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]
