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How Does the Surface Area Definition Apply to 3D Objects?

Images showing the surface area definition of a pyramid, cube and rectangular prism

With three-dimensional shapes, the surface area of the object is defined as the total surface area, or the sum of the areas, on every outward surface. (This is different from the lateral surface area, which excludes the base and top of 3-D shapes).

Just like the area of a two-dimensional shape, the surface area definition is measured in square units. Depending on the shape and surface of the object, there are different surface area formulas to keep in mind. We’ll go through the surface area of each shape in turn.

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What Does PEMDAS Mean, and Why Does It Matter?

what does PEMDAS stand for: Colored blocks with mathematical symbols on top of a wooden surface

You may have heard the phrase, "Please excuse my dear Aunt Sally," (PEMDAS) in math class. But what does PEMDAS stand for, how does it relate to the order of operations, and how does it help solve math problems with multiple mathematical expressions?

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What Is the Slope of a Vertical Line?

what is the slope of a vertical line: Slope of a horizontal line graph

“What is the slope of a vertical line?” is a common question when you start to analyze graphs and linear equations. To answer that, let’s go back to the basic definition.

Slope is defined as the steepness, incline, or gradient of a line. It is also defined as the change in y value ("rise") over the change in x value ("run"). The slope formula is:

what is the slope of a vertical line: Slope formula

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How to Write and Apply the Standard Form of a Linear Equation

The standard form of a linear equation is a way of writing linear functions with x and y on the same sides of the equation.

A linear function is any math equation that includes an x- and y-value and can be represented on a graph. Writing a linear equation in standard form makes it easier to find the x and y-intercepts, which is where the graph crosses the x- and y-axis.

Here is an example of the standard form of a linear equation:

Example of the standard form of a linear equation

In the standard form of a linear equation, coefficients A, B, and C must all be integers (whole numbers without fractions or decimals), and A must always be a positive number.

The following equation of a line is written in standard form:

Standard form of a linear equation using whole numbers

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Your Step-by-Step Guide to Graphing Linear Inequalities

graphing linear inequalities: Calculator, eyeglasses, magnifying glass, pen and papers on a wooden surface

Graphing linear inequalities is similar to graphing linear equations but with the added steps of picking a solid or dotted line and determining what part of the coordinate plane to shade in order to make the inequality a true statement.

To review, a linear inequality is any statement that includes a symbol other than the equal sign. Greater than (>), less than (<), greater than or equal to (≥), and less than or equal to (≤), are all examples of these inequality signs. A statement that contains one of these inequality symbols makes it a linear inequality.

Here are the steps to graphing a linear inequality.

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