Answer:
First choice.
Step-by-step explanation:
You could plug in the choices to see which would make all the 3 equations true.
Let's start with (x=2,y=-6,z=1):
2x+y-z=-3
2(2)+-6-1=-3
4-6-1=-3
-2-1=-3
-3=-3 is true so the first choice satisfies the first equation.
5x-2y+2z=24
5(2)-2(-6)+2(1)=24
10+12+2=24
24=24 is true so the first choice satisfies the second equation.
3x-z=5
3(2)-1=5
6-1=5
5=5 is true so the first choice satisfies the third equation.
We don't have to go any further since we found the solution.
---------Another way.
Multiply the first equation by 2 and add equation 1 and equation 2 together.
2(2x+y-z=-3)
4x+2y-2z=-6 is the first equation multiplied by 2.
5x-2y+2z=24
----------------------Add the equations together:
9x+0+0=18
9x=18
Divide both sides by 9:
x=18/9
x=2
Using the third equation along with x=2 we can find z.
3x-z=5 with x=2:
3(2)-z=5
6-z=5
Add z on both sides:
6=5+z
Subtract 5 on both sides:
1=z
Now using the first equation along with 2x+y-z=-3 with x=2 and z=1:
2(2)+y-1=-3
4+y-1=-3
3+y=-3
Subtract 3 on both sides:
y=-6
So the solution is (x=2,y=-6,z=1).
It will really be helpful in your solution if you draw the rectangle, its diagonal and the altitude of ΔMOP.
By doing so, you will find that ∠MOP is equal to twice m∠AOP and that is equal to 30°. Then, m∠MOP is a vertical angle of m∠NOK which means that they are equal. Therefore, m∠NOK is also 30°.
We know that the sum of the angles of a triangle is equal to 180°.
m∠NOK + m∠OKN + m∠ONK = 180°
And that m∠OKN = m∠ONK
so,
m∠NOK + 2m∠ONK = 180°
Substituting,
30° + 2m∠ONK = 180°
Hence,
m∠ONK = 75°
The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle or square you have to add the lengths of all the four sides. x is in this case the length of the rectangle while y is the width of the rectangle.
The perimeter, P, is:
P=x+x+y+y
P=2x+2y
P=2(x+y)
Hope this helps
Answer:
-5/6, -1/6, 5/3
Step-by-step explanation: