What is the unit rate for each cyclist?

how did you find it?

be sure to include all 4 cyclists.

sample cyclist a's unit rate i found the unit rate

Cyclist A  12 mi/h

Cyclist B  5 mi/h

Cyclist C  9 mi/h

Cyclist D  10 mi/h

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form or

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

In this problem the relation between the distance and the time represent a direct variation

Let

y -----> the distance in miles

x ----> the time in hours

The unit rate is the same that the slope or constant of proportionality of the linear equation

Cyclist A

we have

The cyclist can ride 24 miles in 2 hours

The unit rate is equal to divide the total distance by the total time

so

Cyclist B

Looking at the table

For x=1 h, y=5 mi

substitute

Cyclist C

we have

Remember that the unit rate is equal to the slope

so

Cyclist D

Looking at the graph

For x=1 h, y=10 mi

substitute

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be

the answer is 2/54

step-by-step explanation: