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Radda [10]
2 years ago
14

1 & 2

Mathematics
1 answer:
sveta [45]2 years ago
5 0
The value of x is 13 for the first attachment. 
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For positive acute angles A and B, it is known that tan A = 35/12 and sin B = 20/29. Find the value of sin(A - B ) in the simple
almond37 [142]

Answer:

\displaystyle \sin(A-B)=\frac{495}{1073}

Step-by-step explanation:

We are given that:

\displaystyle \tan(A)=\frac{35}{12}\text{ and } \sin(B)=\frac{20}{29}

Where both A and B are positive acute angles.

And we want to find he value of sin(A-B).

Using the first ratio, we can conclude that the opposite side is 35 and the adjacent side is 12.

Then by the Pythagorean Theorem, the hypotenuse is:

h = \sqrt{35^2 + 12^2} =37

Using the second ratio, we can likewise conclude that the opposite side is 20 and the hypotenuse is 29.

Then by the Pythagorean Theorem, the adjacent is:

a=\sqrt{29^2-20^2}=21

Therefore, we can conclude that:

So, for A, the adjacent is 12, opposite is 35, and the hypotenuse is 37.

For B, the adjacent is 21, opposite is 20, and the hypotenuse is 29.

We can rewrite sin(A-B) as:

\sin(A-B)=\sin(A)\cos(B)-\cos(A)\sin(B)

Using the above conclusions, this yields: (Note that since A and B are positive acute angles, all resulting ratios will be positive.)

\displaystyle \sin(A-B)=\Big(\frac{35}{37}\Big)\Big(\frac{21}{29}\Big)-\Big(\frac{12}{37}\Big)\Big(\frac{20}{29}\Big)

Evaluate:

\displaystyle \sin(A-B)=\frac{735-240}{1073}=\frac{495}{1073}

6 0
3 years ago
Order 56656, 67445, 9199​
gayaneshka [121]

Answer: Least to greatest: 9199, 56656, 67445

Greatest to least: 67445, 56656, 9199

Step-by-step explanation:

6 0
3 years ago
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Create an equation modeling the scenario. Use the equation to solve for the missing number. In your final answer, include the eq
Svetradugi [14.3K]
I think it’s 2(x+7)=3x
5 0
3 years ago
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12, 17, 22... find the 35th term
Leno4ka [110]

Answer:

a₃₅ = 182

Step-by-step explanation:

There is a common difference d between consecutive terms, that is

d = 17 - 12 = 22 - 17 = 5

This indicates the sequence is arithmetic with n th term

a_{n} = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 12 and d = 5 , then

a₃₅ = 12 + (34 × 5) = 12 + 170 = 182

3 0
3 years ago
Does the equation 14 - 3x = -4x have one, many or no solution?​
BabaBlast [244]

Answer:

one solution,x=- 14

Step-by-step explanation:

3 0
3 years ago
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