog in 4 hours?

vekshin1

Answer:

14.4 miles

Step-by-step explanation:

5 goes into 18 3.6 times and 3.6 x 4 = 14.4, she can run 3.6 miles per hour

3 0

3 years ago

Read 2 more answers

How much will have to deposit into an account that pays 5.25% simple interest today, in order to earn $345.45 interest in seven

Ann [662]

To earn $345.45 simple interest in 7 years, you have to invest $940.

<u>Step-by-step explanation:</u>

Step 1:

Given details are Simple Interest Rate (R) = 5.25%, Simple Interest (SI) = $345.45, Time (T) = 7 years

Step 2:

Use the above details to find principal using the formula for Simple Interest (SI) = PRT/100

⇒ 345.45 = (P × 5.25 × 7)/100

⇒ 34545 = 36.75 P

⇒ P = $940

3 0

3 years ago

Evaluate the determinate:

bearhunter [10]

Answer:

39

Step-by-step explanation:

detailed explanation showed in the diagram above

7 0

2 years ago

Which expression is equivalent to 28 + 12? (1 point) 4(7 + 3) 4(24 + 8) 7(4 + 12) 7(21 + 5)

vodka [1.7K]

Answer:

4(7+3)

Step-by-step explanation:

28 and 12 are both divisible by 4.

28 ÷ 4 = 7

12 ÷ 4 = 3

4 0

3 years ago

Read 2 more answers