To determine which ordered pair should be discarded because the values are unreasonable, let's analyze each pair in the context of the height [tex]\( y \)[/tex] of a falling object [tex]\( x \)[/tex] seconds after it is dropped.
### Ordered Pair Analysis
1. [tex]\((-4, 1)\)[/tex]:
- Here, [tex]\( x = -4 \)[/tex] seconds and [tex]\( y = 1 \)[/tex] meter.
- Time cannot be negative, so [tex]\(-4\)[/tex] seconds is not a reasonable value.
2. [tex]\(\left(\frac{9}{4}, 24\right)\)[/tex]:
- Here, [tex]\( x = \frac{9}{4} = 2.25 \)[/tex] seconds and [tex]\( y = 24 \)[/tex] meters.
- Both the time and height values are positive and seem reasonable.
3. [tex]\(\left(5, \frac{3}{2}\right)\)[/tex]:
- Here, [tex]\( x = 5 \)[/tex] seconds and [tex]\( y = \frac{3}{2} = 1.5 \)[/tex] meters.
- Both the time and height values are positive and seem reasonable.
4. [tex]\((6, 0)\)[/tex]:
- Here, [tex]\( x = 6 \)[/tex] seconds and [tex]\( y = 0 \)[/tex] meters.
- Both the time and height values are non-negative. The object hitting the ground at 0 meters seems reasonable.
### Conclusion
Based on the analysis above, the only unreasonable ordered pair is [tex]\((-4, 1)\)[/tex] because time ([tex]\(-4\)[/tex] seconds) cannot be negative.
Thus, the ordered pair [tex]\((-4, 1)\)[/tex] should be discarded because the values are unreasonable.
