Can someone please help me with this question? I really don't get it. Your help would be much appreciated. :) What is the length of CD to the nearest tenth?

5.7

Step-by-step explanation:

The altitude of a right triangle divides it into two smaller triangles, all three of which are similar.

ΔABC ~ ΔADB ~ ΔBDC

Writing and solving a proportion:

AD / BD = BD / CD

(x + 3) / 5 = 5 / (2x + 3)

(x + 3) (2x + 3) = 25

2x² + 9x + 9 = 25

2x² + 9x − 16 = 0

x = [ -9 ± √(81 − 4(2)(-16)) ] / 2(2)

x = [ -9 ± √(81 + 128) ] / 4

x = (-9 ± √209) / 4

x = -5.86 or 1.36

Since x can't be -5.86, x = 1.36.  So the length of CD is:

CD = 2(1.36) + 3

CD = 5.7

- "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."