MATH SOLVE

2 months ago

Q:
# The graph shows the results of a race between Damon and Alex. Both boys begin the race at the same time.Which statements are true about the race?Select each correct answer.Alex runs the race at a rate of 623 yd/s .PDamon is given a 20 yd head start and wins the race.Damon runs the race at rate of 10 yd/s .Alex is given a 20 yd head start and wins the race.Damon finishes the race 2 s after Alex finishes the race.Alex runs the race faster than Damon.

Accepted Solution

A:

Answer:1st and 3rd statements are true.Sep by step explanation: We have been given a graph that shows the results of a race between Damon and Alex. Both boys begin the race at the same time.Let us see which of the given option are correct.1. Let us find Alex's speed using slope of the graph.[tex]\text{Slope}=\frac{80-0}{0-12}[/tex][tex]\text{Slope}=\frac{80}{-12}[/tex][tex]\text{Slope}=-6\frac{8}{12}[/tex][tex]\text{Slope}=-6\frac{2}{3}[/tex]Slope is showing remaining distance per second. The distance is decreasing [tex]6\frac{2}{3}[/tex] yards per second. Therefore, Alex is running at a rate of [tex]6\frac{2}{3}[/tex] yards per second and 1st statement is the true.2. We can see from our graph that before starting the race Damon's distance from finish line is 100 yards and Alex's distance from finish line is 80 yards, therefore, Alex got a 20 yard head start. Therefore, 2nd statement is false. 3. Let us find speed of Damon using slope.[tex]\text{Slope}=\frac{100-0}{0-10}[/tex][tex]\text{Slope}=\frac{100}{-10}[/tex][tex]\text{Slope}=-10[/tex] We can see that slope is showing remaining distance per second. The distance is decreasing 10 yards per second therefore, Damon is running at a rate of 10 yards per second and 3rd statement is true. 4. We have already seen that Alex is given a 20 yard head start but he lost the race as he completed the race 2 seconds after Damon, therefore, 4th statement is false.5. We can see from our graph that Alex completed race in 12 seconds, while Damon completed race in 10 seconds that is 2 minutes before Alex, therefore, 5th statement is false.6. We have already seen that Damon runs at 10 yards per second and Alex runs at rate of [tex]6\frac{2}{3}[/tex] yards per second, therefore, last option is incorrect.