For a certain value of k, the system

has no solutions. what is the value of k?

k = 6

Step-by-step explanation:

The system of three equations has no solutions, when the determinant of the matrix determined by this system is equal to 0.

Write the determinant:

Find it:

Equate it to 0:

  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).