11. This table shows some outcomes from the function [tex]x \rightarrow 2x + 3[/tex]. Complete the output column of the table.

[tex]\[
\begin{tabular}{|c|c|}
\hline
Input & Output \\
\hline
1 & 5 \\
\hline
6 & \\
\hline
9 & \\
\hline
15 & 33 \\
\hline
\end{tabular}
\][/tex]

12. Look at the following equation.

[tex]\[45.6 \div 1.2 = 38\][/tex]



Answer :

Certainly! Let's complete the table by determining the outputs for the given inputs according to the function [tex]\( x \rightarrow 2x + 3 \)[/tex].

The function defines a rule: for any input [tex]\( x \)[/tex], the output is calculated as [tex]\( 2x + 3 \)[/tex].

1. Input: 1
- For [tex]\( x = 1 \)[/tex], the output is:
[tex]\[ 2(1) + 3 = 2 + 3 = 5 \][/tex]
- The table already shows the output for input 1 as 5, which is correct.

2. Input: 6
- For [tex]\( x = 6 \)[/tex], the output is:
[tex]\[ 2(6) + 3 = 12 + 3 = 15 \][/tex]
- So the output for input 6 is 15.

3. Input: 9
- For [tex]\( x = 9 \)[/tex], the output is:
[tex]\[ 2(9) + 3 = 18 + 3 = 21 \][/tex]
- So the output for input 9 is 21.

4. Input: 15
- For [tex]\( x = 15 \)[/tex], the output is:
[tex]\[ 2(15) + 3 = 30 + 3 = 33 \][/tex]
- The table confirms the output for input 15 as 33, which is correct.

Now we can complete the table based on our calculated outputs:
[tex]\[ \begin{array}{|c|c|} \hline \text{input} & \text{output} \\ \hline 1 & 5 \\ \hline 6 & 15 \\ \hline 9 & 21 \\ \hline 15 & 33 \\ \hline \end{array} \][/tex]

Regarding the equation [tex]\( 45.6 \div 1.2 = 38 \)[/tex]:

This equation needs verification, but there's a mistake in it as [tex]\( 45.6 \div 1.2 \)[/tex] should be equal to 38.

By dividing 45.6 by 1.2:

[tex]\[ 45.6 \div 1.2 = 38 \][/tex]

It's clear that something doesn't add up in the equation given. Generally, it maintains relevance to cross-check your work for accuracy.


So, the table filled with the correct outputs is:
[tex]\[ \begin{array}{|c|c|} \hline \text{input} & \text{output} \\ \hline 1 & 5 \\ \hline 6 & 15 \\ \hline 9 & 21 \\ \hline 15 & 33 \\ \hline \end{array} \][/tex]