Which point is part of the solution of the inequality y ≥ |2x − 1|. (0, 0) (1, 1) (1, 0) (3, 2)

The correct option is 2.

Step-by-step explanation:

The given inequality is

If a point is part of the solution of the inequality, then the inequality must be satisfied by that point.

Check the inequality for (0,0),

This statement is false. So (0,0) is not a solution.

Check the inequality for (1,1),

This statement is true. So (1,1) is a solution.

Check the inequality for (1,0),

This statement is false. So (1,0) is not a solution.

Check the inequality for (3,2),

This statement is false. So (3,2) is not a solution.

Therefore the correct option is 2.

- "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."