Circle experts...help! will give to most detailed answer

Explanation:

Line AE is a tangent while line AU is a secant. The angle formed by the secant and tangent lines connects with the arcs through this formula

secant tangent angle = (larger arc - smaller arc)/2

More specifically, we can say:

angle EAI = (arc EU - arc IE)/2

42 = ( (7m+5) - (3m-1) )/2

42*2 = (7m+5) - (3m-1)

84 = 7m+5 - 3m+1

84 = 4m+6

4m+6 = 84

4m = 84-6

4m = 78

m = 78/4

m = 39/2

m = 19.5

Use this value of m to compute each arc

Let's say arc IU is some unknown number x. It must add to the other two arc measures to form 360 degrees, which is a full circle.

(arc IU) + (arc IE) + (arc EU) = 360

x + 57.5 + 141.5 = 360

x + 199 = 360

x = 360-199

x = 161

The measure of minor arc IU is 161 degrees

x = 25/2304

step-by-step explanation:

- "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."