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Answers:All the reviews I've read indicate that this software is great. http://www.sprysoft.com/product_info.php?products_id=26875 Solves YOUR Algebra Problems, Step-By-Step! When it comes to quickly and easily solving your algebra problems, nothing beats Algebra Solved! 2005. From polynomial simplification to quadratic equations, Algebra Solved! 2005 transforms your algebra problems into solutions while providing step-by-step work and explanations along the way. With powerful features including infinite example problems, infinite practice tests, multiple choice quizzes, detailed graphing analysis, and the Bagatrix Input System , Algebra Solved! 2005 is the complete algebra solution you've been looking for. ~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~ http://www.bagatrix.com/reviews.htm Winner of the 10th ANNUAL EDUCATIONAL SOFTWARE REVIEW AWARDS (EDDIES) for Math - ComputED Gazette Winner of the 11th ANNUAL BEST EDUCATIONAL SOFTWARE AWARDS (BESSIES) for Math - ComputED Gazette "The Solved! series of math help programs is just terrific if you're looking for straight-forward, step-by-step assistance in solving math problems... this is a life-saver!" - Today's Catholic Teacher "Highly recommended for anyone who needs a little extra help with pre-algebra." - All Star Review "This program might just make your day." - Children's Software Review Magazine "A wonderful tool for the new algebra student." - Education Clearinghouse "Algebra Solved! does exactly what the title claims it can do" - SuperKids Software Review "PC Pick Award Winner" - Teach-nology.com "Technology Pathfinder for Teachers Pick of the Month" - Technology Pathfinder for Teachers "All in all, this is a very useful, well-designed math tool." - MasterTeacher.com This page (http://www.bagatrix.com/reviews.htm) also contains many customer reviews. ~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~ REVIEW BELOW IS FROM THE 2005 EDITION http://onlinemathstore.com/Software-229534-B0009PV0UA-Algebra_Solved_2005.html Avg. Customer Rating: FIVE STARS Sounds like an excellent investment to me... Good Luck!
Answers:Absolute Value: The distance of a number from the origin. Absolute value is an example of a norm. Arithmetic: Arithmetic is the branch of mathematics dealing with numerical computation. Arithmetical operations include addition, congruence calculation, division, factorization, multiplication, power computation, root extraction, and subtraction. Arithmetic Series: A series in which the difference between any two consecutive terms is a constant. Associative: An operation * is associative if x*(y*z) = (x*y)*z for all x, y, and z. Base: The number of digits in a number system. The same word is used in the context of logarithms. Cartesian Coordinates: The usual coordinate system, originally described by Descartes, in which points are specified as distances to a set of perpendicular axes. Also called rectangular coordinates. Commutative: An operation * is commutative if x*y = y*x for all x and y. Decimal Expansion: The usual "base 10" representation of a real number. Distributive: Having the property, in multiplication, that x(y+z) = xy + xz. Divisor: An integer that divides a given integer with no remainder. A synonym for factor. Factorial: The product of the first n positive integers, denoted n!. Fraction: A rational number expressed in the form a/b, where a is known as the numerator and b as the denominator. Function Graph: The set of points showing the values taken by a function. This type of plot is called simply a "graph" in common parlance, but is distinct from a collection of points and lines that mathematicians refer to when they speak of a "graph." Geometric Series: A series in which the ratio of any two consecutive terms is always the same. Greatest Common Divisor: For two or more integers, the largest integer dividing all of them. Integer: One of the numbers ..., -2, -1, 0, 1, 2, .... Intersection: (1) For two sets A and B, the set of elements common to A and B. (2) For two or more geometric objects, the set of points that are common to both of them. Interval: A connected piece of the real number line. An interval can be open or closed at either end. Irrational Number: A number that cannot be written as a fraction. Irrational numbers have decimal expansions that neither terminate nor become periodic. Least Common Multiple: For two or more integers, the smallest number that is a multiple of all of them. Line: The infinite extension in both directions of a line segment, which is the path of shortest distance between two points. Origin: The point with all-zero coordinates in Cartesian coordinates, or the central point in polar coordinates. Polynomial: A mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. Power: An exponent to which a given quantity is raised. Prime Factor: A divisor that is also a prime number. Prime Factorization: The factorization of a number into its constituent primes. Also called prime decomposition. Prime Number: A positive integer that has exactly one positive integer divisor other than 1 (i.e., no factors other than 1 and itself). Prime numbers are often simply called primes. Pythagorean Theorem: An equation relating the lengths of the sides of a right triangle. Given two sides, the length of the third can be determined. Quotient: The result of dividing one number by another. Rational Number: A real number that can be written as a quotient of two integers. Real Line: A line with a fixed scale so that every real number corresponds to a unique point on the line. Real Number: The set of all rational and irrational numbers. Relatively Prime: A term describing integers that share no common positive divisors except 1. Right Angle: An angle that measures exactly ninety degrees. Rounding: The approximation of a number by truncating and possibly adjusting the last digit of interest based on digits appearing after it. Sequence: A (possibly infinite) ordered list of numbers. Series: An often infinite sum of terms specified by some rule. Set: A finite or infinite collection of objects in which order has no significance and multiplicity is generally also ignored. Square Number: An integer that is the square (i.e., second power) of another integer. Square Root: A square root of x is a number r such that r*r = x.
Answers:Great question! Unfortunately, I don't see any "easy" proofs, and I'm sure if there were one, it would be plastered all over the Internet. It's great that you're asking such questions...number theory is an undervalued part of pre-university mathematics! In high school we never proved this even once we got to calculus, and even looking at the proofs on wikipedia right now, they kind of blow my mind. All the proofs I see for the irrationality involve some combo of: 1) Infinite sequences / limits 2) Integration (ie calculus) 3) Trigonometric functions All of those are out of your reach at this moment probably...but don't worry! You'll get there. I wish I could give you a more satisfactory answer. Hopefully you've encountered the proof that SQRT(2) ir irrational...it's a classic proof because it involves: 1) Proof by contradiction (a VERY important proof technique!) 2) Some basic number theory arguments involving odd and even numbers One other fun fact: pi is even worse than merely irrational. It's transcendental! What does that mean? Well, SQRT(2) is a solution to the equation x^2 = 2. Pi will NEVER be the solution to ANY polynomial with coefficients that are integers. What's the solution to 4x^4 - 3x^3 + 2x^2 + 9x - 39 = 0? NOT PI! So basically, the set of real numbers has both rational and irrational numbers. Within irrational numbers, there are "algebraic" well-behaved numbers like SQRT(2), and "transcendental" numbers like pi. There's another number 'e' that's also famous for being transcendental. It's equal to about 2.71. You'll learn more about e in Algebra II (in a couple of years). There's also one other weird number that's transcendental: 0.1234567891011121314151617.... It's not a simple rational number, because it doesn't have a "repeating" pattern.
Answers:We ordered a pre-algebra book online and if our son was having to much trouble then he would look at the book for help on a question. I'm not sure of the exact link online for the book we ordered but maybe these will help. You can also do a search like typing in free math problem answers algebra solutions and it may show how to solve certain problems. Here is one link for free help http://www.algebra-online.com/math-software/free-algebra-problem-answers.html Here is a link where you can type in a problem and it shows you how to solve some. http://www.math.com/students/worksheet/algebra_sp.htm