Dana is filling a 1.5 gallon watering can at a rate of 0.75 gallon per minute. What is the domain of the function that represents the volume of water in the can after x minutes?

0 ≤ x ≤ 2

Step-by-step explanation:

A function show the relationship between an independent variable and a dependent variable. The independent variable (input) does not depend on other variables while the dependent variable (output) depend on other variables.

In this question, the volume of the water is the dependent variable and the time taken is the independent variable. Let y represent the volume of the water and x represent the time taken. Therefore:

y = 0.75x

The domain of the function is the set of independent variable, it can be gotten by determining x when y is minimum and maximum. Hence:

For y = 0

0 = 0.75x

x = 0/ 0.75 = 0

For y = 1.5 gallon

1.5 = 0.75x

x = 1.5/0.75 = 2

Hence, the domain = 0 ≤ x ≤ 2

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 anwser is d) 75°

step-by-step explanation: