Understanding Inequalities and Graphs

Clinton builds a machine to clean a fish tank, requiring it to meet specific work and battery power inequalities. The video explains these inequalities, how to graph them, and validate points within the graph. It demonstrates that the machine meets the requirements when spending three minutes on each task, but not when testing other points like three and one.

What is the primary function of Clinton's machine?

• To feed fish automatically

• To automatically clean a fish tank

• To monitor water temperature

• To change the water in the tank

Which inequality represents the work done by the machine?

• x - y > 3

• x + 3y > 6

• 4x - 3y < 9

• 3x + 4y < 12

What does the inequality x + 3y > 6 represent?

• The amount of water in the tank

• The battery power level

• The speed of cleaning

• The time spent on cleaning

What is the purpose of graphing the system of inequalities?

• To measure the efficiency of the machine

• To calculate the total cleaning time

• To determine valid combinations of cleaning times

• To find the maximum battery life

What does the shaded region in the graph represent?

• The minimum battery usage

• The maximum cleaning time

• Combinations of minutes that satisfy both inequalities

• Invalid cleaning times

Does the point (3,3) satisfy both inequalities?

• Yes, but only under certain conditions

• Yes, it satisfies both

• No, it satisfies only one

• No, it satisfies none

Why is the point (3,3) considered valid?

• It lies outside the shaded region

• It lies within the shaded region

• It is the only possible solution

• It is on the boundary line

Why does the point (3,1) not satisfy the inequalities?

• It lies within the shaded region

• It is on the boundary line and not included

• It requires more cleaning time

• It exceeds the battery power

What is the significance of the inequality signs in the context of the graph?

• They exclude points on the line

• They change the shape of the graph

• They include points on the line

• They determine the color of the graph

What would happen if the inequalities included equal signs?

• The machine would not function

• The graph would not change

• Fewer points would be valid solutions

• More points would be valid solutions