Purplemath.

Share your videos with friends, family, and the world The Purplemath lessons have been written so that they may be studied in whatever manner the student finds most useful. Different textbooks cover different topics in different orders. The Purplemath lessons try not to assume any fixed ordering of topics, so that any student, regardless of the textbook being, may benefit. The general form of a parabola's equation is the quadratic that you're used to: y = ax2 + bx + c. — unless the quadratic is sideways, in which case the equation will look something like this: x = ay2 + by + c. The important difference in the two equations is in which variable is squared: for regular (that is, for vertical) parabolas, the x ...Lessons and Tutoring - Reviews. The reviews below refer to free (or free-to-try) off-site tutoring and instructional resources. To access the Purplemath lessons and tutoring forums, please use the links to the right. For paid in-home tutoring, please try here. algebra.help: This site has lessons on basic algebra topics and techniques, …Purplemath. Once you've learned the basic keywords for translating word problems from English into mathematical expressions and equations, you'll be presented with various English expressions, and be told to perform the translation. Don't view the lists of keywords as holy writ, handed down from on high. Instead, use these lists …

For the same reason, you can take any odd root (third root, fifth root, seventh root, etc.) of a negative number. Squaring a negative number multiplies it by itself, meaning two minus signs that cancel; e.g. (−3)² … Purplemath. So far, we've dealt with each type of asymptote separately, giving one page to each type, kind of like your textbook probably does, giving one section to each type. But on the test, the questions won't specify which type of asymptote you'll need to find.

Purplemath. In addition to finding lines (axes) of symmetry, you can also look for points of symmetry. A point of symmetry is a point that represents a "center" of sorts for the figure. For any line that you draw through the point of symmetry, if this line crosses the figure on one side of the point, the line will also cross the figure on the ...Purplemath. Another "typical" work problem is the "one guy did part of the job" or "the number of workers changed at some point during the job" type. We'll still need to do the computations for how much each guy does per unit time (usually hours or days), but we may need to use the fact that "a completed task" is represented by " …

Find the mean, median, mode, and range for the following list of values: 1, 2, 4, 7. The mean is the usual average: (1 + 2 + 4 + 7) ÷ 4 = 14 ÷ 4 = 3.5. The median is the middle number. In this example, the numbers are already listed in numerical order, so I don't have to rewrite the list. But there is no "middle" number, because there are an ...In the above example, the degree on the denominator (namely, 2) was bigger than the degree on the numerator (namely, 1), and the horizontal asymptote was y = 0 (that is, it was the x-axis).This property is always true: If the degree on x in the denominator is larger than the degree on x in the numerator, then the … So x = 1 is one of the zeroes. Trying x = −1, I get: 1 − 9 + 11 + 22 − 9 + 11 + 21 = 48. Okay; so that one isn't a zero. But, to reduce my polynomial by the one factor corresponding to this zero, I'll do my first synthetic division: So my reduced polynomial is equation is: x5 + 10 x4 + 21 x3 − x2 − 10 x − 21 = 0. Find the mean, median, mode, and range for the following list of values: 1, 2, 4, 7. The mean is the usual average: (1 + 2 + 4 + 7) ÷ 4 = 14 ÷ 4 = 3.5. The median is the middle number. In this example, the numbers are already listed in numerical order, so I don't have to rewrite the list. But there is no "middle" number, because there are …

My answer is: x = 6. Find the unknown value in the proportion: (2x + 1) : 2 = (x + 2) : 5. Okay; this proportion has more variables than I've seen previously, and they're in expressions, rather than standing by themselves. So this is gonna be a cross-multiplying solution.

Compound (or compounded) interest is interest that is earned on interest. If you invest $300 in a compound-interest fund for two years at 10% interest annually, you will earn $30 for the first year, but then you will earn 10% of $330 (or $33) for the second year, for a total of $63 in interest. Content Continues Below.

Polynomial are sums (and differences) of polynomial "terms". For an expression to be a polynomial term, any variables in the expression must have whole-number powers (or else the "understood" power of 1, as in x1, which is normally written as x ). A plain number can also be a polynomial term. In particular, for an expression to be a polynomial ...Improve your SAT math score with online test prep classes from PurpleMath and MathHelp. Free SAT practice questions and a personal math tutor!Purplemath. The "addition" method of solving systems of linear equations is also called the "elimination" method. Under either name, this method is similar to the method you …Purplemath. In addition to finding lines (axes) of symmetry, you can also look for points of symmetry. A point of symmetry is a point that represents a "center" of sorts for the figure. For any line that you draw through the point of symmetry, if this line crosses the figure on one side of the point, the line will also cross the figure on the ...3,000 + x. 0.075. 1. The total interest earned will be the sum of the interest from each of the two investments, so add down the I column to get the following equation: 150 + 0.09 x = (3,000 + x ) (0.075) To find the solution, solve for the value of x. Advertisement. Free math problem solver answers your algebra homework questions with step-by-step explanations. Purplemath. At first, trigonometric ratios, such as sine and cosine, related only to the ratios of side-lengths of right triangles. Then you learned how to find ratios for any angle, using all four quadrants. Then you learned about the unit circle, in which the value of the hypotenuse was always r = 1 so that sin (θ) = y and cos (θ) = x.

Compound (or compounded) interest is interest that is earned on interest. If you invest $300 in a compound-interest fund for two years at 10% interest annually, you will earn $30 for the first year, but then you will earn 10% of $330 (or $33) for the second year, for a total of $63 in interest. Content Continues Below. Solve x2 − 48 = 0. This quadratic expression has two terms, and nothing factors out, so either it's a difference of squares (which I can factor) or else it can be formatted as " (variable part) 2 equals (a number)" so I can square-root both sides. Since 48 is not a square, I can't apply the difference-of-squares formula. Purplemath. Radians and degrees are two types of units for measuring angles. There are very many such units (such as "gradians" and "MRADs"), but degrees and radians are the ones you are most likely to encounter in high school and college. Degrees. Degrees are used to express both directionality and angle size.Purplemath How do you graph an exponential function by hand? To graph an exponential function by hand, you need to find the intercept(s), plot a few additional points, and then connect the dots and draw the graph, using what you know of exponential behavior and the general shape of the curve.The four directions in which one can move a function's graph are up, down, to the right, and to the left. Usually, translation involves only moving the graph around. Squeezing or stretching a graph is more of a "transformation" of the graph. But these two topics are usually taught at the same time, and usually under the same name.

Purplemath What is a ratio? A "ratio" is just a comparison between, or a relating of, two different things. Ratios are used to create proportions by setting two ratios equal to each other and solving for some unknown, and ratios can also be used to find per-unit rates such as how many mile a car can drive "per liter" or how many hours the average student at a …

You should know the formula for the circumference C and area A of a circle, given the radius r: Acir = π r2. Ccir = 2π r. (" π " is the number approximated by 3.14159 or the fraction 22/7) Remember that the radius of a circle is the distance from the center to the outside of a circle. In other words, the radius is just halfway across. Solve x2 − 48 = 0. This quadratic expression has two terms, and nothing factors out, so either it's a difference of squares (which I can factor) or else it can be formatted as " (variable part) 2 equals (a number)" so I can square-root both sides. Since 48 is not a square, I can't apply the difference-of-squares formula. To factor a quadratic (that is, to factor a trinomial of the form ax2+ bx+ c) where the leading coefficient a is not equal to 1, follow these steps: Multiply the leading coefficient a and the constant term c to get the product ac. Find factors of ac that add up to the coefficient of the constant term b. Use these factors of ac to split the ...A non-linear equation is one with at least one term containing two variables or at least one term containing a variable of degree two or greater. For instance, y = 2x is a linear equation (which will graph as a straight line), while y = 2x2 is a non-linear equation (which will graph as some sort of curved line).Purplemath What are exponents (in math)? Exponents, also called powers or orders, are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the "equals" sign in (5)(5)(5) = 5 3.Purplemath. In the previous two pages, we've looked at solving one-step linear equations; that is, equations that require one addition or subtraction, or that require one multiplication or division. However, most linear equations require more than one step in order to find their solution. What steps then should be used, and in what order?In sum, the steps for graphing radical (that is, square root) functions are these: Find the domain of the function: set the insides of the radical "greater than or equal to" zero, and solve for the allowable x -values. Make a T-chart to hold your plot points. Pick x -values within the domain (including the "or equal to" endpoint of the domain ...To be able to be combined, the terms' variable portions must contain the exact same variable (s) with the exact same power (s). Once you have determined that two terms are indeed "like" terms and can indeed therefore be combined, you can then deal with the terms in a manner similar to what you did in grammar school. The Purplemath lessons have been written so that they may be studied in whatever manner the student finds most useful. Different textbooks cover different topics in different orders. The Purplemath lessons try not to assume any fixed ordering of topics, so that any student, regardless of the textbook being, may benefit. To graph a log function: Always keep in mind that logs are inverses of exponentials; this will remind you of the shape you should expect the graph to have. Pick input values (that is, x -values) that are powers of the base; for instance, if the log's base is 5, then pick x -values like 52 and 5−1. List the corresponding y -values; for ...

Since the first differences are the same, this means that the rule is a linear polynomial, something of the form y = an + b. I will plug in the first couple of values from the sequence, and solve for the coefficients of the polynomial: 1 a + b = 5. 2 a + b = 7. This system solves as: So the formula is y = 2n + 3.

Purplemath. At first, trigonometric ratios, such as sine and cosine, related only to the ratios of side-lengths of right triangles. Then you learned how to find ratios for any angle, using all four quadrants. Then you learned about the unit circle, in which the value of the hypotenuse was always r = 1 so that sin (θ) = y and cos (θ) = x.

Purplemath. The "addition" method of solving systems of linear equations is also called the "elimination" method. Under either name, this method is similar to the method you probably used when you were first learning how to solve one-variable linear equations.. Suppose, back in the day, they'd given you the equation "x + 6 …Simplify the following expression: I'll move the one variable with a negative exponent, cancel off the y 's, and simplify: \dfrac {3 x^ {-2} y} {xy} = \dfrac {3y} {x^2 \cdot xy} xy3x−2y = x2⋅xy3y. Demonstrates how to simplify fractions containing negative exponents. Provides worked examples, showing how the same exercise can be …You should know the formula for the circumference C and area A of a circle, given the radius r: Acir = π r2. Ccir = 2π r. (" π " is the number approximated by 3.14159 or the fraction 22/7) Remember that the radius of a circle is the distance from the center to the outside of a circle. In other words, the radius is just halfway across.Logarithms are inverse functions (backwards), and logs represent exponents (concept), and taking logs is the undoing of exponentials (backwards and a concept). And this is a lot to take in all at once. Yes, in a sense, logarithms are themselves exponents. Logarithms have bases, just as do exponentials; for instance, log5(25) … Using these numbers, I can split the middle −13x term into the two terms −9x and −4x, and then I can factor in pairs: 6 x2 − 13x + 6. = 6 x2 − 9x − 4x + 6. = 3 x (2 x − 3) − 2 (2 x − 3) = (2x − 3) (3x − 2) The factoring method in the last two examples above — in particular, the part where I picked two numbers for ... Purplemath What is a circle? A circle is a geometrical shape. It is defined as having a center, and being the set of all points that are a certain fixed distance from that center. (The fixed distance is called the radius of the circle.) The circle is not of much use in algebra since the equation of a circle isn't a function. Purplemath How do you graph an exponential function by hand? To graph an exponential function by hand, you need to find the intercept(s), plot a few additional points, and then connect the dots and draw the graph, using what you know of exponential behavior and the general shape of the curve.Page 1 Page 2 Page 3. Page 4. Demonstrates how to recognize which of the special-factoring formulas — differences of squares, sums and differences of cubes, and perfect …y ≥ (2/3) x − 4. y ≤ (−1/5) x + 4. x > 0. "Solving" systems of two-variable linear inequalities means "graphing each individual inequality, and then finding the overlaps of the various solutions". So I graph each inequality individually, marking the "solution" side of each line as I go, and then I'll find the overlapping portion of the ... Pre-algebra and algebra lessons, from negative numbers through pre-calculus. Grouped by level of study. Lessons are practical in nature informal in tone, and contain many worked examples and warnings about problem areas and probable "trick" questions. Lessons and Tutoring - Reviews. The reviews below refer to free (or free-to-try) off-site tutoring and instructional resources. To access the Purplemath lessons and tutoring forums, please use the links to the right. For paid in-home tutoring, please try here. algebra.help: This site has lessons on basic algebra topics and techniques, …

Pre-algebra and algebra lessons, from negative numbers through pre-calculus. Grouped by level of study. Lessons are practical in nature informal in tone, and contain many worked examples and warnings about problem areas and probable "trick" questions. Then the GCF is 2 × 3 × 5 × 7 = 210. On the other hand, the Least Common Multiple, the LCM, is the smallest (that is, the "least") number that both 2940 and 3150 will divide into. That is, it is the smallest number that contains both 2940 and 3150 as factors, the smallest number that is a *multiple* that is common to both these values. Therefore, it will be the …Pre-algebra and algebra lessons, from negative numbers through pre-calculus. Grouped by level of study. Lessons are practical in nature informal in tone, and contain many worked examples and warnings about problem areas and probable "trick" questions.Purplemath. Up until now, you've been told that you can't take the square root of a negative number. That's because you had no numbers which were negative after you'd squared them — so you couldn't "go backwards" and return to them by taking the square root. Before now, every number was positive after you squared it.Instagram:https://instagram. nine quarter circle rancheagle auto repairrogue energylowes rockingham nc Purplemath. So far, we've dealt with each type of asymptote separately, giving one page to each type, kind of like your textbook probably does, giving one section to each type. But on the test, the questions won't specify which type of asymptote you'll need to find. Content Continues Below. benjamins calabashbeach properties hilton head Purplemath. In the equation of a straight line (when the equation is written as " y = mx + b "), the slope is the number " m " that is multiplied on the x, and " b " is the y - intercept (that is, the point where the line crosses the vertical y -axis). This useful form of the line equation is sensibly named the "slope-intercept form".Purplemath What are exponents (in math)? Exponents, also called powers or orders, are shorthand for repeated multiplication of the same thing by itself. For instance, the shorthand for multiplying three copies of the number 5 is shown on the right-hand side of the "equals" sign in (5)(5)(5) = 5 3. flowers by michelle Purplemath What are a number's "factors"? "Factors" are the whole numbers you multiply to get another whole number. For instance, factors of 15 are 3 and 5, because 3 × 5 = 15. Some numbers have more than one factorization (more than one way of being factored). For instance, 12 can be factored as 1 ×12, 2 × 6, and also …Purplemath. The "addition" method of solving systems of linear equations is also called the "elimination" method. Under either name, this method is similar to the method you probably used when you were first learning how to solve one-variable linear equations.. Suppose, back in the day, they'd given you the equation "x + 6 … The Algebra 1 course, often taught in the 9th grade, covers Linear equations, inequalities, functions, and graphs; Systems of equations and inequalities; Extension of the concept of a function; Exponential models; and Quadratic equations, functions, and graphs. Khan Academy's Algebra 1 course is built to deliver a comprehensive, illuminating, engaging, and Common Core aligned experience!