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Here’s How To Find the Hypotenuse of a Right Triangle

how to find hypotenuse: Diagram of a triangle with an unknown hypotenuse

The Pythagorean Theorem is an important theorem, as it comes up often in high school math. It makes the question of how to find the hypotenuse of a right triangle is easy to answer.

Plus, we can use it to find the base of a special right triangle and apply the converse of the Pythagorean Theorem. Let’s review this basic but foundational concept in trigonometry and how it relates to finding the hypotenuse of a right triangle.

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What To Remember When Graphing Linear Equations

graphing linear equations: Cartesian graph

Graphing linear equations is key to helping you with making observations or insights about the equation. Before we look at graphing linear equations, let's review graphing basics.

The image above is a Cartesian graph. The x-axis goes left to right, and the x-intercept is wherever a straight line crosses over or intersects this horizontal axis. The y-axis goes up and down, and the y-intercept is wherever a straight line crosses over or intersects this vertical axis. Think of this as a rectangular coordinate system formed with evenly spaced perpendicular lines. Each ordered pair of coordinates (x,y) denotes a singular point on the graph.

The graph of a linear equation can be drawn by finding which x values and y values solve for the equation of the line, meaning those values balance the equation. For example, (2, 5) is a valid graph point for the equation graphing linear equations: y=2x+1 formula, because substituting 2 for x and 5 for y in the equation gives 5 = 2(2)+1, or 5=5. (0, 0) is not a solution because 0≠0+1, or 0≠1, and therefore is not a point on the line. Once you have collected several points, you can graph your equation.

Find the x-coordinate of a point on the graph by counting the number of spaces along the x-axis in accordance with the first value. Then, find the y-coordinate by looking at the second number and counting that number of spaces up or down the y-axis. For example, the point (2,3) would be two spaces to the right and three spaces up.

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How To Find the Axis of Symmetry of a Parabola

how to find axis of symmetry: Graph showing the vertexes of two parabolas

The axis of symmetry is the vertical line that goes through the vertex of a parabola so the left and right sides of the parabola are symmetric. To simplify, this line splits the graph of a quadratic equation into two mirror images.

In this tutorial, we will show you how to find the axis of symmetry by looking at the quadratic equation itself.

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Understanding the Biconditional Statement

Biconditional statement: Logic statement written on a black board

A biconditional statement is a logic statement that includes the phrase, "if and only if," sometimes abbreviated as "iff." The logical biconditional comes in several different forms:

  • p iff q
  • p if and only if q
  • p↔q

Consider the following statement: "You will read carefully on to the end of this article if and only if you are interested in reviewing converse statements, compound statements, and truth tables in order to understand what a true biconditional statement is."

Let's break it down.

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How To Find the Sum of a Finite Geometric Series

A geometric series is a list of numbers where each number, or term, is found by multiplying the previous term by a common ratio r. If we call the first term a, then the geometric series can be expressed as follows:

sum of finite geometric series: Example of a finite geometric series

We call this a finite geometric series because there is a limited number of terms (an infinite geometric series continues on forever.) In this example, there are 10 terms, the common ratio is r, and each of the terms of the geometric sequence follows the same pattern. The first term is a. The second term is the previous term a multiplied by r. The third term is the second term sum of finite geometric series: The second term in a geometric series multiplied again by r to create sum of finite geometric series: The third tem in a geometric series, and so on until the last term.

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