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ipn [44]
3 years ago
10

Ruby worked eight hours more than Isacc.and Svetlana worked 3 times as Ruby.Togethet they worked 150 hours.Find the number hours

each worked.
Mathematics
1 answer:
andrey2020 [161]3 years ago
7 0
Ruby worked X + 8
Isaac worked X
Svetlana worked 3(X+8)
Let's combine all of that by putting it in an equation
X+8+x+3(x+8)=150
Do what's in parentheses first
x+8+x+3x+24=150
Now we add likes
X+x+3x+8+24=150
5x+32=150
We want x on one side of the equation & numbers on the other side
5x+32-32=150-32
5x=118
Solving for X
5x/5=118/5
X=23.6
Isaac worked 23.6
Ruby worked 8 more hours than Isaac so we add 8 to 23.6= 31.6
Svetlana worked 3 times Ruby so 3x31.6= 94.8
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The value of cos(A+B) is 36/325.

<h3>What is Trigonometry?</h3>

The branch of mathematics concerned with specific functions of angles and their application to calculations.

Given:

cos(A)=−5/13

sin(B)=7/25

Now Using identity,

sin²A + cos² A= 1

sin A= √1 - cos² A

sin A = √1- 25/169

sin A= √144/169

sin A= 12/13

Again,

sin²B + cos² B= 1

cos B= √1 - sin² B

cos B = √1- 49/625

cos B= √576/625

cos B= -24/25

Now,

cos (A +B) = cos A cos B - sin A sin B.

= -5/13* (-24/25) - 12/13* 7/25

=  120/325 - 84/325

= 36/325

Hence, the value of cos (A + B) is 36/325.

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