Scott burned 20 calories per minute jogging for x minutes and 5 calories per minute for biking for y minutes. he spent a total of 120 minutes jogging and biking and burned 1,2oo calories. the system of equations shown can be used to determine how much time scott spent on each exercise. what is the value of x, the minutes scott spent jogging? 20x+5y=1200 x+y=120

x = 112

Step-by-step explanation:

We can create two equations 1. one that calculates calories burned and 2.another that calculates minutes:

20*x + 5*y = 1200

x + y = 120

Then we can solve for x

x = 120 - y

then we can plug that into the top equation:

20(120 - y) + 5y = 1200

divide by 5:

4(120 - y) + y = 240

distribute:

480 - 4y + y = 240

and then do all that combining like factors what not and simplify and solve:

480 - 3y = 240

-3y = -240

y = 8

NOW WE CAN JUST PLUG IN THE ANSWER FOR Y TO FIND X

8+x =120

x = 112

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.

i think the answer is d im not sure