Using the coordinate plane below, determine the missing numbers in the following table.

\begin{tabular}{|l|l|}
\hline
\multicolumn{1}{|c|}{} & \\
\hline
4 & (A) \\
\hline
7 & 2 \\
\hline
9 & 4 \\
\hline
17 & 9 \\
\hline
(B) & \\
\hline
\end{tabular}



Answer :

To determine the missing numbers in the given table, we'll analyze the existing pattern in the numerical data provided. Here's the table again for reference:

[tex]\[ \begin{array}{|c|c|} \hline 4 & A \\ \hline 7 & 2 \\ \hline 9 & 4 \\ \hline 17 & 9 \\ \hline B & \\ \hline \end{array} \][/tex]

1. Identify the Pattern in the Second Column:
- For [tex]\( (4, A) \)[/tex]
- For [tex]\( (7, 2) \)[/tex]
- For [tex]\( (9, 4) \)[/tex]
- For [tex]\( (17, 9) \)[/tex]

- We note the changes in the second column as follows:
- [tex]\( 2 - A \)[/tex]
- [tex]\( 4 - 2 = 2 \)[/tex]
- [tex]\( 9 - 4 = 5 \)[/tex]

2. Identify the Possible Values for A:
- Let's observe the first few values and understand how the pattern might have formed:
- Since [tex]\( 4 \rightarrow A \)[/tex] (A is unknown)
- [tex]\( 7 \rightarrow 2 \)[/tex]
- [tex]\( 9 \rightarrow 4 \)[/tex]

Since there’s no clear linear relationship that's immediately apparent, we determine that
[tex]\( A = 2 \)[/tex]. Thus:
[tex]\[ A = 2 \][/tex]

3. Identify the Pattern in the First Column:
- For [tex]\( - \)[/tex]
- For [tex]\( (7, 2) \)[/tex]
- For [tex]\( (9, 4) \)[/tex]
- For [tex]\( (17, 9) \)[/tex]
- For [tex]\( B \rightarrow \)[/tex] none available
- Note the pattern:
- [tex]\( 4 + 3 = 7 \)[/tex]
- [tex]\( 7 + 2 = 9 \)[/tex]
- The pattern sequence up (is now adding next higher non same numerical in first column i.e., 8 [tex]\(\rightarrow new Gap) Values excercise then becomes : - 4, surmise, inputs incrementally 7 + 2 (without repeat too is. Thus \( B= \)[/tex], its first now note as related to previous 17 subtracted

( 17 - 9) "around next preceding second value")

In conclusion:

The missing numbers (A) and (B) in the given table are:
[tex]\[ A = 2 \quad \text{and} \quad B = 9 \][/tex]

Thus final table becomes :

\)
\begin{array}{|c|c|}
\hline
4 & 2 \\
\hline
7 & 2 \\
\hline
9 & 4 \\
\hline
17 & 9 \\
\hline
9 &\\
\hline
\("/",)