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schepotkina [342]
3 years ago
12

Geometry help me please

Mathematics
1 answer:
11Alexandr11 [23.1K]3 years ago
5 0
The first blank is segment addition postulate and the second blank is substitution property of equality
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<img src="https://tex.z-dn.net/?f=cos%20%5B%20arctan%28%5Cfrac%7B12%7D%7B5%7D%29%20-%20arcsin%20%28%5Cfrac%7B-3%7D%7B5%7D%29%5D"
qwelly [4]

Answer: -16/65

Step-by-step explanation:

Drawing the right triangle (as attached) gives us that \arctan \left(\frac{12}{5} \right)=\arcsin \left(\frac{12}{13} \right)

Also, -\arcsin \left(-\frac{3}{5} \right)=\arcsin \left(\frac{3}{5} \right)

This means our original expression is equal to:

\cos \left[\arcsin \left(\frac{12}{13} \right)+\arcsin \left(\frac{3}{5} \right) \right]

Using the cosine addition formula, which states \cos(a+b)=\cos a \cos b-\sin a \sin b, we get this itself is equal to:

\cos \left(\arcsin \left(\frac{12}{13} \right) \right)\cos \left(\arcsin \left(\frac{3}{5} \right)\right)-\sin \left(\arcsin \left(\frac{12}{13} \right) \right)\sin \left(\arcsin \left(\frac{3}{5} \right)\right)

Since \sin^{2} \theta+\cos^{2} \theta=1, we know that:

\sin^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)+\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=1\\\\\frac{144}{169} +\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=1\\\\cos^{2} \left(\arcsin \left(\frac{12}{13} \right)\right)=\frac{25}{169}\\\\cos \left(\arcsin \left(\frac{12}{13} \right)\right)=\frac{5}{13}

Similarly, cos(arcsin(3/5))=4/5.

This means the given expression is equal to:

\left(\frac{5}{13} \right) \left(\frac{4}{5} \right)-\left(\frac{12}{13} \right) \left(\frac{3}{5} \right)\\\\\frac{20}{65}-\frac{36}{65}=\boxed{-\frac{16}{65}}

3 0
2 years ago
A paper company needs to ship paper to a large printing business. The paper will be shipped in small boxes and large boxes. Each
Ostrovityanka [42]

Answer:

There were 7 small boxes and 14 large boxes shipped.

Step-by-step explanation:

This problem may be solved by a system of equations:

I am going to say that:

x is the number of small boxes used

y is the number of large boxes used

There were twice as many large boxes shipped as small boxes shipped

This means that y = 2x

Each small box of paper weighs 45 pounds and each large box of paper weighs 80 pounds. The total weight of all boxes was 1435 pounds.

This means that 45x + 80y = 1435

So we have to solve the following system:

y = 2x

45x + 80y = 1435

45x + 80(2x) = 1435

205x = 1435

x = \frac{1435}{205}

x = 7

y = 2x = 2(7) = 14

There were 7 small boxes and 14 large boxes shipped.

7 0
3 years ago
The vet says that Lena’s puppy will grow to be at most 20 inches tall. Lenas puppy is currently 1 foot tall. How many more inche
Masja [62]

Answer: the answer is 8


Step-by-step explanation:

The reason for this is because the dog is already a foot tall which is 12 inches. So 12+8=20

6 0
4 years ago
5)Sam is traveling. His
arlik [135]

Answer:

15

Step-by-step explanation:

you need to get to 35. if one bag is 5 pounds what else plus 5 is 35. so each bag is 15 pounds

3 0
3 years ago
Read 2 more answers
Helpppppppppppppppppppp mathhhhhhhhhhh
madreJ [45]
B, because a local hardware store most likely will not see 1 million people in its existence. But technically it is possible
4 0
3 years ago
Read 2 more answers
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