Answered

A car increases, then decreases, its speed. Which table could represent the speed of the car?

\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}

\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}

\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}

\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}



Answer :

GinnyAnswer
To determine which table represents the speed of a car that increases and then decreases, let's analyze each of the given tables step-by-step.

Table 1:
[tex]\[ \begin{array}{|l|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 43 & 41 & 42 & 43 \\ \hline \end{array} \][/tex]
- At time 5 min: Speed = 45 mph
- At time 6 min: Speed = 43 mph (decreasing)
- At time 7 min: Speed = 41 mph (decreasing)
- At time 8 min: Speed = 42 mph (increasing)
- At time 9 min: Speed = 43 mph (increasing)

Here, the speed decreases until 7 min, then increases from 8 min onward.

Table 2:
[tex]\[ \begin{array}{|l|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 47 & 49 & 48 & 47 \\ \hline \end{array} \][/tex]
- At time 5 min: Speed = 45 mph
- At time 6 min: Speed = 47 mph (increasing)
- At time 7 min: Speed = 49 mph (increasing)
- At time 8 min: Speed = 48 mph (decreasing)
- At time 9 min: Speed = 47 mph (decreasing)

Here, the speed increases until 7 min, then decreases from 8 min onward.

Table 3:
[tex]\[ \begin{array}{|l|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 45 & 45 & 43 & 41 \\ \hline \end{array} \][/tex]
- At time 5 min: Speed = 45 mph
- At time 6 min: Speed = 45 mph (constant)
- At time 7 min: Speed = 45 mph (constant)
- At time 8 min: Speed = 43 mph (decreasing)
- At time 9 min: Speed = 41 mph (decreasing)

Here, the speed remains constant initially, then it decreases from 8 min onward.

Table 4:
[tex]\[ \begin{array}{|l|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 43 & 41 & 41 & 41 \\ \hline \end{array} \][/tex]
- At time 5 min: Speed = 45 mph
- At time 6 min: Speed = 43 mph (decreasing)
- At time 7 min: Speed = 41 mph (decreasing)
- At time 8 min: Speed = 41 mph (constant)
- At time 9 min: Speed = 41 mph (constant)

Here, the speed consistently decreases until it becomes constant from 7 min onward.

Given these observations, the table that matches a scenario where the car's speed increases first and then decreases is:

Table 2:
[tex]\[ \begin{array}{|l|c|c|c|c|c|} \hline \text{Time (min)} & 5 & 6 & 7 & 8 & 9 \\ \hline \text{Speed (mph)} & 45 & 47 & 49 & 48 & 47 \\ \hline \end{array} \][/tex]

So, the correct table is table 2.