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Lady_Fox [76]
2 years ago
15

I have this quiz for today and I promise I don't understand anything, can someone help me? 15 points

Mathematics
1 answer:
lyudmila [28]2 years ago
3 0

Answer:

Step-by-step explanation:

You are given values for x. Plug them in to the given equations. Graph the two lines. Find the intersection. You can tell from the chart when you get the same y value for both equations

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Question is 15 points
mihalych1998 [28]

This is a doozy so pay attention. First thing you have to recognize is that is a trig identity, the sum identity for cosine to be exact. That formula is

cos(\alpha +\beta )=cos\alpha cos\beta -sin\alpha sin\beta.

So that means you need to find the cosine of alpha and the sin of beta. We are given the sin of alpha being 4/5 in the first quadrant. If you set up the sin ratio which is side opposite over hypotenuse of a right triangle, you put the 4 on the side opposite the reference angle, alpha, and the hypotenuse of 5 on the terminal ray and then you have to find the missing side of the right triangle you created. Using Pythagorean's theorem, you find that the missing side, which is the adjacent side to alpha, is 3. Now you can find the cosine of alpha as well, since cosine is the side adjacent, 3, over the hypotenuse, 5. So far wwe have

sin\alpha =\frac{4}{5} and

cos\alpha =\frac{3}{5} for that first angle. Now moving on to the second angle. The cosine of beta is side adjacent, 5, over the hypotenuse, 13, and we are missing the side opposite the reference angle beta. Using Pythagorean's theorem again to find the side opposite, we have that that side measures 12. Now we can find the sine of beta using that opposite side, 12, over the hypotenuse, 13. What we have now is

cos\beta =\frac{5}{13} and

sin\beta =\frac{12}{13}. According to the identity, we have to multiply those ratios now:

(\frac{3}{5}*\frac{5}{13})-(\frac{4}{5}*\frac{12}{13}).

When you do that you get

\frac{3}{13}-\frac{48}{65}.

Of course in order to subtract those 2 fractions you need a common denominator which is 65 so

\frac{15}{65}-\frac{48}{65} which gives you a final answer of -\frac{33}{65} which is the first choice given above. There you go!

4 0
3 years ago
Simplify the following expression<br> 2x − 6y + 3x2 + 7y − 14x
Setler [38]
2x - 6y + 3x² + 7y - 14y = 3x² + (2x - 14x) + (-6y + 7y) = 3x² - 12x + y
4 0
3 years ago
Use equivalent ratios to find unknown value plz halp!!!!​
iogann1982 [59]

Answer:

21

Step-by-step explanation:

It might be 21/30 , hope it helps though :)

7 0
3 years ago
Read 2 more answers
Use the functions f(x) = 4x² + 3 and g(x) = 3x + 2 to evaluate the following.
natita [175]

Answer:

Step-by-step explanation:

f(-2)= 4(-2)^2 + 3 = 4(4) + 3 = 16 + 3 = 19

g(19) = 3(19) + 2 = 57 + 2 = 59

g(-2)= 3(-2) + 2 = -6 + 2 = -4

f(-4)= 4(-4)^2 + 3 = 64 + 3 = 67

7 0
2 years ago
Read 2 more answers
Suzy is starting a babysitting buisness. She spent $ 36 to make signs to advertise. She charges and intial fee of $ 6 and then $
timofeeve [1]

Answer:

3h - 30 > 0

h > 10

Step-by-step explanation:

To make a profit, subtract $36 in cost from the income coming in.

She charges $6 and then $3 per hour or 3h. Her income coming in is 6 + 3h.

Subtract 36 from it to find the profit.

3h + 6 - 36

3h - 30

To make a profit, she needs to make more than $0 or > 0.

3h - 30 > 0

Solve using inverse operations.

3h - 30 > 0

3h > 30

h > 10

3 0
3 years ago
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