Answer:
- ∠XVR = 125°
- ∠RVS = 55°
- ∠WVS = 125°
Step-by-step explanation:
Any angles on opposite sides of the intersection point of crossing lines are "vertical" angles, and they have identical measure.
Any angles along the same side of the same line are "linear" angles, and they are supplementary (add to 180°).
The angles inside a triangle add to 180°.
Using these relationships, work from the given information to find the rest of the angles.
The system of equations has the solution:
x = 111/42
y = 27/14
z = -15/6
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How to solve the system of linear equations?</h3>
We start with 3 linear equations:
2x+y-z=8
x+4y+z=7
-3x+2y-3z=21
To solve this, first we need to isolate one of the variables. I will isolate x on the second one:
x = 7 - 4y - z
Now we can replace that in the other two:
2*( 7 - 4y - z) + y - z = 8
-3*(7 - 4y - z) + 2y - 3z = 21
Now we need to isolate other variable, let's isolate y on the above one:
14 - 8y - 2z + y - z = 8
-7y - 3z = 8 - 14 = -6
z = (-6 + 7y)/-3 = 2 - (7/3)*y
Now we replace this on the last equation:
-21 + 12y -3z + 2y - 3z = 21
14y - 6z = 42
14y - 6*(2 - (7/3)*y) = 42
14y - 12 + 14y = 42
28y = 42 + 12 = 54
y = 54/28 = 27/14
Now that we know the value of y, we can find the value of z:
z = 2 - (7/3)*y = 2 - (7/3)*27/14 = 2 - 27/6 = -15/6
And the value of x:
x = 7 - 4y - z = 7 - 4*(27/14) + 15/6 = 7 - 48/7 + 15/6 = 111/42
So the solution is:
x = 111/42
y = 27/14
z = -15/6
If you want to learn more about systems of equations:
brainly.com/question/13729904
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The correct answer is D, -5 1/3.
The reason is that on a number line -3 1/4 would be placed to the right of -5 1/3.
The further you are to the right on the number line, the bigger the number.
Answer: The upper control limit is 1.40581
The lower control limit is 0.000
Explanation: Check attachment
Answer: It will take 36 minutes(0.6 hour) until both ferries depart from their docks at the same time again.
Step-by-step explanation:
Given : Ferry A departs every 1.2 hours.
Ferry B departs every 1.8 hours.
To find : Time taken by both ferries until they depart from their docks at the same time again.
= LCM (1.2, 1.8) hours [LCM= Least common multiple]
= LCM (1.2(60 minutes), 1.8(60 minutes)) [Since 1 hour = 60 minutes]
= LCM (72 minutes, 108 minutes)
72 = 2 x 2 x 2 x 3 x 3 , 108 = 3 x 3 x 3 x 2 x 2
LCM (72,108) =2 x 2 x 3 x 3 =36
So, it will take 36 minutes until both ferries depart from their docks at the same time again.
In hour =