<em><u>Answer:</u></em>
MN = 4 units
<u><em>Explanation:</em></u>
<u>1- getting the value of m:</u>
<u>We are given that:</u>
NQ = 4m and NQ = 12
<u>This means that:</u>
12 = 4m
m = 3
<u>2- getting MQ:</u>
<u>We are given that:</u>
MQ = 5m + 1
<u>We have calculated that:</u>
m = 3
<u>Therefore:</u>
MQ = 5(3) + 1 = 15 + 1 = 16 units
<u>3- getting MN:</u>
We are given that point N is located somewhere between points M and Q.
<u>This means that:</u>
line MQ can be divided into two portions: MN and NQ
<u>This also means that:</u>
length of MQ = length of MN + length of NQ
<u>We have calculated that:</u>
MQ = 16 units
<u>We are given that:</u>
NQ = 12 units
<u>Therefore:</u>
16 = length of MN + 12
length of MN = 16 - 12
length of MN = 4 units
Hope this helps :)
MN = 4 units
<u><em>Explanation:</em></u>
<u>1- getting the value of m:</u>
<u>We are given that:</u>
NQ = 4m and NQ = 12
<u>This means that:</u>
12 = 4m
m = 3
<u>2- getting MQ:</u>
<u>We are given that:</u>
MQ = 5m + 1
<u>We have calculated that:</u>
m = 3
<u>Therefore:</u>
MQ = 5(3) + 1 = 15 + 1 = 16 units
<u>3- getting MN:</u>
We are given that point N is located somewhere between points M and Q.
<u>This means that:</u>
line MQ can be divided into two portions: MN and NQ
<u>This also means that:</u>
length of MQ = length of MN + length of NQ
<u>We have calculated that:</u>
MQ = 16 units
<u>We are given that:</u>
NQ = 12 units
<u>Therefore:</u>
16 = length of MN + 12
length of MN = 16 - 12
length of MN = 4 units
Hope this helps :)