In order to burn calories and lose weight, vera is trying to incorporate more exercise into her busy schedule. she has several short exercise dvds she can complete at home. last week, she burned a total of 517 calories by doing 2 body sculpting workouts and 5 yoga sessions. this week, she has completed 2 body sculpting workouts and 1 yoga session and burned a total of 185 calories. how many calories does each workout burn?

each session of body sculpting workouts burns 51 calories.

Each session of Yoga workouts burns 83 calories.

Step-by-step explanation:

Let x represent the number of calories that she burnt doing one body sculpting workout session.

Let x represent the number of calories that she burnt doing one Yoga session.

Last week, she burned a total of 517 calories by doing 2 body sculpting workouts and 5 yoga sessions. This means that

2x + 5y = 517 - - - - - - - - - -1

This week, she has completed 2 body sculpting workouts and 1 yoga session and burned a total of 185 calories. This means that

2x + y = 185 - - - - - - - - - - - - 2

Subtracting equation 2 from equation 1, it becomes

4y = 332

y = 332/4 = 83 calories

Substituting y = 83 into equation 2, it becomes

2x + 83 = 185

2x = 185 - 83 = 102

x = 102/2 = 51 calories

5104.38 inches

step-by-step explanation:

the solution of the equation is 2.23 ⇒ answer b

step-by-step explanation:

* lets revise the meaning of exponential function

- the form of the exponential function is y = ab^x, where a ≠ 0, b > 0 ,  

  b ≠ 1, and x is any real number

- it has a constant base b

- it has a variable exponent x

- to solve an exponential equation, take the log or ln of both sides,  

  and solve for the variable

* lets solve the problem

∵

- the base is 7 and the exponent is x

- insert ㏑ in both sides

∴

- use the rule

∴ x ㏑(7) = ㏑(77)

- to find x divide both sides by ㏑(7)

∴

* the solution of the equation is 2.23 to the nearest 2 decimal places