Find the value of x and MN

x =13, MN = 71

Step-by-step explanation:

ΔNMP and ΔNPO and equal, this is true because of the two lines on MO telling that they are parallel,

So, MN  =  ON

=> 4x + 19 = 6x - 7

=> 4x - 6x = -7 -19

=> -2x = -26

=> 2x = 26

=> x =26/2

=> x =13

therefore x =13, now we can solve for MN,

=> 4x + 19

=> 4 * 13 + 19

=> 52 + 19

=> 71

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x = 13 ; MN = 71

Step-by-step explanation:

NP is perpendicular bisector of OM.

=> MP = OP

Also here we get 2 right angled triangles named MPN & OPN.

In triangle MPN ,

because MP = OP.

In triangle OPN ,

But

Hence ,

Value of MN = 4x + 19

Value of ON = 6x - 7

So,

So MN = 4×13 + 19 = 71

y = 3x+4

step-by-step explanation:

to find the slope

slope = (y2-y1)/ (x2-x1)

    = (-8-4)/ (-4-0)

    = -12/-4

  = 3

using the slope intercept form of a line

y= mx+b

we know the slope is 3

we know the y intercept is 4 ( the point where it crosses the y axis or x=0)

y = 3x+4