Joe goes to the gym to run and swim. when running he burns 35
calories per minut, and when he swims he burns 30 calories per
minute. he has burned 730 calories after exercising for a total of
23 min. how long on each activity?

the length of time he spent running is 8 minutes.

the length of time he spent swimming is 15 minutes.

Step-by-step explanation:

Let x represent the length of time he spent running.

Let y represent the length of time he spent swimming.

He exercised for a total of 23 minutes. This means that

x + y = 23

When running he burns 35 calories per minute, and when he swims he burns 30 calories per minute. He has burned 730 calories after exercising. It means that

35x + 30y = 730 - - - - - - - - - -1

Substituting x = 23 - y into equation 1, it becomes

35(23 - y) + 30y = 730

805 - 35y + 30y = 730

- 35y + 30y = 730 - 805

- 5y = - 75

y = - 75/ -5

y = 15

Substituting y = 15 into x = 23 - y, it becomes

x = 23 - 15 = 8

11.2

step-by-step explanation:

when doing tangent the tangent of the angle is equal to the opposite side from the angle over the adjacent side to the angle.

tan43 = x / 12

move 12 over by multiplying each side by 12

12tan43 = x

x = about 11.2