On a city map, a library is located at (6, 2) and a school is located at (3, 3). If each unit equals one mile, what is the distance (in a straight line) between the library and the school rounded to the nearest tenth?

3.2 miles

Step-by-step explanation:

Given the coordinate  point (6,2) and (3,3)

The distance between the two points is expressed using the formula;

D = √(x2-x1)²+(y2-y1)²

D = √(3-2)²+(3-6)²

D = √1²+(-3)²

D = √1+9

D = √10

D = 3.2

Hence the distance (in a straight line) between the library and the school rounded to the nearest tenth is 3.2 miles

- "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."