The first few steps in solving the quadratic equation 8x2 + 80x = −5 by completing the square are shown.

8x2 + 80x = −5

8(x2 + 10x) = −5

8(x2 + 10x + 25) = −5 +

which number is missing in the last step?

200

Step-by-step explanation:

8x^2 + 80x = −5

Factor out an 8

8(x^2 + 10x) = −5

Take the coefficient of the x term, divide by 2 and then square it

10/2 = 5, 5^2=25

Remember we have the 8 outside, so we are multiplying by 8

8*25 =200

Add 200 to each side

8(x^2 + 10x + 25) = −5 + 200

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

answer is 1

step-by-step explanation: