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How To: Solve a quadratic equation

In this video the instructor shows how to solve a quadratic equation. If you have a quadratic equation with complex fractional terms and you find that a particular term is repeating then equate that term to a new variable and replace the variable in the given equation. Now try to get the equation a*x*x + b*x + c = 0, and solve for the roots of the equation which gives the values of the intermediate variable. But this variable was replaced instead of another term. So equate that term to the va...

How To: Solve radical equations easily

In this video, the instructor demonstrates how to solve radical equations and inequalities. If you have an equation that contains radicals, re-,arrange the equation so that all the radicals are on one side and the integers are on the other side. To cancel a square root from an equation, square both sides of the equation. The square of the equation cancels out the square root, thereby removing the radical. Even after squaring if you still have a radical left, treat it as a new problem and appl...

How To: Factor a number

The following are the steps to describe how-to factor a number: 1. First we go into factoring a number we first need to know the prime numbers 2, 3, 5, 7, 11, 13, 17, 19, 23 etc.

How To: Apply the Pythagorean Theorem to right triangles

In this video the instructor talks about Pythagorean theorem and how to apply it to right triangles. Pythagorean theorem states that in any right triangle if a and b are the lengths of the legs and c is the length of the hypotenuse the sum of the squares of the lengths of the legs is equation to the square of the length of the hypotenuse. That is a*a + b*b = c*c. This theorem works only for right angled triangle. So if you have the lengths of the two legs of a right triangle substitute the va...

How To: Find the equation of a line

In this video the instructor shows how to find the equation of the line given its slope and a point that lies on it. If the slope of the line is m and the point that lies on it is (x,y) then you can find the equation of the line by substituting the values in the slope-intercept form of an equation which is y = mx + b. Now substitute the values in the above equation and solve it for the value if the y-intercept y. Now you have the slope m and y intercept b. Substitute these values in the gener...

How To: Simplify rational expressions

When you need to compute the square root of a number you can do it by breaking it into perfect squares. When you can split the given number into small perfect squares you can cancel out the square root of the expression to the square of the perfect squares. You cannot always write the number inside the square root as a perfect square, but try to write this number as a product of a perfect square and another number. Now you can pull out the perfect square out of the radical and leave the remai...

How To: Understand nth roots and operations on radicals

This video teaches us the concept of nth roots. The video starts with the square root of constants. We find the number which when multiplies by itself for two times results in the constant inside the square root. Then we find the square root of variables. Here again the same concept is used. We find the variable which when multiplied by itself for two times results in the given variable. Then we find the cube root. Here we find the number which when multiplied by itself for three times result...

How To: Find the area of triangle using fraction measurement

This video demonstrates the way to find the area of a triangle using fraction measurements. The person presenting this video first writes the actual formula for calculating the area of the triangle. The formula is: the area of the triangle denoted by ‘A’ is equal to half of ‘b’ times ‘h’ where ‘b’ and ‘h’ are the base and height of the triangle, respectively. Now, to make it into fractions, he writes ‘b’ and ‘h’ over ‘1’. Then he asks you to calculate “what is one times ‘b’ times ‘h’” which i...

How To: Divide decimals

Here we are, learning how to divide decimals. So we are dividing a whole number or a fraction by a fraction. How this presenter does this is by moving the decimal two places to the right on both the top and bottom of the sum. In other words, he multiplies the two numbers by 100. So 2 becomes 200 and .25 becomes 25. So much easier to divide 200 by 25 than to divide 2 by .25. Provided you've multiplied both the top and bottom by the same amount, the result will be the same, because the relative...

How To: Interpret a graph

YouTube user NotesCollegeAlgebra teaches you how to interpret a graph. You will learn how to read it and extract information. You go to the graph to see that f(-4)=-2. f(1.5)=2, so it's positive. You then have the question: For what x-values is f(x)<0? You go to the graph and see that you come up with (-5,3). The x-int is (3,0) (4,0). The y-int is (0,4). The domain is (-5,4) and the range is (-4,4). You then have the question: how often does y=7/5 intercept the graph? The answer is 4 times. T...

How To: Solve an equation using the point slope form

In this video the instructor shows how to derive a general equation for a line in Point-Slope form. The slope of an equation is the ratio of difference of y coordinates to the difference of x coordinates. In other words, slope is the change of y up on change of x. So you have the basic slope equation m = (y2 - y1)/(x2 - x1). When you have fractions you can simplify them by multiplying the denominator to the numerator on both sides. So multiply the equation by (x2-x1) on both sides. This gives...

How To: Prove congruent triangles with SSS and SAS

This is a video tutorial on how to prove congruent triangles with SSS and SAS test. SSS means side-side-side and SAS means side-angle-side. For applying the SSS test of congruency, each side of one triangle must be congruent to the corresponding side of the other triangle. For applying the SAS test of congruency, two corresponding sides of the two triangles must be congruent as well as the angle between those two sides of each triangle must be congruent. Follow the rest of the video to unders...

How To: Convert temperature using a point slope equation

In this video the instructor shows how to convert temperature using the point slope form. In this kind of problem sometimes you are given a temperature in Fahrenheit and its equivalent in Celsius and an other temperature similarly in both Fahrenheit and Celsius. Now you are asked to find a linear equation for these pair of temperatures. To solve these kind of problems assume that the given temperatures represent the point (x, y). Now you have two points. Substitute this value in the point slo...

How To: Figure out the area and circumference of a circle

Bill, Bobbie, and Drew present information on a circle. The presentation defines the key points of a circle. The area of a circle is Pi (3.14) x radius x radius. The diameter of a circle is the line drawn from one end to another inside the circle. The radius is the center of the circle to the edge. To find Pi, one simply takes the circumference/diameter. Circumference/diameter will always equal Pi (3.14) no matter the circle’s size. The final point is “what makes a circle a circle”? It is a b...

How To: Solve problems about linear equation

In this video the instructor shows how to write a linear equation. If you need to find the equation of a line that passes through the two given points then you need to find the linear equation of that line. The first step is to find the slope of the line that passes through these points. The slope can be calculated by finding the ratio of the difference of y coordinates to the difference of the x coordinates i.e. the change in y up on the change in x. Now substitute the value of slope and any...

How To: Calculate the area of a triangle using a basic formula

Free Math Tutoring teaches you in this video how to calculate the area of a triangle using a basic formula. The area of a triangle is (b times h)/2. B is the base of the triangle and h is the height. This formula works for all kinds of triangles. Sometimes you won't have the height in the triangle, so you need to draw a line from one angle to the base opposite that, at a 90 degree angle. Measure that and you have your height. It might seem difficult at first, but practice helps you understand...

How To: Add & subtract rational expressions

In this video the instructor shows how to add and subtract rational expressions. When you have an addition or subtraction problem of rational expressions, first look and compare the denominator of all the terms. If all of them have the same denominator then the expression can be written as a fraction whose denominator is the original common denominator and whose numerator is the sum of numerators of all the other terms. Simplifying the numerator by adding and subtracting the like terms gives ...

How To: Complete the square and solve the quadratic equation

In order to solve a quadratic equation by completing the square, take a quadratic equation and make sure that the coefficient of the first squared term in one. If it is not factor it by pulling the term out to get it to one. Now just write down the first two terms in side a bracket and after it add the third term. Now take the coefficient of the x term and take one half of it and square it and put that number back into the bracket. Now as you added a new number, to cancel it out subtract it f...

How To: Solve direct & inverse variation word problems

In this video the instructor teaches about direct and inverse variation. Two variables x and y are said to be in direct variation with each other if you can write them in the form y = K * x. The value of y varies directly corresponding to the value of x. Y is said to be directly proportional to x. If you have a sample value of x and y, you can substitute the values in the above equation to compute the value of the constant K. Using this formula you can always find the value of one variable x ...

How To: Figure out the slope of a line

In this video you will learn how to find a slope of a line. The man in the video shows in a practical and easy way, how to do it with formulas. First he teaches how to find slopes of lines containing both negative and positive points. He shows with formulas how to do it. He teaches how to find slopes on a flat line and demonstrates that the slope of it is equal to 0. Next, he teaches a "trick" to help students learn how to identify zero and no slope lines. In the last example, he demonstrates...

How To: Find the parallel line to a given equation

This videos explains how one can easily find the parallel line to a given mathematical equation. He starts by explaining what it means for two lines to be parallel mathematically speaking. Defining two lines, then comparing the slope of both lines you can mathematically determine that they are in fact parallel. He then moves to common math problems found on tests where you are given a point and a linear equation. He then forms a T-table with one column being line one and line two and illustra...

How To: Find the geometric mean

It doesn’t matter how long ago your last geometry class was, you can still impress your friends by finding a geometric mean. The geometric mean can be used to find the average of numbers with out unusually high or low results effecting the result.

How To: Draw a hypercube

This clip shows how you can draw a hypercube, which is a complex shape composed of cubes. You start with a series of equally spaced horizontal lines. Then you draw a vertical line from the origin (o, o, o). From the same point, you draw a horizontal line of the same length and two more lines at 45 degrees and 135 degrees from the horizontal. The vertical line and the 45 degree line form two of the vertices of one of the cubes. The vertical line and the 135 degree line form two of the vertices...

How To: Determine the area of a trapezoid

Need to figure out the area of a trapezoid for a household project? Even if you just want to sound smart, there is a simple formula that can be used every time you need to find the area of a trapezoid. Try the formula and see how good you are at geometry.

How To: Graph using the slope intercept equation of a line

This video shows us how to draw a linear equation using the slope and intercept technique. First, the narrator explains how to simplify the equation in order to get the slope and intercept out. He then shows how the coefficient of x equals the slope and the constant term tells us the y position of the intercept point. The technique for drawing the final line is plotting the intercept at the right height on the y axis, then running for some distance along the x axis and rising some amount. Thi...

How To: Add rational expressions with different denominators

This video shows the method to add rational expressions with different denominators. The first step in this process involves finding the LCD. After this is done, the numerator and denominator are multiplied by a specific number so that the fractions are rewritten with common denominators. In the second step the numerators are added or subtracted according to the problem with LCD in the denominator. Simplify the numerator by adding or subtracting like terms. After this, we get a rational expre...

How To: Find the percent increase or decrease in a quantity

This video shows us the method to find the percent increase or decrease in a quantity. This can be done in 30 seconds. The formula states that the percentage increase or decrease is equal to the product of the ratio of amount (increase or decrease) and the original amount and 100. This is explained by two examples. In the first example the amount of increase of the price of groceries is found by taking the difference of the new price and the old price. This is divided by the original price an...

How To: Understand the basics of matrices

In this video you learn how to understand the basics of matrices. The video includes how to do matrices with addition, subtraction and multiplication. The teacher explains in this exercise that you will need to know the number of rows and columns. He breaks down all of the steps required to solve these problems. Not only does he show how to understand the basics of matrices, but he does it dressed up like a king and with a little reggae music. You can hear the class's reactions to his jokes i...

How To: Solve systems by substitution

You can solve systems by using the substitution method. Here are two examples. One says y=3x+2 and the second says 7x-4y=7. The math teacher explains that if y is the same thing as 3x+2, then 3x+2 can be substituted for y in 7x-4y=7. Once it is substituted, your equation will then read 7x-4(3x+2)=7. The next step is to solve for x. Once you have worked out this equation, you will see that x=-3. Finally, your last step is to solve for y. To solve for y, simply substitute x with -3. The equatio...

How To: Translate a word problem into algebra

This video shows the method to change a word problem into algebra and to identify rational numbers among a group of numbers. In the first part of the video we take a word problem namely - The product of 9 and seven, less than a number. 9 multiplied by something can be expressed as 9(). The unknown number can be expressed as 'x'. Seven less than a number can be expressed as x - 7, so that the final equation becomes 9(x - 7). In the second part we are given a list of numbers. A rational number ...

How To: Shift a graph

This video will demonstrate exactly how to shift a graph on a x,y axis. When shifting a graph on the x axis you will need to replace x with x-h; where h is the variable to shift the graph. No matter how far you need to shift a graph, h is always the number of units you are shifting; shifting up or right is represented as a positive and down or left is negative. Just plug in your units into your equation and you will have your shifted graph.

How To: Translate a sentence into math symbols

We will be translating the sentence "twice y differs from 5 by more than two, “into a mathematical equation. The word twice generally means two times, so 2*y (because y comes next in the sentence). Differs normally means is different and a difference from something in a mathematical sentence means subtraction most of the time, thus minus five. We don't know if we’re talking about below 5 or above 5 on the number line, so we put absolute value around the equation. More than implies a greater t...

How To: Find points on y-axis a certain distance from a point

This is video on mathematics. It specifically deals with geometry. The video describes how to determine where the y-intersects are when a point and distance to the y-intersect are given. The author starts out by giving an example ordered pair. The speaker next shows an example of how to solve such a problem. The speaker uses the distance formula along with the given distance and x-coordinate in order to solve for the y-intersect values in question. Most of the video entails solving this example.

How To: Simplify square roots

This is a video tutorial on how to simplify square roots. To simplify square roots, one must have the knowledge of splitting numbers into prime factors. For example,12 can be split into 4*3 and further more into 2*2*3. Here we see that all the factors are prime numbers. So the square root of 12 can be written as 2*square root of 3(as shown in the video). The method used in the video is applicable for simplifying any square roots as any number can be split into prime factors. Follow the video ...

How To: Solve a linear system by elimination method

This video is about using the elimination method to solve a linear system. The lady presenting this video says that elimination method means that one of the two variables has to be eliminated while adding up the two linear equations. She then explains the example equations 6x-2y=66 and 5y=-29-2x. She asks you to first line up x and y. So the second equation is rewritten as 2x+5y=-29. Then she says that, to eliminate a variable, we should have their variables equal in value but of opposite sig...

How To: Divide rational expressions

In this video the instructor shows how to divide rational expressions. To divide rational expressions follow this simple four step approach. In the fist step change the division to multiplication by flipping the second fraction. Now the original division simplifies to multiplication. In the second step factor the terms of numerators and denominators in the two fractions. In the third step cancel the common terms in the numerator and the denominator. Now finally in the fourth step multiply all...

How To: Complete a proof involving angles

Money math is back for a chill lesson on completing a proof involving angles. This proof touches on complementary angles, definition of congruent angles, Angle Addition Postulate, and substitution. YAY MATH! This video will demonstrate exactly how to complete a proof involving angles.

How To: Calculate a limit by getting a common denominator

This video explores how to get the limit by getting a common denominator. When you try and plug in a limit, for example when the denominator goes to zero, you can get yourself into a situation where you get the answer (0/0) which is mathematically irrelevant. To solve this problem, you must find a common denominator and split the problem up into its various parts. By setting common denominators in the numerator, you can then flip the fraction around allowing you to properly calculate the limi...