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From Sean Sanford
What is an Equation? How do equations behave?Here we give some definitions and list some important properties of equality. -
From Sean Sanford
Here we go through the process of graphing an equation given in general form. This time, we offer a technique where we plot only the X and Y intercepts, and then… -
From Sean Sanford
Here we go through the process of graphing a line that is given in slope-intercept form. We begin by making a table of values. From the table, we plot several points,… -
From Sean Sanford
Here we cover a very common type of problem. We are given a point and a slope, and asked to calculate the y-intercept. -
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From Sean Sanford
Here we discuss vertical lines and give the definition of slope of a non-vertical line. -
From Sean Sanford
Here we define and discuss parallel and perpendicular lines. One example problem is given for each topic. -
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From Sean Sanford
Here we examine a scenario where price and demand satisfy a linear relationship. We utilize the techniques in this section to estimate the demand at a certain price… -
From Sean Sanford
Here we go over an example of finding an equation for a line that passes through a given point, and is perpendicular to a given line. We give the equation in both… -
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From Sean Sanford
Here we discuss solving a consistent system.using both substitution and addition methods. -
From Sean Sanford
Here we discuss solving a dependent system.using both substitution and addition methods. Clarification: at 5:50 I say "consistent system" because the system… -
From Sean Sanford
Here we discuss the different types of systems and the number of solutions that are possible. The conclusion is that the only possibilities are 0 solutions, or … -
From Sean Sanford
Here we discuss solving an inconsistent system.using both substitution and addition methods. -
From Sean Sanford
Here we discuss the two main algebraic methods for solving 2D systems of linear equations. -
From Sean Sanford
Here we use a 2x2 linear system to show how matrices can be used to streamline the elimination technique. -
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From Sean Sanford
Here we introduce interval notation, and give several examples. We also discuss what happens when we take the intersection or the union of two intervals. -
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From Sean Sanford
Here we introduce inequalities, and discuss an example where dividing by a negative forces us to flip the sign. -
From Sean Sanford
Here we graph a system of three inequalities. We also do some algebra to verify the coordinates of a certain point. -
From Sean Sanford
Here we continue the example from pt1. This time we use the addition method to verify the coordinates of the last point of the triangle. -
From Sean Sanford
Here we introduce the idea of graphing systems of inequalities. A short example is given. -
From Sean Sanford
Here we work through a word problem about buying tables for a cafeteria. This problem is similar to [4.4, Example 4, pages 244-245] in your textbook, so please take a… -
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From Sean Sanford
Here we finish the warehouse example, by investigating the values of the objective function. -
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From Sean Sanford
Here we discuss what it means for a set to be empty. We give several examples of empty sets, and make an argument for why we should think of them all as THE Empty Set. -
From Sean Sanford
Here we talk about two operations: union and intersection. These are ways of combining sets to make new sets. -
From Sean Sanford
Here we discuss universal sets, or universes, and explain what it means to take a complement of a set with respect to a given universe. -
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From Sean Sanford
Here we give some examples of how Venn diagrams can be used to help reason about sets. -
From Sean Sanford
I forgot to turn off my webcam >_< Is it better to see my face? Does it make a difference? -
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From Sean Sanford
Here we go over the different methods or counting and how they relate to each other.