Question

Yolanda does a weekly exercise program consisting of cardiovascular work and weight training. Each week, she exercises for at least 10 hours. She spends at most 6 hours doing cardiovascular work. She spends at most 8 hours on weight training. Let x denote the time (in hours) that Yolanda spends doing cardiovascular work. Let denote the time (in hours) that she spends on weight training. Shade the region corresponding to all values of x and y that satisfy these requirements.

Answer 1

Explanation:

Let x is the hours of doing cardiovascular work

Let y is the hours of doing weight training

Given that :

Each week, she exercises for at least 6 hours.

<=> x + y ≥ 6 (1)

She spends at most 11 hours doing cardiovascular work.

<=> x ≤11 (2)

She spends at most 4 hours on weight training

<=> y ≤ 4 (2)

Note that times x and y are always no less than 0, so

x ≥0 (3)

y≥0 (4)

After that, we have the system of of inequalities (1) (2) (3) (4)

Please have a look at the attached photo, This diagram shows the triangle with vertices that is the solution set (triangle and all points inside triangle)

Answer 2

See explanation

Explanation:

Let x denote the time (in hours) that Yolanda spends doing cardiovascular work. Let y denote the time (in hours) that she spends on weight training.

1. Each week, she exercises for at least 10 hours. Thus,

`x+y\ge 10`

2. She spends at most 6 hours doing cardiovascular work. So,

`x\le 6`

3. She spends at most 8 hours on weight training. Then,

`y\le 8`

Note that times x and y are always no less than 0, so

`x\ge 0\\ \\y\ge 0`

Plot the system of inequalities

`\left\{\begin{array}{l}x+y\ge 10\\ \\x\le 6\\ \\y\ge 8\\ \\x\ge 0\\ \\y\ge 0\end{array}\right.`

on the cooordinate plane - see attached diagram. This diagram shows the triangle with vertices at (2,8), (6,8) and (6,4) that is the solution set (triangle and all points inside triangle)