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 TOPICS This page:   basic algebra    Search   Dr. Math See also the Dr. Math FAQ:   cubic and   quartic equations and   order of operations Internet Library:   basic algebra T2T FAQ:   algebra help HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Basic Algebra Stars indicate particularly interesting answers or good places to begin browsing. Negative Exponents [10/23/1996] I have to simplify this expression with non-negative exponents: x^5. Negative Numbers Combined with Exponentials [03/09/2001] Why in the order of operations is negation a multiplication done after exponentiation, rather than as a part of the base? What about polynomials? Negatives and Inequalities [09/10/1998] Why when we multiply or divide an inequality by a negative number do we reverse the inequality sign? Negative vs. Subtraction in Order of Operations [10/30/2002] I am trying to find some definitive source for treatment of leading negative numbers in simplifying with order of operations. Nested Negative Exponents [8/2/1996] How do I deal with nested negative exponents? Net Result of Consecutive Percentage Increases [12/11/2003] Suppose a quantity is increased by some percentage, and then is later increased again by another percentage. How can I calculate the overall percentage increase? Nonlinear Factors [10/12/1998] I have been told that factoring the sum of two squared numbers is not possible, but factoring x^4 + 4 is possible. Please explain. Non-Linear Simultaneous Equations [12/07/2003] I have four simultaneous equations with four variables, but each one has a non-linear term in it (e.g., ab + c + d = 3). So none of the usual techniques will work! How can I solve the system? Normalization [08/01/2001] How do I figure out: 90 + 70 + 88 + 94 + x / 5 = 85 ? The Nth Root of N [11/28/2000] Is the nth root of n (a whole number other than 1) ever a rational number? Number of Equations Needed in a Simultaneous Linear System [10/29/2003] Could you tell me why we need the same number of equations as variables in order to get a unique solution to a system of simultaneous linear equations? Number * Sum of Remaining Four Numbers [04/03/2003] Find 5 numbers such that when each number is multiplied by the sum of the remaining 4 numbers, the following values will result: 152, 245, 297, 320, 360. Objects in a Pyramid [7/8/1996] Objects are stacked in a triangular pyramid... how many objects are in the nth layer from the top? Old Test Questions Answered [1/23/1995] I am studying for my midterm, and I've come across two questions that I got wrong and don't understand why.... One Unknown, Decimal Power: By Inspection [10/18/2015] An adult seeks to solve by hand for a variable raised to a decimal exponent. Doctor Ali first simplifies the original equation to obtain its critical points and approximate its maximum before re-introducing its factors and commenting on their effect. One Variable Equations with Decimals [02/11/1997] How do you solve 8.25x + 3 = 17.5 + x? Open Sentence, Statement [09/18/2001] What is an open sentence? Operator Precedence [08/13/2003] Since the following statement is true: (1+1)**(5-2) is 8, why is the following statement true and not false: 2**1+1 is 3 and not 4, and 3*1**3 is 3 and not 27...' ? Ordering Exponents and Variables [04/08/2000] Is there a rule for putting terms in descending order if the variables have the same exponent? What about negative exponents and descending order? Ordering Products, Powers, and Parameters of Trigonometric Functions [10/31/2010] A student wants to know how to unambiguously interpret strings of trigonometric functions, multiplication, and exponentiation. Doctor Peterson digs into a history book -- as well as another math doctor's conversation -- to illuminate the vagaries of the notation. Order in Linear Expressions [11/20/2001] Can you give me a convincing argument as to why, in an equation such as y=13-7x, where y is a function of x, it should be written as y=-7x+13? Order of Operations [05/19/1999] Given a, b, x, and y, find ax/by. Order of Operations with Percentages [04/05/2001] Why does the order of operations exclude percentage, square roots, etc.? Other Ways to Get the Quadratic Formula [02/19/2010] Doctor Jacques shares two ways to derive [-b +/- SQRT(b^2 - 4ac)]/2a without explicitly completing the square. Pairs of Odd Integers [09/24/1997] Find all pairs of odd integers a and b that satisfy the equation: a + 128b = 3ab. Parabola with Horizontal or Vertical Axis [05/03/2001] How can I find the focus and directrix of a parabola whose axis is either horizontal or vertical, like 2x^2 = -y? Parabolic Golf Shot Equations [01/24/2002] Does the ball reach the green? Parallel and Perpendicular Lines [01/14/1999] How do you tell without graphing whether the graphs of these equations are parallel, perpendicular, or neither? Parallel Lines [12/31/1998] What are some ways of proving lines parallel - geometrically and algebraically? Parametric Form for Equation of a Line [6/30/1996] How can you convert an equation such as y = -3x/4 + 7/2 to parametric vector form? Parity [8/2/1996] How do I determine if the given function is odd, even or neither? What's the symmetry of the graph? Partial Fractions [01/29/1998] How do I express 3/1-(x^3) in partial fractions? Pascal's Triangle Pattern [04/22/1999] What pattern does multiplying each entry by 1, 2, 3, 4, 5... in order, and adding the products yield? Perfect Square: Solving Two Equations [6/14/1996] x^2 + 5 is a perfect square, and x^2 - 5 is a perfect square. Perimeter Equals Area in a Triangle [4/2/1996] When will the area and perimeter of a right triangle be numerically equal? Picture Frame, Triangle Measurements [5/20/1996] My teacher gave us ten questions to answer and I could do all except two: 1) A framed rectangular picture is 35cm long and 25cm wide... 2) The base of a triangle is 9cm more than the perpendicular height... Plus or Minus Sign [03/08/2002] What does this equation mean: y = +- k ? The - sign is directly under the + sign. Point Equidistant from 3 Other Points [04/11/1999] How do you find a point that is equidistant from three other points? Point on a Line [03/23/2001] Can you please tell me a formula to find if a point exists on a line? Both are in x,y form. Polynomial Brain-Twisters [12/4/1995] I'm stumped on some similar polynomial problems... Page: []

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