To determine which expression can correctly be used to find the output numbers from the given input numbers, let's evaluate each given expression using the inputs and comparing the results with the outputs.
We need to assess the following expressions given the input-output pairs:
- Input (p): [108, 117, 126, 135]
- Output: [12, 13, 14, 15]
### Expression 1: [tex]\( p \div 9 \)[/tex]
Let's divide each input by 9 and see if it matches the corresponding output.
For [tex]\( p = 108 \)[/tex]:
[tex]\( 108 \div 9 = 12 \)[/tex]
For [tex]\( p = 117 \)[/tex]:
[tex]\( 117 \div 9 = 13 \)[/tex]
For [tex]\( p = 126 \)[/tex]:
[tex]\( 126 \div 9 = 14 \)[/tex]
For [tex]\( p = 135 \)[/tex]:
[tex]\( 135 \div 9 = 15 \)[/tex]
The calculated outputs [12, 13, 14, 15] match perfectly with the given outputs. Hence, this expression works!
### Expression 2: [tex]\( 9p \)[/tex]
Let's multiply each input by 9 and check the results:
For [tex]\( p = 108 \)[/tex]:
[tex]\( 9 \times 108 = 972 \)[/tex]
For [tex]\( p = 117 \)[/tex]:
[tex]\( 9 \times 117 = 1053 \)[/tex]
For [tex]\( p = 126 \)[/tex]:
[tex]\( 9 \times 126 = 1134 \)[/tex]
For [tex]\( p = 135 \)[/tex]:
[tex]\( 9 \times 135 = 1215 \)[/tex]
The calculated outputs [972, 1053, 1134, 1215] do not match the given outputs. So, this expression does not work.
### Expression 3: [tex]\( \frac{9}{p} \)[/tex]
Let's divide 9 by each input and verify the results:
For [tex]\( p = 108 \)[/tex]:
[tex]\( \frac{9}{108} = 0.0833 \)[/tex]
For [tex]\( p = 117 \)[/tex]:
[tex]\( \frac{9}{117} = 0.0769 \)[/tex]
For [tex]\( p = 126 \)[/tex]:
[tex]\( \frac{9}{126} = 0.0714 \)[/tex]
For [tex]\( p = 135 \)[/tex]:
[tex]\( \frac{9}{135} = 0.0667 \)[/tex]
The calculated outputs [0.0833, 0.0769, 0.0714, 0.0667] are far from the given outputs. Thus, this expression does not work either.
### Expression 4: [tex]\( 96 - p \)[/tex]
Now, let's subtract each input from 96:
For [tex]\( p = 108 \)[/tex]:
[tex]\( 96 - 108 = -12 \)[/tex]
For [tex]\( p = 117 \)[/tex]:
[tex]\( 96 - 117 = -21 \)[/tex]
For [tex]\( p = 126 \)[/tex]:
[tex]\( 96 - 126 = -30 \)[/tex]
For [tex]\( p = 135 \)[/tex]:
[tex]\( 96 - 135 = -39 \)[/tex]
The calculated outputs [-12, -21, -30, -39] do not match the given outputs, so this expression is also incorrect.
### Conclusion:
The correct expression that matches the given input-output pairs in the table is [tex]\( p \div 9 \)[/tex].
