Three joggers are running around a circular track. one of them completes one lap in 6 minutes, the second one in 9 minutes, and the third one in 15 minutes. what time will they arrive at their starting point together if they start at the same time from the same point at 10: 00 am and maintain their jogging pace

At 11:30 am they will arrive at their starting point together

Step-by-step explanation:

we know that

One of them completes one lap in 6 minutes

The second one in 9 minutes

The third one in 15 minutes

step 1

Find the least common multiple (LCM)

6=2*3

9=3²

15=3*5

so

LCM=(3²)*(2)*(5)=90 minutes

step 2

Find the number of laps of each jogger for the LCM

jogger 1

90/6=15 laps

jogger 2

90/9=10 laps

jogger 3

90/15=6 laps

If they start at 10:00 am

then

10:00 am + 90 minutes=11:30 am

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

false

step-by-step explanation:

the reason i say this is because for a certain length of sides you can pick any two and the length is wither equal or greater than the third side and in this case it's not.

3 + 5 = 8

8 is smaller than 9 which is the third side.

hope this : )