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Sagot :
To determine which table represents the speed of the car increasing and then decreasing, we need to analyze the speed pattern over time for each table.
Let's look at each table in detail:
### 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]
- From 5 to 6 minutes: speed decreases from 45 to 43.
- From 6 to 7 minutes: speed decreases from 43 to 41.
- From 7 to 8 minutes: speed increases from 41 to 42.
- From 8 to 9 minutes: speed increases from 42 to 43.
This table does not show a consistent pattern of increasing then decreasing speed.
### 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]
- From 5 to 6 minutes: speed increases from 45 to 47.
- From 6 to 7 minutes: speed increases from 47 to 49.
- From 7 to 8 minutes: speed decreases from 49 to 48.
- From 8 to 9 minutes: speed decreases from 48 to 47.
This table shows the pattern of speed increasing then decreasing. Therefore, this table matches the required pattern.
### 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]
- From 5 to 6 minutes: speed remains constant at 45.
- From 6 to 7 minutes: speed remains constant at 45.
- From 7 to 8 minutes: speed decreases from 45 to 43.
- From 8 to 9 minutes: speed decreases from 43 to 41.
This table shows a pattern of constant speed followed by a decrease. So, it does not match the required pattern.
### 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]
- From 5 to 6 minutes: speed decreases from 45 to 43.
- From 6 to 7 minutes: speed decreases from 43 to 41.
- From 7 to 8 minutes: speed remains constant at 41.
- From 8 to 9 minutes: speed remains constant at 41.
This table shows a pattern of decreasing speed followed by a constant speed. So, it does not match the required pattern.
### Conclusion:
The table that represents the speed of the car increasing then decreasing is:
[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]
Thus, the answer is Table 2.
Let's look at each table in detail:
### 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]
- From 5 to 6 minutes: speed decreases from 45 to 43.
- From 6 to 7 minutes: speed decreases from 43 to 41.
- From 7 to 8 minutes: speed increases from 41 to 42.
- From 8 to 9 minutes: speed increases from 42 to 43.
This table does not show a consistent pattern of increasing then decreasing speed.
### 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]
- From 5 to 6 minutes: speed increases from 45 to 47.
- From 6 to 7 minutes: speed increases from 47 to 49.
- From 7 to 8 minutes: speed decreases from 49 to 48.
- From 8 to 9 minutes: speed decreases from 48 to 47.
This table shows the pattern of speed increasing then decreasing. Therefore, this table matches the required pattern.
### 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]
- From 5 to 6 minutes: speed remains constant at 45.
- From 6 to 7 minutes: speed remains constant at 45.
- From 7 to 8 minutes: speed decreases from 45 to 43.
- From 8 to 9 minutes: speed decreases from 43 to 41.
This table shows a pattern of constant speed followed by a decrease. So, it does not match the required pattern.
### 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]
- From 5 to 6 minutes: speed decreases from 45 to 43.
- From 6 to 7 minutes: speed decreases from 43 to 41.
- From 7 to 8 minutes: speed remains constant at 41.
- From 8 to 9 minutes: speed remains constant at 41.
This table shows a pattern of decreasing speed followed by a constant speed. So, it does not match the required pattern.
### Conclusion:
The table that represents the speed of the car increasing then decreasing is:
[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]
Thus, the answer is Table 2.
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