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Blababa [14]
3 years ago
5

URGENT EXPLANATION AND SOLVING

Mathematics
2 answers:
Alex787 [66]3 years ago
7 0
\cfrac{a}{\sin(a)} = \cfrac{b}{\sin(b)} 


\cfrac{31}{\sin(42)} = \cfrac{37}{\sin(x)} 


31\sin(x) = 37 \sin(42)

\sin(x) = \cfrac{37 \sin(42) }{31}

x = \sin^{-1}(\cfrac{37 \sin(42) }{31} )

x = 53 \textdegree

Answer: 53°
Shalnov [3]3 years ago
6 0

We've moved on to inverting the sine.


First let's criticize the question. Question writers: x is a terrible name for an angle; help the kids out and use capital letters like A and B and C for angles and small letters for the sides.


Second, when we have two sides and and an angle not included, there are often two solutions, two angles, supplementary to each other which solve the problem. Supplementary means they add up to 180 degrees, so one acute, one obtuse. Asking to type "the number" doesn't even recognized the possibility.


Let's call this triangle XYZ with vertices X,Y,Z and respective opposite sides x,y,z. We're solving for X and given x=37, z=31, Z=42 deg.


The Law of Sines says


\dfrac{x}{\sin X} = \dfrac{z}{\sin Z}


\sin X = \dfrac{x \sin Z}{z}


\sin X =\dfrac{37 \sin 42}{31} \approx 0.7986


That's a perfectly regular sine, so there will be two triangle angles whose sine is that. The acute one is the principal value,


X_1 = \arcsin 0.7986 \approx 53.0 ^\circ


That's probably the answer they're looking for but of course


X_2 = 180^\circ - 53.0^\circ =127.0^\circ


has the same sine and has an equally valid triangle with those given sides and angle. Bad question.


Will the green box accept 127.0?  Inquiring minds want to know.



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Calculate S58 for the arithmetic sequence {an}= {5/6n+1/3} If you could show me the steps that would be great. I keep following
Amanda [17]

Answer is 8671/6 which is the third choice

===================================

Work Shown:

Find the first term of the sequence by plugging in n = 1

a_n = (5/6)*n + 1/3

a_1 = (5/6)*1 + 1/3    replace n with 1

a_1 = 5/6 + 1/3

a_1 = 5/6 + 2/6

a_1 = 7/6

Repeat for n = 58 to get the 58th term

a_n = (5/6)*n + 1/3

a_58 = (5/6)*58 + 1/3    replace n with 58

a_58 = (5/6)*(58/1) + 1/3

a_58 = (5*58)/(6*1) + 1/3

a_58 = 290/6 + 1/3

a_58 = 145/3 + 1/3

a_58 = 146/3

Now we can use the s_n formula below with n = 58

s_n = (n/2)*(a_1 + a_n)

s_58 = (58/2)*(a_1 + a_58)    replace n with 58

s_58 = (58/2)*(7/6 + a_58)   replace a_1 with 7/6

s_58 = (58/2)*(7/6 + 146/3)   replace a_58 with 146/3

s_58 = (58/2)*(7/6 + 292/6)

s_58 = (58/2)*(299/6)

s_58 = (58*299)/(2*6)

s_58 = 17342/12

s_58 = 8671/6


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If 3(x+2)=5(x-8) what is the value of x+2?<br><br>A. 23<br>B.25<br>C.40<br>D.46
lorasvet [3.4K]

3*x

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Story short the answer is 25

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3 years ago
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masya89 [10]
The fraction would be 5/20=1/4=.25 in decimal form.

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2 years ago
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PLEASE HELP ASAPPP !! Instructions: State what additional information is required in order to know that the triangles are congru
Svetllana [295]
<h3>Answer: angle T = angle W</h3>

Explanation:

We are given the sides are congruent due to the tickmarks. Specifically

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So we just need the "A" of "SAS". The A is between the two S letters, so the angle is between the two sides. For triangle TUV, the angle T is between the two sides with the tickmarks. Similarly, angle W is between the tickmarked sides of triangle WVX.

If we know that angle T = angle W, then we have enough information to use SAS.

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