Question

Mai does a weekly exercise program consisting of cardiovascular work and weight training . Each week , she exercises for at least 6 hours She spends at most cardiovascular work . She spends at most 8 hours on weight training . Let denote the time in hours ) that spends doing cardiovascular work reion corresponding to all of x and y that satisfy these requirements. Give the graph

Answer 1

To represent Mai's exercise routine mathematically, we graph inequalities related to cardio and weight training within her 6-hour minimum and 8-hour maximum constraints for a week's exercise program. The graphed inequalities form a feasible region that indicates all possible hours Mai could be exercising according to her routine.

Step-by-step explanation:

The student in question, Mai, has a weekly exercise program that consists of cardiovascular work and weight training. Let x represent the time Mai spends doing cardiovascular work, and let y represent the time spent on weight training. According to the question, Mai exercises for at least 6 hours each week in total, and she spends at most 8 hours on weight training.

To illustrate this situation, we can use inequalities to represent the constraints mentioned:

1. x + y ≥ 6 (Mai exercises for at least 6 hours a week in total),
2. y ≤ 8 (Mai spends at most 8 hours on weight training).

Additionally, since time spent cannot be negative, we have two more inequalities:

• x ≥ 0,
• y ≥ 0.

These inequalities describe a region in the coordinate plane. To graph this region, we'd plot the lines corresponding to the equations x + y = 6 and y = 8, and then shade the region that satisfies all of these inequalities, which is the feasible region representing Mai's possible exercise hours.

Mai does a weekly exercise program consisting of cardiovascular work and weight training, meeting health guidelines that recommend a combination of aerobic and muscle-strengthening activities.