A medical rescue helicopter is flying at an average speed of 172 miles per hour toward its base hospital. At 2:42 p.m., the helicopter is 80 miles from the hospital. Use this information for Items 4-5.
Which equation can be used to determine m, the number of minutes it will take the helicopter to reach the
hospital?

The equation that can be used to determine m, the number of minutes it will take the helicopter to reach the  hospital is .

Step-by-step explanation:

We are given that a medical rescue helicopter is flying at an average speed of 172 miles per hour toward its base hospital. At 2:42 p.m., the helicopter is 80 miles from the hospital.

As we know that the Distance-Speed-Time formula is given by;

Here, Distance = 80 miles

          Speed = 172 miles per hour

          Time = m (the number of minutes)

Firstly, as we can see that the speed is in miles per hour but the time is in minutes, so we will convert the time in hours, i,e;

           Time =

So,  

       m = 27.91 ≈ 28 minutes.

Hence, it will take 28 minutes for the helicopter to reach the  hospital.

B:  4 solutions

Step-by-step explanation:

Combining the two equations results in 2x² = 52, or x² = 26.

This equation has two solutions:  x = ±√26.

As before, x² = 26.  If we substitute 26 for x² in the 1st equation, we get:

26 - 4y² = 16, or 4y² = 10, or y = ±√5/2.  Again:  two solutions.

If we take x to be +√26, y could be ±√(5/2).

Check:  is ( √26, √(5/2) ) a solution of the system?

Subbing these values into the first equation, we get:

26 - 4(5/2) = 16.  Is this true?

Then 10 = 10.  Yes.

Through three more checks, we find that this system has FOUR solutions.