Question

If NO = 2y + 11, OP = 3y - 2, NP = 6y +3, and
MP = 64, find each value.
a. NO
b. MN

Answer 1

A line segment can be divided into several subsegments. The values of NO and MN are 15 and 49, respectively.

Given that:

$NO = 2y + 11$

$OP = 3y - 2$

$NP = 6y + 3$

$MP = 64$

The equation of NP is:

$NP = NO + OP$

So, we have:

$6y + 3 = 2y + 11$

Collect like terms

$6y -2y = 11 - 3$

$4y = 8$

Divide by 4

$y = 2$

So, the value of NO is:

$NO = 2y + 11$

$NO = 2 \times 2 + 11$

$NO =15$

And the value of MN is:

$MN = MP - NP$

Substitute values for MP and NP

$MN = 64 - 6y -3$

Substitute $y = 2$

$MN = 64 - 6\times 2 -3$

$MN = 49$

Hence, the values of NO and MN are 15 and 49, respectively.

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