Answer:

n = 3/10, or N = 0.3

Step-by-step explanation:

For the first problem:

Since QE = QI + EI, we can substitute the given values to get:

2m + 3 = QI + (m + 10)

Simplifying this equation gives:

QI = m - 7

To find m, we can substitute QI back into the original equation and solve for m:

QE = 2m + 3 = QI + EI = (m - 7) + (m + 10) = 2m + 3

Simplifying this equation gives:

2m + 3 = 2m + 3

This means that the equation is true for any value of m, so m can be any real number.

Therefore, m is undefined, and QI = m - 7 is also undefined.

For the second problem:

We are given that TU = 34 and EU = 4n + 1. We can use this information to find N by solving for n:

TU = TE + EU

TE = TU - EU = 34 - (4n + 1) = 33 - 4n

We know that TE = TN + NE, so we can substitute the given values to get:

TN + NE = 33 - 4n

Since NE = EU = 4n + 1, we can substitute this into the equation to get:

TN + 4n + 1 = 33 - 4n

Simplifying this equation gives:

TN = 32 - 8n

We also know that TN = TM + MN, so we can substitute the given value of TU to get:

TU = TM + TN + NE

Substituting the values we've found for TN and NE gives:

34 = TM + (32 - 8n) + (4n + 1)

Simplifying this equation gives:

TM = -5n + 1

We know that TM = TN + NM, so we can substitute the given value of TE to get:

TE = TN + NM

Substituting the values we've found for TM and TN gives:

33 - (4n + 1) = (32 - 8n) + NM

Simplifying this equation gives:

NM = 5n - 2

Therefore, we have found that TM = -5n + 1 and NM = 5n - 2. To find N, we can set these equations equal to each other:

-5n + 1 = 5n - 2

Simplifying this equation gives:

10n = 3

Therefore, n = 3/10, or N = 0.3.