Point n is on line segment \overline{mo} mo . given mo=3x+6,mo=3x+6, no=5x,no=5x, and mn=x,mn=x, determine the numerical length of \overline{no}. no .

The numerical length of NO is 10

If point N is on line segment MO, this means that:

Given the following parameters

MO=3x+6

NO=5x

MN = x

Substitute the given values into the formula:

x + 5x = 3x + 6

6x = 3x + 6

6x - 3x = 6

3x = 6

x = 6/3

x = 2

Get the length NO:

NO = 5x

NO = 5(2)

NO = 10

Therefore the numerical length of NO is 10

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  NO = 10

Step-by-step explanation:

The segment addition theorem tells you ...

  MN + NO = MO

Substituting the given expressions for these lengths, we have ...

  x + 5x = 3x+6

  3x = 6 . . . . . . . . . subtract 3x

  x = 2 . . . . . . . . . . divide by 3

We can use this value to find the length NO:

  NO = 5x = 5(2) . . . . substitute for x

  NO = 10