A personal trainer designs exercise plans based on a combination of strength-training and aerobic exercise. A beginner plan has
15 minutes per session of strength-training and 20 minutes per session of aerobic exercise for a total of 90 minutes of exercise in a week. An advanced plan has 20 minutes per session of strength-training and 30 minutes of aerobic exercise for a total of 130 minutes of exercise in a week. Which statement describes when the plans are based on the same number of aerobic exercise sessions?
Each plan utilizes a combination of 2 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 2 aerobic exercise sessions per week.
Each plan utilizes a combination of 3 strength-training sessions and 3 aerobic exercise sessions per week.
Let y be the number of strength-training exercises per week. Let x be the number of aerobic exercises per week. For the beginner plan: 15y + 20x = 90 ..........(1) For the advanced plan: 20y + 30x = 130 ........(2) Multiply both sides of (1) by 3 to get: 45y + 60x = 270 ........(3) Multiply both sides of (2) by2 to get: 40y + 60x = 260 .......(4) Subtracting (4) from (3) we get: 5y = 10 y = 2 Plugging in the value of 2 for y in equation and solving, we find x = 3. Therefore the correct statement is: "Each plan utilizes a combination of 2 strength-training sessions and 3 aerobic exercise sessions per week."
yes, there are infinitety many polynomial that have exactly one real root just like your example, to determine the real root first let the real root is a, and the complex roots are b±ic the polynomial satisfy
-9x³ + 19x² + 17 = -(x - a)(x - b - ic)(x - b + ic)
