Miguel needs 4 gallons of milk to make 12 milkshakes. how much milk does he need to
make 30 milkshakes? use at least two different methods to support your answer. is this a
proportional relationship?

see the procedure

Step-by-step explanation:

Part 1) using proportion

we know that

Miguel needs 4 gallons of milk to make 12 milkshakes

so

Using proportion

Find out how much milk he needs to make 30 milkshakes

Let

x ----> gallons of milk needed

Miguel needs 10 gallons of milk to make 30 milkshakes

Part 2) we know that

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

This problem represent a proportional relationship

Let

x ----> the number of gallons of milk

y ----> the number of milkshakes

we know that

Miguel needs 4 gallons of milk to make 12 milkshakes

so

For x=4, y=12

Find out the constant of proportionality k

substitute the values

The linear equation is equal to

For y=30

substitute in the equation and solve for x

Divide by 3 both sides

- "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."