The larger of two numbers is twelve more than twice the smaller number. The sum of the numbers is fifty one. Find each number

13 and 38

Step-by-step explanation:

Let the smaller number be y.

Larger number will be 2y+12

Since the sum of the numbers is 51,

y + 2y + 12 = 51

3y + 12 = 51

3y = 51 - 12

3y = 39

y = 39/3

y = 13

The smaller number is 13

The bigger number will be 2y + 12= 2(13) + 12 = 26 + 12 = 38

13 and 38

Step-by-step explanation:

So we know that one number is 2 times the smaller number plus 12. We can use the variable x for the smaller number and the bigger number will be 2x + 12. Now we need to put the numbers into an equation.

2x + 12 + x = 51

To isolate x, we have to subtract 12 from the left side of the equation.

2x + x = 39

Now we add the x's together.

3x = 39

Now we have to divide by 3.

x = 13

But we're not done yet, although we know the smaller number is 13 we have to plug x into the larger number. So because it is 2x the amount, we multiply 13 to get 26 and then add another 12 to get 38.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

351.23

step-by-step explanation: