The sum of two numbers is 15. four times one of the numbers is twelve more than two times the other number. what are the two numbers?

Let a and b be our two numbers.

Here is the set up:

a + b = 15A

4a = 2b + 12B

We have a system of equations in two variables.

Solve equation A for either a or b. I decided to solve for a.

a + b = 15

a = 15 - b

Plug into equation B.

4(15 - b) = 2b + 12

Solve for b.

60 - 4b = 2b + 12

-4b - 2b = 12 - 60

-6b = -12

b = -12/-6

b = 2

We now know that b is 2. To find a, plug b = 2 into either equation A or B.

As you can see, equation A is easier to deal with.

a + b = 15

a + 2 = 15

a = 15 - 2

a = 13

The two missing numbers are 2 and 13.

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.