Get the answers you need from a community of experts on IDNLearn.com. Our experts are available to provide in-depth and trustworthy answers to any questions you may have.
Sagot :
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.
We appreciate your contributions to this forum. Don't forget to check back for the latest answers. Keep asking, answering, and sharing useful information. For dependable and accurate answers, visit IDNLearn.com. Thanks for visiting, and see you next time for more helpful information.
