Let's analyze the tables to determine the values of [tex]\( m \)[/tex] and [tex]\( n \)[/tex].
### First Table
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & & 25 & m & 51 \\
\hline
y & 10 & 11 & 12 & 13 & & n & 39 & 60 \\
\hline
\end{array}
\][/tex]
To identify the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[
\begin{align*}
x = 1 & \implies y = 10 \\
x = 2 & \implies y = 11 \\
x = 3 & \implies y = 12 \\
x = 4 & \implies y = 13 \\
\end{align*}
\][/tex]
The consistent pattern here shows that [tex]\( y = x + 9 \)[/tex].
Given [tex]\( y = 25 \)[/tex]:
[tex]\[ m = 25 + 9 = 34 \][/tex]
Now with [tex]\( x = m = 34 \)[/tex], let's find [tex]\( n \)[/tex]:
### Second Table
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|c|}
\hline
x & 1 & 2 & 3 & 4 & & m & 30 & 60 \\
\hline
y & 2 & 4 & 6 & 8 & & 22 & n & 120 \\
\hline
\end{array}
\][/tex]
Identifying the relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex]:
[tex]\[
\begin{align*}
x = 1 & \implies y = 2 \\
x = 2 & \implies y = 4 \\
x = 3 & \implies y = 6 \\
x = 4 & \implies y = 8 \\
\end{align*}
\][/tex]
The consistent pattern here shows that [tex]\( y = 2x \)[/tex].
Now with [tex]\( x = m = 34 \)[/tex], we find [tex]\( n \)[/tex]:
[tex]\[ n = 2 \times 34 = 68 \][/tex]
### Final Intermediate Results and Conclusion
So, from the patterns and given calculations:
- The value of [tex]\( m \)[/tex] is 34.
- The value of [tex]\( n \)[/tex] is 68.
Thus:
[tex]\[ m = 34 \][/tex]
[tex]\[ n = 68 \][/tex]
