In a rectangle, the length is 7 m less than three times the width and the area is 111 m. Approximate the dimensions to the nearest tenth of a meter.

The dimensions are 7.4m by 15.1 m (to the nearest tenth).

Step-by-step explanation:

Area = length * width

If the width = x then the length = 3x - 7 so

Area x(3x - 7) = 111

3x^2 - 7x - 111 = 0

Using the quadratic formula:

x  = [ -(-7) +/- √((-7)^2 - 4*3*-111)] / (2*3)

x =  7.36, -5.03.

The width must be positive s it is 7.36 m.

The length = 3(7.36) - 7

= 15.08 m.

  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).