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Sagot :
To determine which table represents a car that increases and then decreases its speed, we need to evaluate each table for this pattern. We'll do this step-by-step for each table.
1. First Table:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline Time (min) & 5 & 6 & 7 & 8 & 9 \\ \hline Speed (mph) & 45 & 43 & 41 & 42 & 43 \\ \hline \end{tabular} \][/tex]
- At 6 minutes, the speed decreases to 43 mph.
- At 7 minutes, the speed further decreases to 41 mph.
- At 8 minutes, the speed increases to 42 mph.
- At 9 minutes, the speed further increases to 43 mph.
This table shows a decrease, followed by an increase. It doesn't show an increase followed by a decrease.
2. Second Table:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline Time (min) & 5 & 6 & 7 & 8 & 9 \\ \hline Speed (mph) & 45 & 47 & 49 & 48 & 47 \\ \hline \end{tabular} \][/tex]
- At 6 minutes, the speed increases to 47 mph.
- At 7 minutes, the speed further increases to 49 mph.
- At 8 minutes, the speed decreases to 48 mph.
- At 9 minutes, the speed further decreases to 47 mph.
This table demonstrates an increase in speed followed by a decrease, which matches the required pattern.
3. Third Table:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline Time (min) & 5 & 6 & 7 & 8 & 9 \\ \hline Speed (mph) & 45 & 45 & 45 & 43 & 41 \\ \hline \end{tabular} \][/tex]
- The speed remains constant at 45 mph from 5 to 7 minutes.
- At 8 minutes, the speed decreases to 43 mph.
- At 9 minutes, the speed further decreases to 41 mph.
This table shows a constant speed followed by a decrease. It does not show an increase followed by a decrease.
4. Fourth Table:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline Time (min) & 5 & 6 & 7 & 8 & 9 \\ \hline Speed (mph) & 45 & 43 & 41 & 41 & 41 \\ \hline \end{tabular} \][/tex]
- At 6 minutes, the speed decreases to 43 mph.
- At 7 minutes, the speed further decreases to 41 mph.
- The speed then remains constant at 41 mph at 8 and 9 minutes.
This table shows a decrease and then constant speed. It does not show an increase followed by a decrease.
After analyzing all the tables, we can see that the second table is the only one that shows a speed increase followed by a decrease. Therefore, the table that could represent the speed of the car when it increases and then decreases its speed is:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline Time (min) & 5 & 6 & 7 & 8 & 9 \\ \hline Speed (mph) & 45 & 47 & 49 & 48 & 47 \\ \hline \end{tabular} \][/tex]
1. First Table:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline Time (min) & 5 & 6 & 7 & 8 & 9 \\ \hline Speed (mph) & 45 & 43 & 41 & 42 & 43 \\ \hline \end{tabular} \][/tex]
- At 6 minutes, the speed decreases to 43 mph.
- At 7 minutes, the speed further decreases to 41 mph.
- At 8 minutes, the speed increases to 42 mph.
- At 9 minutes, the speed further increases to 43 mph.
This table shows a decrease, followed by an increase. It doesn't show an increase followed by a decrease.
2. Second Table:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline Time (min) & 5 & 6 & 7 & 8 & 9 \\ \hline Speed (mph) & 45 & 47 & 49 & 48 & 47 \\ \hline \end{tabular} \][/tex]
- At 6 minutes, the speed increases to 47 mph.
- At 7 minutes, the speed further increases to 49 mph.
- At 8 minutes, the speed decreases to 48 mph.
- At 9 minutes, the speed further decreases to 47 mph.
This table demonstrates an increase in speed followed by a decrease, which matches the required pattern.
3. Third Table:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline Time (min) & 5 & 6 & 7 & 8 & 9 \\ \hline Speed (mph) & 45 & 45 & 45 & 43 & 41 \\ \hline \end{tabular} \][/tex]
- The speed remains constant at 45 mph from 5 to 7 minutes.
- At 8 minutes, the speed decreases to 43 mph.
- At 9 minutes, the speed further decreases to 41 mph.
This table shows a constant speed followed by a decrease. It does not show an increase followed by a decrease.
4. Fourth Table:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline Time (min) & 5 & 6 & 7 & 8 & 9 \\ \hline Speed (mph) & 45 & 43 & 41 & 41 & 41 \\ \hline \end{tabular} \][/tex]
- At 6 minutes, the speed decreases to 43 mph.
- At 7 minutes, the speed further decreases to 41 mph.
- The speed then remains constant at 41 mph at 8 and 9 minutes.
This table shows a decrease and then constant speed. It does not show an increase followed by a decrease.
After analyzing all the tables, we can see that the second table is the only one that shows a speed increase followed by a decrease. Therefore, the table that could represent the speed of the car when it increases and then decreases its speed is:
[tex]\[ \begin{tabular}{|l|c|c|c|c|c|} \hline Time (min) & 5 & 6 & 7 & 8 & 9 \\ \hline Speed (mph) & 45 & 47 & 49 & 48 & 47 \\ \hline \end{tabular} \][/tex]
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