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To determine which table represents the speed of the car appropriately increasing and then decreasing, we'll analyze each speed sequence provided in the tables step-by-step.
Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time } (min) & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed } (mph) & 45 & 43 & 41 & 42 & 43 \\ \hline \end{array} \][/tex]
For the speed to first increase and then decrease, we need to identify a pattern where the initial speeds rise before falling. In Table 1:
- Speed at 6 min (43 mph) is less than speed at 5 min (45 mph) -> Decrease
- Speed at 7 min (41 mph) is less than speed at 6 min (43 mph) -> Decrease
- Speed at 8 min (42 mph) is more than speed at 7 min (41 mph) -> Increase
- Speed at 9 min (43 mph) is more than speed at 8 min (42 mph) -> Increase
This table does not show a clear increase before decrease. Thus, Table 1 is not valid.
Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time } (min) & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed } (mph) & 45 & 47 & 49 & 48 & 47 \\ \hline \end{array} \][/tex]
In Table 2:
- Speed at 6 min (47 mph) is more than speed at 5 min (45 mph) -> Increase
- Speed at 7 min (49 mph) is more than speed at 6 min (47 mph) -> Increase
- Speed at 8 min (48 mph) is less than speed at 7 min (49 mph) -> Decrease
- Speed at 9 min (47 mph) is less than speed at 8 min (48 mph) -> Decrease
This table shows the speed increasing before decreasing. Thus, Table 2 is valid.
Table 3:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time } (min) & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed } (mph) & 45 & 45 & 45 & 43 & 41 \\ \hline \end{array} \][/tex]
In Table 3:
- Speed at 6 min (45 mph) is equal to speed at 5 min (45 mph) -> Constant
- Speed at 7 min (45 mph) is equal to speed at 6 min (45 mph) -> Constant
- Speed at 8 min (43 mph) is less than speed at 7 min (45 mph) -> Decrease
- Speed at 9 min (41 mph) is less than speed at 8 min (43 mph) -> Decrease
This table does not show any increase. Thus, Table 3 is not valid.
Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time } (min) & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed } (mph) & 45 & 43 & 41 & 41 & 41 \\ \hline \end{array} \][/tex]
In Table 4:
- Speed at 6 min (43 mph) is less than speed at 5 min (45 mph) -> Decrease
- Speed at 7 min (41 mph) is less than speed at 6 min (43 mph) -> Decrease
- Speed at 8 min (41 mph) is equal to speed at 7 min (41 mph) -> Constant
- Speed at 9 min (41 mph) is equal to speed at 8 min (41 mph) -> Constant
This table does not show any increase. Thus, Table 4 is not valid.
Based on this analysis, the table that correctly represents the car's speed increasing and then decreasing is Table 2.
Table 1:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time } (min) & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed } (mph) & 45 & 43 & 41 & 42 & 43 \\ \hline \end{array} \][/tex]
For the speed to first increase and then decrease, we need to identify a pattern where the initial speeds rise before falling. In Table 1:
- Speed at 6 min (43 mph) is less than speed at 5 min (45 mph) -> Decrease
- Speed at 7 min (41 mph) is less than speed at 6 min (43 mph) -> Decrease
- Speed at 8 min (42 mph) is more than speed at 7 min (41 mph) -> Increase
- Speed at 9 min (43 mph) is more than speed at 8 min (42 mph) -> Increase
This table does not show a clear increase before decrease. Thus, Table 1 is not valid.
Table 2:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time } (min) & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed } (mph) & 45 & 47 & 49 & 48 & 47 \\ \hline \end{array} \][/tex]
In Table 2:
- Speed at 6 min (47 mph) is more than speed at 5 min (45 mph) -> Increase
- Speed at 7 min (49 mph) is more than speed at 6 min (47 mph) -> Increase
- Speed at 8 min (48 mph) is less than speed at 7 min (49 mph) -> Decrease
- Speed at 9 min (47 mph) is less than speed at 8 min (48 mph) -> Decrease
This table shows the speed increasing before decreasing. Thus, Table 2 is valid.
Table 3:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time } (min) & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed } (mph) & 45 & 45 & 45 & 43 & 41 \\ \hline \end{array} \][/tex]
In Table 3:
- Speed at 6 min (45 mph) is equal to speed at 5 min (45 mph) -> Constant
- Speed at 7 min (45 mph) is equal to speed at 6 min (45 mph) -> Constant
- Speed at 8 min (43 mph) is less than speed at 7 min (45 mph) -> Decrease
- Speed at 9 min (41 mph) is less than speed at 8 min (43 mph) -> Decrease
This table does not show any increase. Thus, Table 3 is not valid.
Table 4:
[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline \text{Time } (min) & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed } (mph) & 45 & 43 & 41 & 41 & 41 \\ \hline \end{array} \][/tex]
In Table 4:
- Speed at 6 min (43 mph) is less than speed at 5 min (45 mph) -> Decrease
- Speed at 7 min (41 mph) is less than speed at 6 min (43 mph) -> Decrease
- Speed at 8 min (41 mph) is equal to speed at 7 min (41 mph) -> Constant
- Speed at 9 min (41 mph) is equal to speed at 8 min (41 mph) -> Constant
This table does not show any increase. Thus, Table 4 is not valid.
Based on this analysis, the table that correctly represents the car's speed increasing and then decreasing is Table 2.
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