Solutions of the equation 4x2-7x=3x+24

Let's solve your equation step-by-step. 4x^2−7x=3x+24
Step 1: Subtract 3x+24 from both sides.
4x^2−7x−(3x+24)=3x+24−(3x+24)
4x^2−10x−24=0
Step 2: Factor left side of equation.
2(2x+3)(x−4)=0
Step 3: Set factors equal to 0. 2x+3=0 or x−4=0x=−32 or x=4
x=−3/2 or x=4
Hope this helps!:)

  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.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

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

the table tells us

g(-2) = 1g(1) = 31

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).