Find the rate of change in the table below

x 18,20,22,24
y 4.5,5,5.5,6

.25

Step-by-step explanation:

Rate of change is the same as slope.

Slope is rise/run.

The rise between each y coordinate is consistently .5

The run between each x coordinate is consistently 2

Rise/Run = .5/2

Rate of change = .25

8

Step-by-step explanation:

Let one of the multiples of 8 be 8x and the second multiple of 8 be 8(x+1). Using x and x+1 ensure that the resulting multiples are one multiple apart, or consecutive. Next, recall that these two consecutive multiples of 8 have a product of 2,688. We can thus write the equation:

.

To solve the equation, we must simplify and distribute. We can isolate the non-zero terms on one side the equation and solve the remaining quadratic equation for x:

This means that x=-7 or x=6. Using the positive result x=6 gives the multiples of 8×6 and 8(6+1) or 48 and 56. Subtract the two numbers ot find the difference is 56-48 or 8.