Which sets of side lengths could form a triangle? A. 3 centimeters, 4 centimeters, 9 centimeters
B. 3 centimeters, 6 centimeters, 9 centimeters
C. 4 centimeters, 5 centimeters, 9 centimeters
D. 4 centimeters, 6 centimeters, 9 centimeters

D. 4 centimeters, 6 centimeters, 9 centimeters

Step-by-step explanation:

Considering side length for forming a triangle, most of the time it is about Triangle Inequality Theorem, which for 3 sides length a,b,c, it must satisfy the following set of inequalities:  

By checking each of them only D satisfy:

For simplicity you only have to check if the two shortest sides add up to be larger than the longest side:

- "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."