Question

Whats the definition for an open circle, a closed circle, a solution set, a dashed boundary line, a solid boundary line, a system of inequalities, and a number line?

Answer 1

Open and closed circles are used to mark the end points of intervals. If the circle is open, it means the end point is NOT included in the interval, but if the circle is closed, it means the end point is included. Consider the interval . In this interval, the low endpoint, the 3, is not included because you have a 'less than' sign. The high endpoint, the 6, is included because you have a 'less than or equal' sign. It is the presence or absence of the 'or equal' part that determines whether the circle is closed or open. The interval would be marked on the number line with an open circle at 3, a closed circle at 6, and a heavy line connecting the two.

Answer 2

An open circle is not included in the graph, whereas a closed circle is included. A solution set is a set of values that satisfies an equation or inequality. A dashed boundary line is not included, while a solid boundary line is included.

Step-by-step explanation:

An open circle in mathematics is a symbol used to represent a point that is not included in the graph. It is represented with an empty circle (◯). On a number line, this means that the point is not included in the solution set.

A closed circle, on the other hand, is a symbol used to represent a point that is included in the graph. It is represented with a filled circle (●). On a number line, this means that the point is included in the solution set.

A solution set is a set of values that satisfy a given equation or inequality. It represents all the possible solutions to the equation or inequality.

A dashed boundary line is a line used to represent an inequality that is not included in the solution set. It is typically represented by a dashed line on a graph.

A solid boundary line, on the other hand, is a line used to represent an inequality that is included in the solution set. It is typically represented by a solid line on a graph.

A system of inequalities is a set of multiple inequalities that are solved together. The solution to a system of inequalities is the set of values that satisfy all of the given inequalities.

A number line is a line that represents numbers and their values. It is typically used to visually represent the solutions to equations or inequalities.