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If O N = 8 x − 8 , L M = 7 x + 4 , N M = x − 5 , and O L = 3 y − 6 , find the values of x and y for which LMNO must be a parallelogram. The diagram is not drawn to scale.

If O N 8 x 8 L M 7 x 4 N M x 5 and O L 3 y 6 find the values of x and y for which LMNO must be a parallelogram The diagram is not drawn to scale class=

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TaeKwonDoIsDead

Answer:

[tex]x=12\\y=\frac{13}{3}[/tex]


Step-by-step explanation:

For it to be a parallelogram, opposite sides have to be of same length.

  • OL = NM, and
  • ON = LM

Using the expressions given, we can make 2 equations:

Equation 1:

[tex]OL=NM\\3y-6=x-5\\-x+3y=1[/tex]


Equation 2:

[tex]ON=LM\\8x-8=7x+4\\[/tex]


Solving equation 2, we have x:

[tex]8x-8=7x+4\\8x-7x=4+8\\x=12[/tex]

Plugging this value of x into equation 1, we can solve for y:

[tex]-x+3y=1\\-(12)+3y=1\\-12+3y=1\\3y=13\\y=\frac{13}{3}[/tex]

So,

[tex]x=12\\y=\frac{13}{3}[/tex]



doxiluv3

Answer:

x=12 and y=13/3

Step-by-step explanation:

!!This is the right answer, other one the math is wrong!!

For a parallelogram, opposite sides must be equal.

ON = LM

8x-8 = 7x+4

x = 12

OL = NM

3y-6 = x-5

3y-6 = 12-5

3y = 13

y = 13/3

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