Answer:
x=12 and y=4.3
Step-by-step explanation:
Given the sides of quadrilateral that are O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6. we have to find the value of x and y so that LMNO be a parallelogram.
we know opposite sides of parallelogram are equal.
Hence, we have to find the value of x and y such that opposite sides becomes equal which implies LMNO is a parallelogram.
Equating opposite sides equal, we get
8x-8=7x+4 ⇒ 8x-7x=8+4=12 ⇒ x=12
implies, NM=x-5=12-5=7
NM=OL ⇒ 3y-6=7 ⇒ 3y=13 ⇒ y=4.3
Hence, x=12 and y=4.3
Because the last equation already has the y eliminated so just need to get the other two to eliminate the y too
multiply 4 to the first equation to eliminate y, and you get
-4x-4y-4z=-32
-4x+4y+5z=7
now get rid of y so all you have left is
-8x+z=-25 (let call this equation #4)
now take equation #3 and #4 together to solve for one of the variables, i’ll solve for z first so i’ll get rid of x by multiply the equation #4 all by 4, you get
8x+8z=16
-8x+z=-25
solve it and get 9z= -9; z=-1
now you have z so take it and ply it into equation #3
2x+2(-1)=4
2x=6; x=3
take both of them, plug it in equation #1
-3-y-(-1)=-8
-y=-6 ; y=6
done so the answer is (x,y,z) = (3,6,-1)
Answer:
x ≈ 41
Step-by-step explanation:
All the angles in a quadrilateral add together to equal 360°
So set up the equation:
a + b + c + d = 360°
Now fill in the values we know:
x + _ + 4x + 2x - 10 + 85 = 360
7x + 75 = 360
Now subtract both sides by 75:
7x + 75 - 75 = 360 - 75
7x = 285
Divide both sides by 7:
7x / 7 = 285 / 7
x = 40.714
Round:
x = 41
Now to check our answer, substitute 41 for x in the equation:
(41) + _ + 4(41) + 2(41) - 10 + 85
(41) + 164 + 82 - 10 + 85 = 362
The answer is close to 360, so we know it is correct
