Answer:
The answer to your question is ∠FSH = 42°; ∠NSF = 78°; ∠NSH = 120°
Step-by-step explanation:
Data
∠ FSH = 5x - 8
∠NSF = 9x - 12
∠NSH = 10x + 20
Process
1.- Write a equation to solve this problem
∠NSH = ∠NSF + ∠FSH
2.- Substitute values
10x + 20 = 9x - 12 + 5x - 8
3.- Solve for x
10 x - 9x - 5x = - 12 - 8 - 20
10x - 14x = - 12 - 28
- 4x = - 40
x = -40 / -4
x = 10
4.- Find the measure of all three angles
∠FSH = 5(10) - 8
= 50 - 8
= 42°
∠NSF = 9x - 12
= 9(10) - 12
= 90 - 12
= 78°
∠NSH = 10(10) + 20
= 100 + 20
= 120°
5.- Check the answers
120° = 78° + 42°
120° = 120°
The answers are correct
95000 Is rounded to the nearest ten thousands
Equation 1) -x - y - z = -8
Equation 2) -4x + 4y + 5z = 7
Equation 3) 2x + 2z = 4
Solving for three variables is quite similar to solving for two variables. Just like when solving for two variables, you look for like variables & solve them one-by-one. So, let's get started! :)
Multiply ALL of equation 1 by four.
1) 4(-x - y - z = -8)
Simplify.
1) -4x - 4y - 4z = -32
Both equations 1 & 2 have the same three variables (x, y, z), so, we must look at these equations together.
1) -4x - 4y - 4z = -32
2) -4x + 4y + 5z = 7
Add these equations together, and create a fourth equation.
4) -8x - z = -25
Now, notice how both equations 3 & 4 have the same two variables (x, z).
So, we must look at these equations together.
3) 2x + 2z = 4
4) -8x - z = -25
Multiply ALL of equation 4 by 2.
4) 2(-8x - z = -25)
Simplify.
4) -16x - 2z =-50
3) 2x + 2z = 4
Now, add the equations together, so that we can solve for x.
-14x = -42
Divide both sides by -14.
x = 3
Now, plug in 3 for x into our 3rd equation.
3) 2x + 2z = 4
3) 2(3) + 2z = 4
Simplify.
6 + 2z = 4
Subtract 6 from both sides.
2z = 4 - 6
Simplify.
2z = -2
Divide both sides by 2.
z = -1
Now, plug in -1 for z & 3 for x in our 1st equation.
1) -x - y - z = -8
-(3) - y - (-1) = -8
Simplify.
-3 - y + 1 = -8
Simplify.
-2 - y = -8
Add 2 to both sides.
-y = -8 + 2
Simplify.
-y = -6
Divide both sides by -1.
y = 6
SO :
x = 3, y = 6, z = -1
~Hope I helped!~
area = pi * r^2
here, the radius is 2 as its the diameter/2.
so the area is 4pi.
circumference = 2*pi*r.
so the circumference is 4pi as well.
