Algebra

• Acid Concentration, Heating Bill [Chu, 7/6/1996]
  1) A pharmacist has 8 liters of a 15 percent solution of acid. How much distilled water must she add.... 2) By installing a $120 thermostat, a family hopes to cut its annual heating bill...

• Algebra and Trig Equation [Silva, 4/20/1996]
  I need to know how can I solve this equation: 1 = sin(3x) - cos(6x).

• All About Functions [Bonie, 11/06/1996]
  Could you please explain functions?

• Completing the Square [Shea, 09/08/1997]
  Please explain 2x^2 = x + 5 .

• Concept of Factoring [Torres, 03/22/1997]
  Could you explain the concept of factoring and give examples of its practical uses?

• Diagonals and Tiles [Kamie, 11/17/2001]
  Jay tiled a 15x21' rectangular ballroom with 1 ft. sq. tiles. Then he drew diagonals connecting opposite corners of the room. How many tiles did the diagonals pass through?

• Direct and Indirect Variation [Adam, 6/12/1996]
  Please explain direct and indirect variation.

• Distributive Property, Illustrated [Tom, 09/28/2001]
  How can I show (12*2) + (12*5) using the distributive property?

• Equations: the "Elimination" Method [Collin, 11/20/1996]
  Is there an easier way to solve a system of two equations than by the substitution method?

• Exp, Log, and Ln Functions Explained [Ojanen, 7/31/1996]
  What is the exp function? When is it needed? Also, how do I calculate Log and Ln functions with basic arithmetic and logic?

• Explaining Algebra Concepts and FOIL [Rachel, 08/04/1998]
  Some ideas for learning algebra that may help prevent frustration.

• Factoring Polynomials [Cairns, 11/14/1996]
  Is there a logic behind the factorization of polynomials?

• Factoring Polynomials [Emily, 11/07/2001]
  Factoring polynomials like 12x^3y^9 + 20x^5y^4.

• Factoring to Solve a Problem [Keerthi, 7/31/1996]
  I have problems understanding the solution I get when I factor an expression to solve: x (x + 1) = 132...?

• Finding the Equation of a Line [Lauren, 01/08/1997]
  Given either a point and a slope or two points, how do you find the equation of a line in both point-slope and standard form?

• Geometric Objects and Properties using Algebra [Liu, 06/29/1998]
  Why does y = mx+b, and what does it mean?

• Horizontal and Vertical Asymptotes [David, 12/5/1995]
  I am confused about horizontal and vertical asymptotes. Please tell me how to find them, and their definition.

• Linear Expressions [Eubanks, 08/17/1999]
  What are linear expressions, and how will I use them in my life?

• Linear Programming [Anderson, 01/30/1997]
  Maximize the profit of a nutrition center given information about the energy trail mixes they sell.

• Locus and Equations of Lines [Marguerite, 01/10/1999]
  Describe the locus of points that are 3 units from the line x = -1...

• Loosening the Earth's Belt [Lozowski, 1/18/1996]
  The earth has a belt around the equator that is perfectly fit. If a measurement of 1 foot is added to the belt, theoretically the belt will no longer touch the earth at any point. What is the new distance between the surface of the earth and the belt?

• Long Division of Polynomials [Parrill, 6/26/1995]
  How do you use long division to solve polynomials with remainders?

• Man and Train on a Bridge [Sayre, 2/1/1996]
  When a man is 3/8 of the way across a railroad bridge that goes from point A to point B, he hears a train approaching at 60 mph. If he runs back he will meet the train at A, and if he runs forward the train will overtake him at B. How fast can the man run?

• Meaning of Irrational Exponents [Knobler, 03/17/1997]
  y^x is the product of x factors of y. Where do irrational exponents fit in this? How can you have an irrational number of factors?

• Mixing Milk and Butterfat [Nicky, 09/04/2001]
  Milk that has 5% butterfat is mixed with milk that has 2% butterfat. How much of each is needed to obtain 60 gallons of milk that has 3% butterfat?

• Negative Ratios and Dividing by Zero [Berni, 6/8/1995]
  How can 1 : -1 = -1 : 1 ? Is x divided by 0 = infinity? Are there different infinities?

• No Solution, Infinite Solutions [Corinne, 01/03/2002]
  Solve: 8(2x-3) = 4(4x-8); -3(x-3) is greater than or equal to 5-3x.

• The Particular and the General Case [Phil, 11/06/2001]
  If a+b+c=3 and a(^2)+b(^2)+c(^2)=5 and a(^3)+b(^3)+c(^3)=7 what is a(^ 4)+b(^4)+c(^4)? And how is it done?

• Polynomial Inequality Problem [Zangla, 2/7/1996]
  A student asks for help with solving algebraic inequalities.

• Proof by Induction [Lutter, 07/13/1997]
  Prove by induction on n that |A^n|=|A|^n.

• Purpose of Algebra [Stuckey, 10/15/1996]
  What is the purpose of algebra and who came up with the idea?

• Rational Inequality [Alan, 10/09/2001]
  Solve this rational inequality and give an answer in interval notation: -5/(3h+2) greater than or equal to 5/h.

• Real and Complex Equations [Cathy, 09/21/1998]
  I'm having trouble simplifying some real and complex equations for Algebra II. Can you help?

• Regrouping Polynomials [Jessica, 11/19/2001]
  I'm stuck on problems like a^2x - bx - a^2y + by + a^2z - bz.

• Renting Bike Safety Equipment [Jessica, 10/09/2001]
  The Park Department rents a bike with safety equipment for $5 a day. If you provide your own safety equipment, the bike rental is $3 a day. You could buy equipment at a sports store for $28. How many times must you use the trail to justify buying your own safety equipment?

• A Simple Formula? [Mannell, 02/21/1997]
  If one person takes two hours to paint a wall and another only one hour, how long will it take them to paint the wall together?

• Simplifying Algebraic Expressions [Heidi, 03/23/2002]
  Please explain how to simplify algebraic expressions.

• Sketch an Equation [April, 10/07/1997]
  How do I rearrange -3x+2y = -6 to sketch it?

• Slope [Cummings, 9/2/1996]
  What is a slope, and if given a slope = n equation, how do you apply that slope number to another graph problem?

• Solving Inequalities [Polse, 9/8/1995]
  Can you help me with this problem? 1 is less than or equal to (4 - 5K) is less than 9.

• Solving Quadratic Equations [Slab, 5/23/1996]
  5x+x(x-7)= 0

• Solving the Quartic [Cowan, 05/27/1998]
  Can you show me how to solve quartic equations directly?

• Solving Simultaneous Equations and Factoring [Fitzpatrick, 3/18/1996]
  Vanessa built a rectangular pen for her dogs. She used an outside wall of the garage for one of the sides of the pen. She had to buy 20m of fencing...

• Train, Distance, and Speed [Jenny, 09/20/1997]
  How fast does Bobo run?

• Transformations [Sroy, 12/14/1995]
  A 10th grade student asks Dr. Math to check a problem concerning transformations.

• Two Methods of Factoring Quadratics [Moss, 04/14/1998]
  Could you describe how to factor quadratic trinomials?

• Unions and Intersections [Warren, 2/9/1995]
  In my text, there are these upside-down horseshoe looking things, and there is no explanation of what they are or why they exist...

• Unsolvable Equations [Shawn, 11/10/2001]
  If I have an equation in the form of x^n+y^n=z, how do I solve for n?

• Unsolvable Equations, Feedback Loops, Existence Proofs... [Goh, 04/14/1997]
  How do you solve equations like (9/4)^x = x^(9/4) ?

• Upstream and Downstream Speed [Maggy, 08/16/1998]
  It takes a ferryboat 2 hours to travel 30 miles going downstream and 3 hours for the return trip upstream. What is the ferryboat's speed in still water?

• What is a Quadratic Equation? [Thacker, 08/04/1997]
  What is a quadratic equation? What is it used for? How can we use it to solve everyday problems?

• When do the Cars Meet? [Jennifer, 01/23/1997]
  Two cars are 635 kilometers apart. They start at the same time and drive toward each other. One travels at 70 km/h and the other travels at 57 km/hr. In how many hours do they meet?

• Which Barrel is Unsold? [Leng, 3/1/1995]
  There are six barrels with volumes of 8, 13, 15, 17, 19, and 31 litres respectively. These barrels contain either petrol or diesel oil. The price of petrol is twice the price of diesel oil per litre...

• Write in Slope-Intercept Form [Cobra, 11/06/1997]
  Write and sketch x - y + 2 = 0 .

• X greater than 25, OR less than 30 [Larcson, 8/17/1996]
  x > 25 or x < 30. The "or" part of the problem bugs me. Is the answer {26, 27, 28, 29}?

• Functions [Mark M., 11/12/1994]
  I'm a first year algebra student having difficulty learning about functions. Exactly how do they work?

• Triangle inequality [Wadler, 11/14/1994]
  Is it possible to prove that the absolute value of (a-b) is greater than or equal to the absolute value of a minus the absolute value of b?

• Is this Right? [Seguin, 1/9/1995]
  How do you do a question like this: 2y(3y+1)-3(3y+1)+y(y+2)?

• Old Test Questions Answered [Backman, 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....

• Math Team Test Question [Roy, 1/30/1995]
  We have been working on this for a week: a^b - b^a = 10^x. Given a=1000, b=1001; and the answer is x=3002.99. Would you know how to help us?

• Empty Set Classification [Lowe, 2/20/1995]
  We would like to know if you would classify an empty set as being finite, infinite, or with another classification.

• Logarithmic Problem [Olson, 2/22/1995]
  Can you help me solve this: log 3^x = 6 + (1/2)log 9^x?

• Competition Questions [Ramser, 2/25/1995]
  We are trying to prepare students for competitions and have two problems we cannot solve....

• Cube and Square Roots [Ramser, 3/1/1995]
  What is the sum of the cubes of the roots of 3x^3 + 4x + 2 = 0, and simplify sqrt(3-sqrt(5))/(sqrt(2) + sqrt(7-3sqrt(5))?

• Polynomial Problem [Anna-Jonesboro, 3/11/1995]
  A remainder of 9 results when the polynomial p(x) is divided by x-2, a remainder of -3 when p(x) is divided by x+2, and a remainder of 3 when divided by x-1. Find the remainder when p(x) is divided by (x-2)(x+2)(x-1).

• Rearranging an equation [Carkenord, 3/15/1995]
  I need this equation solved for V....

• What's the Second Part? [Eckersley, 3/21/1995]
  If x = root3 + root2, show that x^4 - 10x^2 +1 = 0. Hence prove that root3 + root2 is irrational.

• Help with a Proof [Dachary, 4/6/1995]
  I'm trying to figure out how to prove that a is less than b implies that a*a is less than b*b is true in R+....

• Distance Between Telephone Poles [Boynes, 4/15/1995]
  If you have 6 equally spaced telephone poles, and the distance between the first and sixth telephone pole is 1260 feet, what is the distance between the first and fourth telephone poles?

• Solving a Complicated Equation [Navid, 4/25/1995]
  Please solve this equation for variable X with parameter k: sin(X) + sin(5*X) + sin(9*X) + ... + sin((4*k+1)*X)=k+1

• Calculate Gross Salary From Net Salary [Jung, 4/27/1995]
  I would appreciate some help with a formula to calculate the gross salary from the net salary. How would the formula look like if you have this: Gross * Rate - Rebate = Tax + Net; x * 0.19 - 2625 = y + 14775 ? How could you calculate x and y?

• Quadratic Problem [Salaz, 7/12/1995]
  Find the quadratic functions with vertex (3,-1) and one x-intercept at x=1.

• Hints for Algebra 101 [Pudggy, 7/31/1995]
  Do you have any helpful hints for algebra 101?

• Division of Polynomials [Sharpe, 8/10/1995]
  Please send me some examples of polynomial divisions.

• Quadratic Trinomials [Rider, 8/14/1995]
  How do you factor quadratic trinomials as the product of linear binomials?

• Graphing [Rider, 8/18/1995]
  I've got questions concerning graphing.

• The Fourth Dimension [Dixon, 8/24/1995]
  What is the fourth dimension mathematically?

• Rotating Matrices [Mitchell,8/28/1995]
  What if there's a spinning thing, and it has an axis, and you have to line up the axis of the real thing with the math of a model? Where's information on rotating matrices to do this???

• Trapezoid Vectors [Lakhani, 9/9/1995]
  In a trapezoid TXYZ, the vector TX = the vector bZY. If the diagonals meet at O, find an expression for the vector TO in terms of the vector TX and the vector TZ.

• The Difference of Two Squares [Moshfeghian, 9/21/1995]
  In the following problem, I factor the same problem two different ways. Why do I not get the same answer?

• Using the Slope-Intercept Formula [Plotkin, 9/27/1995]
  How can I write an equation for the line when I have the x-intercept and the slope?

• Arithmetic and Geometric Progressions [Sharpe, 10/10/1995]
  In an Arithmetic Progression, whose first term and common difference are both non-zero, U(n) denotes the nth term and S(n) denotes the sum of n terms. If U(6), U(4), U(10) form a Geometric Progression show that S(10) = 0, show that S(6) + S(12) = 0, and deduce that U(7) + U(8) + U(9) + U(10) = U(11) + U(12).

• Graphing an Equation with Absolute Value [Tucker, 10/15/1995]
  How would you approach graphing negative 2 times the absolute value of x plus 2?

• Preparing for an Algebra Test [Nerlekar, 11/1/1995]
  A 9th grade math student asks for help preparing for final exams. What is the difference between the terms: solve and simplify? How do you find the gradient in a graph?

• Finding Your Position on a Football Field [Reichel, 11/1/1995]
  Write a function F(x) that represents your position on the football field after walking x yards from the goal line. Give the domain and range of this function.

• Factoring to Find the Limit [Florance, 11/5/1995]
  Factoring the numerator of a limit problem.

• Consecutive Integers [Oullette, 11/7/1995]
  Finding consecutive integers.

• Simplifying Equations [Deborah, 11/7/1995]
  Simplifying a fractional equation.

• The Ratio of the Speed of a Colonel to his Soldiers [Sismondo, 11/7/1995]
  A colonel leads a column of soldiers. He marches to the rear of the column at a speed different from the column's and then at the same speed marches back to the front of the column. During this time the column marches a distance equal to its length. What is the ratio of the speed of the faster to the slower?

• A Trick for Solving Equations with Fractions [Vic, 11/12/1995]
  Help solving an equation with fractions.

• Simultaneous Equations [Bromberg, 11/28/1995]
  A student asks about solving simultaneous equations.

• Polynomial Brain-Twisters [Howard, 12/4/1995]
  I'm stumped on some similar polynomial problems...

• Finding the Dimensions of a Room [Neumank, 12/5/1995]
  After studying statistical data, Fariba surmises that a club should seat a minimum of 1152 people at tables. The tables will be 3 x 6 feet, and each one will seat 6 customers...

• Rules of Exponent Manipulation [Hearn, 1/22/1996]
  f sub r equals the reciprocal of ...

• Finding the Roots of a Cubic [Nigel, 1/27/1996]
  Find all the roots of x + y = x^2 + y^2 = x^3 + y^3.

• Go for the Gold! [Shua, 1/28/1996]
  Your job is to prepare the women's athletes for the Olympic 1,500-meter race.

• Wind Chill Formula [Gunderson, 2/1/1996]
  Could you tell us the formula used for finding the wind chill?

• Solving for Variable [Bradie, 2/7/1996]
  Given the equation P=V*R/(1-(1+R)e^(-N)), how is this simplified to solve for R (rate) if Pt, PV, and N are known?

• Substitution to Eliminate Linear Terms [Damato, 2/9/1996]
  Are there any substitutions for eliminating the linear term in both quadratic and quartic equations?

• Algebra 1: Sum of all Values of X [Roy, 2/15/1996]
  Find the sum of all values of X such that 6(X) is an integer and (X-4)/(X-2) >= 3.

• Expressing a Code Algebraically [Mazza, 3/19/1996]
  I am to express a code algebraically. The code is the alphabet reversed.. a=z, b=y, etc...

• Two Algebra Word Problems [Aweare, 3/23/1996]
  Two people decide to open a music store. A building is available for rent for $6000 per year. Heat, electricity, taxes, etc... are estimated at $5000 per year. Each person wants to make $7 per hour...

• Interval Notation [Kelly, 4/1/1996]
  I need to learn about interval notation in terms of domain and ranges.

• Graphing an Equation [Garb, 4/4/1996]
  How do you graph 2x-y = 10?

• Factoring with 3 Variables [Fibranz, 4/8/1996]
  This one has been frustrating. Factor: 9a^2+4bc-4c^2-b^2

• Simplifying Equations [Mody, 4/11/1996]
  I need to solve this by factoring, finding the lowest common denominator, then multiplying by the reciprocal. Simplify: (1+(1/x-1))/(1+(1/x^2-1))

• Graphing points [pg06, 4/13/1996]
  Given f(x)=4 and g(x)=2, which is the Y axis and which is the X axis? f(x)=x-2(3)+4 ; g(x)=x-2(3)+4.

• A Quadratic Inequality [Ender, 4/27/1996]
  Solve the inequality: (3x+1)(5-10x)>0

• Algebra [CJS, 5/10/1996]
  Find the domain, range, and zeros of g(x)=x(squared)-6x+4.

• Cubic Functions [Matt, 5/13/1996]
  Investigate the cubic functions of f(x) = ax^3+bx^2+cx+d...

• Picture Frame, Triangle Measurements [Coleco, 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...

• Comparison of On-line Rates [Magee, 5/20/1996]
  Jack is interested in two on-line companies, Easy Comp and Destruct Comp...

• Factor and Multiply to Check [Jenkins, 5/21/1996]
  Is x to the second power plus 6x plus 5 factorable?

• Associative Property [Humphus, 5/22/1996]
  What is the associative property in algebra?

• Completing the Square [Robert, 5/22/1996]
  How do you complete the square of a polynomial?

• Value Excluded from the Domain [Judy, 5/23/1996]
  f(x) = 3x^3 + x^2 - 2x/(9x^2 - 4).

• Equations and Inequalities [Quittkat, 5/24/1996]
  a) 7(4y+69)-8(2y-3) = 5(3y+7); b) (2x-5)(3x+2) = (6x+1)(x-7); c) (3x-2)(3x+2)+(x+4)(x-5) = (5x-1)(2x-3)

• Factoring Quadratic Equations [Betz, 5/27/1996]
  What's the fastest way to solve any type of quadratic equation?

• Equations for Lines [Milburn, 5/29/1996]
  Write an equation of the line containing the point P(1,-3)...

• Completing the Square [Marta, 5/30/1996]
  I have to solve two equations by completing the square...

• Multiplicative Inverse [padeban, 6/2/1996]
  Find the multiplicative inverse of 2+5i.

• Asymptotes [Veranes, 6/3/1996]
  Will you please explain when asymptotes occur?

• Asymptotes [Margot, 6/3/1996]
  What are the vertical and horizontal asymptotes?

• Sets and Integer Pairs [Gemilang, 6/10/1996]
  A) Prove that the sum of a specified element of one set is greater than or equal to a specific number (n + 1)/2; B) Find all the ordered pairs of integers (m, n) that satisfy the equation (n^3 + 1) / (mn - 1).

• Derivation of quadratic formula [Lopez, 6/12/1996]
  I would like to derive the solution to ax(2) + bx + c = 0.

• Perfect Square: Solving Two Equations [sw4569, 6/14/1996]
  x^2 + 5 is a perfect square, and x^2 - 5 is a perfect square.

• Factoring Algebraic Expressions [Miller, 6/15/1996]
  Factor (xy+1)(x+1)(y+1)+xy and ...

• Quadratic Formulas, Equations, Parabolas, Graphing [McKenzie, 6/16/1996]
  Given 6x^2 + x - 1 = 0, how do I find the roots, the vertex, some coordinates, and from these graph it?

• Solving an Inequality [Novica, 6/17/1996]
  6/(2X+1) > (1/X) (1+log2 (2+X))

• First Year Algebra [Brinkman, 6/19/1996]
  What should a person have learned after one year of Algebra I? I want to be prepared for Geometry next year.

• A Function of a Function [Turner, 6/19/1996]
  Suppose that f(x) is O(g(x)). Does it follow that 2 to the power f(x) is O(2 to the power g(x))?

• Simplifying Algebraic Expressions [Cheliu, 6/20/1996]
  a-{2b+c2[d-3a+e4]a2b3c5}afg(5a-e3=cd3)2f+4g+f9 = ?

• Equilateral Triangles [Flack, 6/22/1996]
  Draw an equilateral triangle of side n units...

• Quadratic Equation [Ajwcpa, 6/22/1996]
  What is a quadratic equation used for?

• Andy's Averaging Machine [Yuen, 6/23/1996]
  How can Andy get a card with 3/32 on it? How can he get a card with 1/5 on it?...

• Infinite sums [Gerard, 6/26/1996]
  Given the function f(x) = x^2/(1+x^2) find the sum f(1/n)+f(2/n)+...+ f(n-1/n)+f(n/n) for any positive integers "N".

• Cycling Motion Problem [Booth, 6/26/1996]
  A cyclist travels from A to B over a high pass...

• Given n Points, find a Polynomial Function... [Richard, 6/27/1996]
  Find a polynomial F(x) of degree less than n so that the graph of F passes through all of the points.

• Find all Integer Values of x.... [Richard, 6/27/1996]
  Find all integer values of x for which [12(x^2-4x+3) / (x^3-3x^2-x+3)] has a positive integer value.

• Parametric Form for Equation of a Line [Roberts, 6/30/1996]
  How can you convert an equation such as y = -3x/4 + 7/2 to parametric vector form?

• Difference of Squares of Two Integers [Geldermann, 7/2/1996]
  Which positive integers can be written as the difference of the squares of two integers?

• Double Quadratic Equation [Duperray, 7/5/1996]
  Is there a simple solution to ax^2 + bx + cy^2 + dy + e = 0?

• Objects in a Pyramid [Geldermann, 7/8/1996]
  Objects are stacked in a triangular pyramid... how many objects are in the nth layer from the top?

• Cycling Uphill [Booth, 7/8/1996]
  I don't know how to handle the unknown speed at which the cyclist travels uphill.

• Factoring Quadratic Equations [Trm, 7/22/1996]
  Are there common points or rules I can apply in every situation?

• Triples of Numbers [Meschel, 7/23/1996]
  Find two triples of positive integers such that their sum equals their product.

• Recommended Algebra Software [BenDor, 7/23/1996]
  I am looking for math software programs with a focus on algebra.

• Volume of Irregular Pyramid of Human Arm [Bakhtiary, 7/24/1996]
  I form an irregular pyramid from my arm, forearm, shoulder and wrist in the rest position (forearm rested on a table). Is there any way to measure the volume of this irregular pyramid?

• Two Equations, Two Unknowns [Pooh, 7/27/1996]
  How do I solve for x and y in terms of a and b for the equations x^4 + y^4 = b^4 and x + y = a?

• Algebra Terms: 'Evaluate' and 'Simplify' [Ware, 7/30/1996]
  What do the terms "evaluate" and "simplify" mean in expressions like "evaluate 3-{2-3(2-7)}" or "simplify -3x{7-(3x-5)}"?

• Prove Triangle of Sides with Length... [Chen, 8/1/1996]
  Let a, b and c be the lengths of the sides of a triangle. Prove that the square root of (a+b-c) plus the square root of (b+c-a) plus the square root of (c+a-b) is equal to or less than the sum of the square roots of a, b and c. Determine when equality occurs.

• Inverse Function [Alfred, 8/2/1996]
  If z(x) = 4x + 15, what is the inverse of z(x)?

• Parity [Alfred, 8/2/1996]
  How do I determine if the given function is odd, even or neither? What's the symmetry of the graph?

• Negative Exponents [Alfred, 8/2/1996]
  How do I deal with nested negative exponents?

• Mixing Alcohol, Cable TV Pricing [Alfred, 8/2/1996]
  What amounts of 9 percent and 12 percent alcohol do you mix to get 300,000 gallons of 10 percent alcohol? For each 5-cent increase in the monthly subscription price, 4 people will decide not to subscribe to cable TV...

• Finding the Equation of a Line [Alfred, 8/2/1996]
  What is the equation of the line that contains the point (4, -4) and is perpendicular to the line defined by 2x-5y+3 = 0?

• Finding Multiplier of Constants [Mishra, 8/5/1996]
  What is a common multiplier of the positive constants a, b, and c such that x/3 = a^2/b^2c?

• Exponents in Algebra [Ware, 8/8/1996]
  Evaluate: (2^-3)-(2^-2).

• Solving for Rate [Bradie, 8/8/1996]
  In the equation P=V*R/(1-(1+R)^(-n)), how do you solve for "R"?

• Squares of Positive Integers [Davsmy, 8/13/1996]
  The positive integers a and b: the numbers 15a+16b and 16a-15b are both squares of positive integers...

• Multiplying and Dividing Fractions [DSK, 8/18/1996]
  Three hard problems, illustrated.

• Manipulation of (Imaginary?) Roots [Michael, 8/18/1996]
  Let r,s, and t be the roots of x^3-6x^2+5x-7=0. Find 1/r^2+1/s^2+1/t^2...

• Simplification Problems [Majure, 8/20/1996]
  Simplify 2x(4-2x+y) - 5x(y^2+x-y)

• Width and Area of a Field [Amcree, 8/22/1996]
  Find a quadratic equation that relates the area of a field to its width.

• Why Does the Order of Square/Square Root Matter? [Mead, 8/28/1996]
  Why does the square root of x^2 equal absolute value of x, but the square of the square root of x equals just plain old x?

• Inverse Function [Enzo, 8/28/1996]
  What is the inverse function of f(x) = 1 - 2x? What is the general method for finding an inverse function?

• Pythagorean Triple [Patrick, 8/28/1996]
  What is the formula for finding the three lengths in a Pythagorean triple where the shortest side is even?

• Quadratic Equation [Al, 8/28/1996]
  What is the formula for the quadratic equation?

• Inequalities and Absolute Value [Brian, 8/28/1996]
  How do I find the solution set for problems like |X| > X and |X + 2| - X >= 0?

• Inverses of Functions [Senter, 9/2/1996]
  How do I find the inverses and determine whether the inverses are functions?

• Find Values of x... [Atienza, 9/4/1996]
  Determine all values of x for which (x^2-5x+5)^(x^2-2x-48)=1.

• Reduce Expression of Two Variables [Hoskinson, 9/4/1996]
  How do I reduce (3xy)/(xy+x)?

• Set Inclusion Notation [Feichtl, 9/12/1996]
  When using the defining property version of set notation, why do we write {x|x<2} instead of {x<2} to mean "the set of all x's such that x is less than 2"?

• Domain of a Function [Spoth, 9/13/1996]
  What is the domain of f(x)= x/sqrt(x^2-4)?

• Compound Inequality [Greenlee, 9/15/1996]
  5x-1 > 4 and 6x+3 < 4x-1

• Finding Solutions to Systems of Equations [Sheehy, 10/18/1996]
  I need help solving systems of equations, i.e. 3m+5n=21 and 4m+10n=38.

• Tangent to Parabola [Spoelhof, 10/21/1996]
  What is the slope of the lines tangent to the parabola y = x^2 that pass through the point (2,1)?

• Two Hot-Air Balloons [Koziol, 10/21/1996]
  The height h of the first balloon at time t is h(t)=50+34t. The height g of the second balloon is g(t)=400-16t. When will they be at the same height and how high will they be?

• Linear Systems [Farley, 10/22/1996]
  I need to solve this system of equations for x and y in terms of a, b, c, d, e, and f: ax + by = e; cx + dy = f.

• Intersecting Graphs [Peters, 10/22/1996]
  The graph of x^2 + xy + y^2 = 3 intersects the graph of x + xy + y + 1 = 0 in k distinct points. What is the value of k?

• Discriminants [Barrow, 10/22/1996]
  Find the discriminant and determine the nature and the number of roots of 2x^2+x-6 = 0 without solving the equation.

• Negative Exponents [Mike, 10/23/1996]
  I have to simplify this expression with non-negative exponents: x^5.

• Root-Mean-Square [Jang, 10/26/1996]
  Compute the smallest integer n, greater than one, for which the root- mean-square of the first n positive integers is an integer.

• Rational Root Test [Wu, 10/28/1996]
  How do you solve the system that consists of the equations xy+6=0 and x^2+y^2-6y-1=0?

• Solving Systems of Equations [Hobson, 10/30/1996]
  Solve for a, b, and c: 2a+6b+c = 5, a+b-c = -1, a+8b+2c = 0.

• Three Sample SAT Questions [Mike, 11/12/1996]
  How do you find the length of diagonal of a square? If (x+2)^2=25 and x>0 what is the value of x^2? Find the value of the denominator that ensures that a set of fractions is in reduced form.

• 33 Pearls Problem [Fletcher, 11/14/1996]
  On a string of 33 pearls, the middle pearl is the most expensive one - find its value.

• Fitting a Picture to a Frame [Stoll, 11/14/1996]
  I have a picture frame that needs to have twice as much border on the side of the picture as on the top. If the photo is half the area of the frame, how wide should the borders be?

• Difference of Two Cubes [Fletcher, 11/18/1996]
  What two positive integers satisfy the condition that the difference of their cubes is 56,765?

• Completing the Cube [Smolka, 11/28/1996]
  Is there some method analogous to completing the square for higher dimension polynomials?

• Using Interval Notation to Express Answers [Johnston, 12/03/1996]
  Solve for x in the inequality x/(x+3) >= 1/(x-1) and express the answer in interval notation.

• Using Relative Primes [Chin, 12/07/1996]
  Given a floor 105 tiles wide and 135 tiles long, how many tiles will a diagonal drawn from one corner to the opposite corner intersect?

• 24 Factors [Fletcher, 12/08/1996]
  What is the smallest positive integer with exactly 24 different positive factors?

• Electrical Relationships [Fishman, 12/10/1996]
  The resistance in an electrical circuit is related to the diameter of the wire and the length of the wire. How does resistance vary with diameter?

• Finding Equations of Parabolas [Duguay, 12/12/1996]
  Determine the equation of the parabola whose vertex is at (1,3) and whose directrix is y=x.

• Arithmetic Progression [Sushant, 12/19/1996]
  If (b+c-a)/a, (c+a-b)/b and (a+b-c)/c are in arithmetic progression, show that 1/a, 1/b and 1/c are also in arithmetic progression.

• Quarter Circles [Cheung, 12/20/1996]
  Find a function that graphs a quarter of a circle in quadrants II and IV.

• Using Graphs to Solve Problems [Gambill, 12/29/1996]
  How do you use graphs to find the answers to questions?

• Solving for X [Greshilov, 01/13/1997]
  Solve for x in 3(x*x)-2x+2 = 2/(3(x*x)-2x+1).

• Completing the Square [Holley, 01/14/1997]
  How do you complete the square? Can you use this to factor polynomials?

• Graphing Parabolas [Mui, 01/16/1997]
  How do you know how to graph a parabola from looking at its equation?

• Factoring Expressions [Heather, 01/19/1997]
  Factor 3x-21, 5x^2y-15xy^2, 18x^2-27x, and 2a-8b-10.

• Simplifying with Cube Roots [Grossman, 01/22/1997]
  Simplify cube root(3)/[cube root(6) + cube root(3)].

• Domain/Range of a Function [Jennifer, 01/22/1997]
  How do you find the domain and range of the function f(x) = 2x^2-3x+1? (Both with and without calculus.)

• Finding the Center of a Circle [McClung, 01/24/1997]
  Given two points on a circle and the circle's radius, find the center coordinates of the circle.

• Multi-Variable Equations [Lisa, 02/07/1997]
  Solve for s in d = (log(f/e) + s * s * 0.5 * t)/(s * s * sqrt(t))

• Redundant Sets of Equations [Crowder, 02/07/1997]
  Is there a solution to the set consisting of these three equations: x + y + z = 50, 2x + 3y + 4z = 158, and 4x + 3y + 2z = 142?

• One Variable Equations with Decimals [Charnesha, 02/11/1997]
  How do you solve 8.25x + 3 = 17.5 + x?

• Learning Algebra [McArthur, 03/02/1997]
  I need a lot of help with Algebra!

• Cancelling Exponents [McArthur, 03/02/1997]
  How did they turn 2^29/2 x 3^16 / 2^32 x 3^15 into 3 / 2^3?

• Equation of a Parabola [Croman, 03/04/1997]
  Determine the equation of a parabola given its vertex and either the equation of the directrix or the coordinates of the focus.

• Dividing Polynomials [Binnig, 03/06/1997]
  The polynomial p(x) with integer coefficients satisfies (1) if p(x) is divided by x^2-4x+3, the remainder is 65x-68, and (2) if p(x) is divided by x^2+6x-7, the remainder is -5x+a. Find a.

• Solving Quadratic Equations [Caitlin, 03/07/1997]
  A rectangle has an area of 80 square units. Its length is one more than three times its width. What are the dimensions of the rectangle?

• Formula for Slope of 3-D Line [Cory, 03/12/1997]
  Is there a formula that gives the slope of a 3-D line?

• Quadratic Equation [Hubert, 04/08/1997]
  The sum of two numbers is 15 and their product is 54. Find the numbers...

• Algebraic expressions and fractions [Dean, 04/10/1997]
  If X/A+Y/B+Z/C = 1 and A/X+B/Y+C/Z = 0, what is (X^2)/(A^2)+(Y^2)/(B^2)+(Z^2)/(C^2)?

• Finding the Inverse Function [Merri, 04/10/1997]
  How do I find the inverse function of f(x)=4x/(x+2), where x does not equal -2? What is the domain and the range?

• Radical Equation [Bob, 04/12/1997]
  How do I solve the radical equation 3x+(5x^(1/2))-28=0?

• Rational Equations [McDonald, 06/07/1997]
  How do you solve 1/(x+1) - 1/(x+2) = 1/2?

• Equation Solving Steps [Jett, 04/28/1997]
  Solve for x in the equation: 4-2(x-2b) = ax+3.

• Using the Distance Formula [Calphool, 05/03/1997]
  Given a line going through the points (10,10) and (20,15), find the coordinates of a third point on the line that is 3 units from the point (10,10).

• Simplification [Guan, 05/04/1997]
  Which is more simplified: (1/a) + (1/b) or (a+b)/ab?

• Solve It Numerically [Riviera, 05/21/1997]
  How do you solve the equation x^x = 100?

• Diophantine Equations [Anna, 06/08/1997]
  Mick has $5.63 worth of bananas and apples. Bananas are 13 cents each and apples are 7 cents each. How many different combinations of apples and bananas can he have and what are they?

• Factoring Quadratics [Nieto, 06/10/1997]
  How do you factor 2x^2 - 11x + 15 or 6a^2 + 7a - 5?

• Closure Axiom [Stojakovic, 06/12/1997]
  What is the closure axiom?

• SAT Algebra Question [Kristen, 06/20/1997]
  A woman drove to work at an average speed of 40 miles per hour and returned at 30 miles per hour. If her total traveling time was 1 hour, what was the total number of miles in the round trip?"

• Interval Notation [Wade, 06/25/1997]
  How do you express answers in interval notation?

• Buying Cows, Pigs, and Chickens [Thomas, 07/09/1997]
  A farmer buys 100 animals for $100. The animals include at least one cow, one pig, and one chicken. If a cow costs $10, a pig costs $3, and a chicken costs $0.50, how many of each did he buy?

• Rationalizing Denominators [Summerlin, 07/12/1997]
  How can I rationalize a denominator with odd power radicals?

• Triangle Perimeter [Caraher, 07/20/1997]
  How many triangles have sides whose lengths total 15 units?

• Binomials: Completing the Square [Brady, 08/01/1997]
  Find two binomials whose product is X ^ 2 - 25 and two binomials whose product is X ^ 2 - 6X + 9.

• Inequalities [Reiss, 08/01/1997]
  How do I deal with an equation with a greater than or less than sign?

• Synthetic Division [Slator, 08/05/1997]
  Please explain synthetic division.

• Lagrange Polynomial Interpolation [Wang, 08/08/1997]
  Please give me the definition and a brief example of how it works.

• Empty Sets [Hood, 08/15/1997]
  Can you help me understand empty sets?

• Difference of Two Squares [Ghory, 08/17/1997]
  Prove that every cube can be expressed as the difference of two squares.

• Absolute Value [Pedro, 08/21/1997]
  Could you please explain |7+3a| = 11-a ?

• Matrix Algebra [Offerman, 08/28/1997]
  I am not sure which formula of matrices to use in this situation.

• Two Airplanes [Gilbert, 08/28/1997]
  Draw a diagram using coordinate system with origin O - how far apart are the airplanes? Express the answer in radical form.

• Prize Money [Vickers, 09/04/1997]
  If first prize wins $1,000 out of $6,000 and twentieth prize wins $100, how much money do second through nineteenth place win? Is this a geometric sequence?

• Algebraic Systems [Hoffman, 09/07/1997]
  Is * associative or commutative for the equation a*b = b h? for a*b = ab+1?

• Equation for an Arch [Cashell, 09/09/1997]
  I am trying to draw an arch that will go in the ceiling of a building. The arch will be at a maximum height of 28 inches...

• Compound Inequalities [Kalaw, 09/10/1997]
  Can you write compound inequalities that use "or" the same way you write compound inequalities that use "and"?

• Math Analysis [Raymond, 09/13/1997]
  I have to figure out the boundaries for the inequality...

• Swimming Upstream and Down [Brown, 09/19/1997]
  A man swims 200 meters upstream in 3 minutes (180 seconds) and downstream 150 meters in .7 minutes. How fast is the man swimming and how fast is the water?

• Advanced Algebra [Bailey, 09/23/1997]
  My teacher gave us this problem: 1+1/(1+1/(1+1/(1+1/1+...)))

• Pairs of Odd Integers [Lam, 09/24/1997]
  Find all pairs of odd integers a and b that satisfy the equation: a + 128b = 3ab.

• Completing the Square [Walse, 09/30/1997]
  I really need help with this problem: 1 + 7/x + 2/x^2 = 0.

• Infinite Geometric Progression [Lum, 10/02/1997]
  How do you go about solving .27 repeating into a fraction?

• Linear Equations and Functions [Hartman, 10/11/1997]
  The digits of a positive 2-digit integer N are interchanged to form an integer K. Find all possibilities for N... the average of N, K, and 35 is 30.

• Raising Sqrt(2) [Benno, 10/14/1997]
  What is the value of x in the following equation: x^x^x^x^x ... = 2 ?

• Burning 300 Calories [Devenell, 10/15/1997]
  Liam burns 8.3 Cal/min when using a rowing machine, and 5.9 CAl/min when using an exercise bike...

• Sum or Difference of Two Cubes [Henderson, 10/16/1997]
  Factor and check: c^3 + d^3; b^3 - c^3; x^3 + 8; y^3 - 125.

• Inequalities and Absolute Value [Trupiano, 10/17/1997]
  What's the definition of absolute value?

• Distributive Property [Nicole, 10/29/1997]
  I don't understand the Distributive Property at all.

• Interval Notation [Phil, 11/01/1997]
  Solve for x and write the answer in interval notation: -3 < -x < 2 / 3.

• The Sum of Two Numbers is 20... [Hurley, 11/03/1997]
  Twice one number is 4 more than four times the other. Find the numbers.

• Factoring (x - 1)(x^2 - x - 2) [Michelle, 11/04/1997]
  I don't remember how to factor.

• A Container Holds 5/8 Gallon... [Brook, 11/05/1997]
  If the container is 4/5 full and then 25 percent of the liquid is lost due to evaporation, how much liquid is left in the container?

• Graph Intercepts [Guenther, 11/06/1997]
  How would I find the intercept for a problem such as 3x-2y = 12?

• Divisibility by 37 [Renselaar, 11/08/1997]
  Take a 3-digit number and add to that its "rotation". Prove that the sum can always be divided by 37.

• Graphing an Equation [Loh, 11/08/1997]
  Please explain how to graph this equation: y = a + b(x) + c(x^2) + ...

• Mixture Problem [Lower, 11/11/1997]
  How much pure antifreeze should be added to 3 gallons of a 30 percent antifreeze solution to get 65 percent antifreeze?

• Recursive Function for Loan Problem [Hotetz, 11/13/1997]
  What is the recursive function formula for a loan of $100,000, payable at 6 percent, over 20 years?

• Strategy: Finding a Formula [Betsy, 11/14/1997]
  Jill needs three pieces of lumber a total of 27 ft. long for a dog pen. The second piece has to be 4 ft. longer than the first and the third 4 ft. longer than the second...

• Absolute Value [Triplett, 11/24/1997]
  Where is absolute value used in people's work?

• Solving Pairs of Equations by Substitution [Lana, 11/26/1997]
  x + 3y = - 5; 3x - 2y = 7.

• Linear Inequalities [Maura, 11/26/1997]
  How do I solve the problem (x-2)/(x+1)<(x-4)/(x-1) ?

• State the Value of K [Jennifer, 11/26/1997]
  State the value of k so the given point lies on the graph of the equation 2x + ky = 21.

• Find the Average Speed [Haider, 11/27/1997]
  A motorist has to travel 160km. His average speed is 8km/h slower than he anticipated and he takes 1 hour longer than intended...

• Analytical Solution [Atia, 12/01/1997]
  Can you give me an analytical solution of S[N] = Sum[k^2, {k,1,N}] ?

• Raising Sides of an Equation to the 0 Power [LaVergne, 12/04/1997]
  If you raise both sides of an equation to the 0 power, will both sides then be equal to one?

• Three Weights [MacDougall, 12/07/1997]
  A boy selling fruits has only three weights, but with them he can weigh any whole number of pounds from 1 pound to 13 pounds inclusive. What three weights does he have?

• Topology [Bullard, 12/31/1997]
  Is there a simple definition for homeomorphism? for topology?

• Algebra Refresher [Cottrell, 12/31/1997]
  I am trying to figure out how to solve this equation: (x^3 + 3x^2 - 4x + 3) / (x+1).

• Money Puzzle [Vedachal, 01/05/1998]
  A man goes to the bank and asks for x dollars and y cents.

• Height of the Ball [Trupiano, 01/05/1998]
  A football player kicked a 41-yard punt. The path of the ball was modeled by y= -0.035x(squared) + 1.4x + 1, where x and y are measured in yards. What was the maximum height of the ball?

• Radioactive Decay of an Isotope [Butler, 01/05/1998]
  I know the decay of the 226Ra isotope involves the use of logarithms (an exponential function ae^x), but I'm having trouble fitting my information to my equation...

• Finding Equations from Relations [Khan, 01/06/1998]
  Can you give me simple steps for how to do a chapter in the book called "Finding Equations from Relations"?

• Factoring 8 - t^3 [Jones, 01/07/1998]
  Factor the given expression completely: 8 - t^3.

• Math and Music: Harmonic Series [Panter, 01/09/1998]
  Could you supply me with information on how math relates to music?

• Completing the Square [Mason, 01/13/1998]
  Put y = 10x^2 + 10x + 1 into vertex form (y-k = a(x-h)^2.

• Who Will Win the Race? [Smith, 01/14/1998]
  Harry runs 3/4 mile every 6 minutes and Tortisha runs 1/2 mile every 5 minutes. Harry says, "I'll give you a 2 mile head start and still beat you in the race."

• Solving Inequalities [Rebeka, 01/19/1998]
  How do you do these inequalities? x+1 > -2 and 3x < 6

• Cubic Equations [Colin, 01/19/1998]
  How would you solve a problem like 3x^3+x^2+15x+27 = 0?

• Horner's Method of Solving Irrational Roots [Chilo, 01/29/1998]
  Can you give a method, formula, and answer for this equation? x^3 - 3x^2 - 2x + 5 = 0

• Partial Fractions [Yanzhen, 01/29/1998]
  How do I express 3/1-(x^3) in partial fractions?

• Completing the Square: Alternate Method [Wang, 02/06/1998]
  Instead of dividing by the coefficient of the quadratic term, I multiply the equation to get a perfect square coefficient for the quadratic term...

• Factor Completely [Red, 02/13/1998]
  The problems are: x^12-y^12 and x^12+y^12.

• Zero Product Property [Jessica, 02/14/1998]
  How do you find the answer to a zero product property question?

• Natural Numbers Coprime to 6 [Pushcar, 02/16/1998]
  Let N(x) denote the number of natural numbers less than x which are coprime to 6. Show that lim as x goes to infinity of [N(x)/x] = 1/3.

• The Sum of the First N Squares [Agosto, 02/20/1998]
  Find a formula for the sum of the first N squares (i.e. 1^2 + 2^2 + 3^ 2+.....+N^2) by mathematical induction.

• Functions that are their own inverses [Gaab, 02/28/1998]
  Can a function ever be its own inverse?

• Polynomial Degrees and Definition of a Field [Metelli, 03/02/1998]
  The degree of polynomials added together, and definition of a field.

• Theorem About Sum and Product of Quadratic Roots [laura, 03/07/1998]
  Explain why 1/2 and 3/4 are NOT the roots of 0 = 4x^2 + 5x + 8.

• Understanding Parallel and Perpendicular [Amanda, 03/23/1998]
  Can you explain parallel and perpendicular lines and slopes?

• Lines Intersecting Polygons [Lado, 03/23/1998]
  Given two points and polygons between them, if you draw a line between the two points, how do you find which polygons it crosses?

• Equations with Two Variables [Gina, 03/25/1998]
  Identify and find solutions to systems of equations or inequalities by graphing.

• Focus of a Hyperbola [Komatireddy, 04/06/1998]
  When you rotate the focus point of a hyperbola around the center, why does it hit the asymptote with the same x coordinate as the vertex?

• Maximizing Horizontal Distance [Carter, 04/10/1998]
  Using algebra, prove that an object needs to be thrown at 45 degrees to travel the greatest possible horizontal distance.

• Doubling Opposite Integers [Bailey, 04/19/1998]
  On a number line, a certain integer is 24 units away from the double of its opposite. What is the integer?

• Deriving the Hyperbola Formula [Gauteaux, 04/27/1998]
  When speaking of hyperbolas, why does C^2 = A^2 + B^2?

• Solving Multivariable Diophantine Equations [Jin, 05/03/1998]
  Finding general solutions to two diophantine equations.

• Solving Logistic Equations for a Variable in the Exponent [Cavenett, 05/03/1998]
  Using natural logarithms to solve for the time variable in two logisitic growth equations.

• Linear and Circular Parametric Equations [Preston, 05/05/1998]
  Using parametric equations to plot a line segment connecting any two points on the plane.

• Solving Systems of Three Equations [Claire, 05/07/1998]
  Can you help me solve the following system of three equations with three unknowns?

• Cramer's Rule in Action [Moriah, 05/08/1998]
  Explaining Cramer's Rule by applying it to a system of equations.

• Differentiability, Intervals, Inflection Points of Piecewise Function [Emineth, 05/13/1998]
  For what values of k and p will the function be continuous and differentiable? On what interval will it be increasing? Find all points of inflection.

• Top 10 Algebra Mistakes [Hodgson, 05/23/1998]
  What do you think are the top 10 mistakes that are made in algebra?

• Factoring by Grouping [Bullard, 05/27/1998]
  How do you factor 2r^2 + rt - 6t^2 ?

• Solving Quadratics with Imaginary Roots [Fernandez, 05/28/1998]
  Different ways to solve the quadratic equation 3x^2 + 2x + 5 = 0.

• Solving Linear Inequalities with Absolute Values [Carolyn, 05/31/1998]
  Finding neighborhoods on the number line to solve 3 <= |x + 2| < 8.

• Simultaneous Equations and the Addition Method [Hamler, 06/01/1998]
  Solving two unknowns in two equations.

• System of Equations and the Substitution Method [Poindexter, 06/07/1998]
  Can you explain the "substitution" method of solving systems of equations, and provide an example?

• Solving Fractional Systems of Equations [Mannon, 06/08/1998]
  I need help solving the following system of equations - the fractions have confused me: 1/x + 3/y = 7 and 4/x -2/y = 1.

• Finding a Set, Solving a System [Bailey, 06/24/1998]
  Find the solution set: 3-1/4x <_ 2+ 3/8 x; solve the system...

• Finding Coefficients of Simultaneous Equations [Emma, 06/24/1998]
  The equations ax^4 + bx^3 + c = 0 and cx^4 + bx^3 + a = 0 have a common root. Find all possible values of b, if a + c = 100.

• Absolute Value [Presley, 07/03/1998]
  Solve for x: |x+3|<|x-2|

• Graphing a Function with Asymptotes [Hasan, 07/05/1998]
  How do you find the asymptotes of f(x) = (2x + 1)/(x - 3)? How do you use the asymptotes to graph the function?

• Finding Asymptotes [Robinson, 07/06/1998]
  In the equation y = (m/x) + c, how do the values of m and c affect the graph? How do you find the asymptotes?

• Traveling Trains and Nonlinear Systems [Shen, 07/16/1998]
  A train leaves town A and travels 540 miles at a uniform speed, followed an hour later by another train.... What were the speeds of the trains?

• Solving Absolute Value Functions [Rich, 07/19/1998]
  How do you solve |4/7x + 6| + 3 = 15?

• The Discriminant of Quadratic Equations [Leung, 08/06/1998]
  Can you explain more about the discriminant, b^2 - 4ac? Why is it sometimes represented by a triangle (delta)?

• Manipulating Roots [Wave, 08/08/1998]
  If a and b are the roots of the equation 3x^2 - 5x + 1 = 0, find the equation whose roots are a/b and b/a.

• Distance Between a Point and a Line [Liz, 08/23/1998]
  Find the distance between the origin and the line 3x + 4y = 5.

• Solving Inequalities [Bross, 08/31/1998]
  How do you graph these inequalities...?

• Inequalities and Absolute Value [Lex, 09/01/1998]
  What is the case method? How does it apply to inequalities with absolute values?

• Negatives and Inequalities [Jain, 09/10/1998]
  Why when we multiply or divide an inequality by a negative number do we reverse the inequality sign?

• Interpreting Slopes [Poss, 09/14/1998]
  Does the graph of each of these equations rise to the right, fall to the right, is it horizontal, or is it vertical?

• Straight Line on the Graph [Elsa, 09/10/1998]
  Let f(x) = ae^(kx) where a>0 and k are constants. Show that the graph of y = ln(f(x)) is a straight line.

• Inequalities and Absolute Values [Nazir, 09/16/1998]
  Can you explain two different ways to solve inequalities with absolute values?

• Factoring and the Factor Theorem [Katus, 09/28/1998]
  I need help factoring x^3 - x^2 + x - 2 = 4.

• Formulas for the Equation of a Line [Michelle, 09/28/1998]
  Can you explain the meaning behind the point-slope formula? What about other formulas for the equation of a line?

• Adding and Subtracting Inequalities [Fernandez, 09/29/1998]
  Can you explain the rules? What if two inequalities are in the same or opposite directions?

• Using Substitution [Gronsbell, 10/05/1998]
  Can you explain the use of substitution in your cubic polynomial frequently asked question?

• Intercept Equation [Sara, 10/07/1998]
  I found a plane using the intercepts (4,0,0), (0,-5,0), and (0,0,3). Now I want an equation for those points using Ax + By + Cz = D.

• Maximum Number of Intersections of n Distinct Lines [Sally, 10/07/1998]
  Find a pattern for the maximum number of intersections of n lines, where n is greater than or equal to 2.

• Nonlinear Factors [Turner, 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.

• Deriving the Quadratic Formula [Smith, 10/15/1998]
  How do you derive the quadratic formula from ax^2 + bx + c = 0?

• Relations versus Functions [Nicole, 10/27/1998]
  What is the difference between a relation and a function? What about the domain and range of a function?

• Length of a Copper Helix [Kim, 11/15/1998]
  Can you help me find a formula to determine the length of straight wire needed to form a helix of a certain length when twisted with another wire?

• Derivations of Heron's Formula [Hath, 11/24/1998]
  How is Heron's formula (Hero's formula) derived?

• Angle Measurements of Triangles inside Semicircle [Braha, 11/26/1998]
  If the area of a triangle inside a semicircle is equal to the area outside the triangle within the semicircle, then find the values of the acute angles in the triangle.

• An Ellipse Or A Circle? - Parametric Equations [Sands, 12/05/1998]
  Is this parametric equation elliptical or a circle?... And how do I compute the slopes at points 0, pi/4, pi/2, 3pi/2,and 2pi?

• Trinomial Expansion [Achille, 12/08/1998]
  I need to expand (1+x+x^2)^n to four terms. Is there a formula?

• Completing the Square [Jim, 12/21/1998]
  Steps for solving quadratic equations.

• Parallel Lines [McHatton, 12/31/1998]
  What are some ways of proving lines parallel - geometrically and algebraically?

• First Principle Hyperbolas [Janis, 01/05/1999]
  How do you solve for the standard equation of a hyperbola given its properties?

• What is a Partial Fraction? [Ishmael, 01/08/1999]
  What do partial fractions have to do with polynomials?

• A Right Triangle of Points [Strenz, 01/14/1999]
  Determine the values of x that would make the points (x,0), (-2,1), and (3,4) the vertices of a right triangle.

• Completing the Square [Dena, 01/20/1999]
  Can you explain why completing the square works? How exactly do you do it?

• Constructing Polynomials [Zhong, 01/20/1999]
  I need to find polynomials given certain properties. For example, find a polynomial P(x) that is of degree 4, where P(x) = P(-x), ...

• Equations with Absolute Value [Angela, 01/24/1999]
  I know that if an equation has an absolute value, you need to have a positive and a negative part when you solve it. How do you get both answers?

• The Algebra of Complements and Supplements [Rogers, 01/25/1999]
  What are complements and supplements? How do you translate these concepts into algebra?

• Ships in the Fog [Kelly, 02/01/1999]
  Given the locations and speeds of two ships, find whether (and when) they will collide.

• Absolute Value (Real Numbers: Rational) [Laura, 02/02/1999]
  Find the solutions of |1/(x-2)| >= 4.

• Solving Systems of Linear Equations [Taylor, 02/09/1999]
  Can you help me solve simultaneous equations?

• Algebra Paper-Folding Problem [Lauren, 02/10/1999]
  Fold a paper x times in half, keeping the creases perpendicular to the longest edge. Find an equation for the number of intersections in terms of x.

• Graphing Slope Intercept [Jeremy, 02/13/1999]
  When given the slope intercept form, how do you know whether you rise or drop when looking at the slope?

• A Velocity-Time Problem [Sarah, 02/16/1999]
  If you drive 40 mph instead of 30 mph, you save 30 seconds per mile, but if you make the same 10 mph increase from 70 mph to 80 mph, you only save 5.6 seconds per mile. Why?

• Slope and (x, y) Intercept [Alison, 02/19/1999]
  Does slope depend on (x, y) intercept or does (x, y) intercept depend on slope?

• Population and Percentage [Ian, 03/07/1999]
  Given population data, find the number of women in two different years.

• Inequalities and Negative Numbers [Rob, 03/09/1999]
  Why do we reverse the inequality symbol when dividing/multiplying by a negative number?

• Intersection Points [Sara, 03/13/1999]
  A line goes through the point A(1, 2) to cut 2y = 3x-5 at P and x+y = 12 at Q. If AQ = 2AP, find the coordinates of P and Q.

• Circle Center's Cartesian Coordinates [Cuartiella, 03/24/1999]
  How do you find the Cartesian coordinates of a circle's centers if you know two points on its perimeter?

• Multiplying or Dividing by a Negative Number [Yap, 04/08/1999]
  When x(x-4) is less than 0...

• Ferrari's Method for Quartics [Cathelain, 04/16/1999]
  Could you explain Ferrari's method for quartics?

• Pascal's Triangle Pattern [Dieter, 04/22/1999]
  What pattern does multiplying each entry by 1, 2, 3, 4, 5... in order, and adding the products yield?

• Hiking Up and Down [Kwan, 04/24/1999]
  How many kilometers is it from the base to the top of the mountain?

• Factoring Trinomials [Becky, 05/28/1999]
  How do you factor trinomials with a number in front of the first variable? For example: 6y^2 - 19y + 10.

• Enlarging the Penguin Pond [Crystal, 06/03/1999]
  By how much should its length and width be increased to double the area of the 12 meter x 8 meter penguin pond at the zoo?

• Intercept of Two Lines [Burger, 06/07/1999]
  How can you calculate the exact location of the intercept point of two lines without graphing?

• Solving Linear Inqualities [Leon, 06/10/1999]
  How can I solve 9 <= 2x-1 <= 15 for x?

• How Long Did She Walk? [Logan, 06/12/1999]
  A woman usually takes the 5:30 p.m. train, arriving at her station at 6:00, and her husband picks her up and drives her home...

• Inequality with Absolute Value [Schroeter, 06/14/1999]
  Why can't I just write the inequality |x| > a as (-a) > x > a?

• Combining Positive and Negative Exponents [Fortner, 06/30/1999]
  When you simplify exponential expressions using the power rule, how do you combine positive and negative exponents in the numerator and denominator?

• Using Trial Solutions [Edward, 07/28/1999]
  How can I solve the system of equations x-sqrt(yz)=42, y-sqrt(xz)=6, z-sqrt(xy)=-30 to find x, y and z?

• Two Cars [Sandi, 08/11/1999]
  How long does it take car B to draw even with car A, and how far does car B travel?

• Factoring a 3-Variable Polynomial [Baumgartner, 08/13/1999]
  Is it possible to factor the polynomial k1*x^2 + k2*y^2 + k3*z^2 + k4*xy + k5*xz + k6*yz into (g1*x + g2*y + g3*z)(h1*x + h2*y + h3*z) over the complex field for every choice of k1 through k6?

• Young's Formula [Smith, 08/21/1999]
  Calculating a child's dose of medicine based on the adult dose.

• Precedence of Unary Operators [Longman, 09/01/99]
  The PEMDAS rule for order of operations ignores unary operators. Can you explain the proper precedence for them, and give an example showing how not knowing the rule can cause an incorrect result?

• Proof Using Pell's Equation [Nandung, 09/18/1999]
  Given Pell's equation for sqrt(D) and p/q = [a1;a2;...;an], can you prove that p^2 - D.q^2 = (-1)^n.k?

• Prime Factors of 4,194,305 [Offutt, 09/20/1999]
  How can I find the prime factors of 2^22+1?

• Distribution and Absolute Values [Smith, 09/22/1999]
  Is it okay to distribute through an absolute value sign? For example, is 2|3x+1| = |6x+2|?

• Quadratic Formula [Panagos, 10/01/1999]
  Could you give me some ideas for how to use the quadratic formula, and some practice problems?

• Proof with Inequalities [James, 10/10/1999]
  1. How can I prove that a^6 + 4*b^6 >= 4 if ab = 1? 2. At each vertex of a polygon, a number is written... How many sides does the polygon have?

• Equation for undefined slope [Andy, 10/24/1999]
  How do you write an equation for a vertical line with an undefined slope? For example, a vertical line with an x-intercept of 8.

• Finding Howlers [Nagpal, 10/25/1999]
  Howlers are fractions like 16/64; when you cross out the 6 on the top and the bottom, you are left with 1/4, which is the simplified fraction. How can I find all 2-digit, 3-digit and 4-digit howlers?

• Complex Roots of a Quadratic Equation [Aoun, 10/25/1999]
  If 1+i is a root of the equation z^2 + (a+2i)z + 5+ib = 0, and a and b are real numbers, how can I determine the values of a and b?

• Applying the Remainder Theorem [Aimee, 10/25/1999]
  If the expression 6x^2 + x + 7 leaves the same remainder when divided by (x-a) and by (x+2a) where a is not equal to 0, how can I find the value of a?

• Completing the Square Using a Diagram [Ko, 11/09/1999]
  How can I draw a diagram that represents the "completing the square" operation of x^2 - 6x + ...?

• Complex Numbers in Quadratic Equations [Oya, 11/09/1999]
  How are imaginary numbers used in solving quadratic equations? How can solutions of this type be represented graphically?

• Factoring Polynomials [Wong, 11/29/1999]
  How can I factor 4x^2 - 36, or x^2 + yz + xy + xz?

• Gaussian Elimination [Harper, 01/11/2000]
  How can you solve a system of linear equations using Gaussian elimination?

• Minimum and Maximum Problems Using Algebra [Hadila, 04/05/2000]
  Can you show me how to solve these minimum and maximum problems using algebra?

• Ordering Exponents and Variables [Cherie, 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?

• Using Cardan's Formula to find Real Roots [Salman, 04/13/2000]
  How can I show that, although the cubic equation x^3 - 6x = 4 has three real solutions, Cardan's formula can find them by subtracting appropriate cube roots of complex numbers?

• Integer Solutions to AX + BY = C [Prufrock, 04/25/2000]
  How do you prove that, for any equation of the form ax + by = c, where a, b and c are integers, if an integer solution exists, there will be an infinite number of integer solutions for x and y?

• Rates of Paddling [Stan, 04/25/2000]
  I can travel 12 miles downstream in six hours less than it takes me to travel the same distance upstream... How fast is this river's current?

• A Train and Clock Problem [Stan, 04/29/2000]
  A train leaves the station exactly on the minute. After traveling 10 miles at an average speed of 66 mph, the minute hand is directly over the hour hand. At what time does the train leave the station?

• Proof That Equation Has No Integer Roots [Liu, 05/09/2000]
  How can I prove that if p is a prime number, then the equation x^5 - px^4 + (p^2-p)x^3 + px^2 - (p^3+p^2)x - p^2 = 0 has no integer roots?

• Solving for b [Armstrong, 05/10/2000]
  When solving 10 + 2*sqrt(b) = 0 we get b = 25, but when we insert 25 into the equation, we end up with 20 = 0. What are we doing wrong?

• Probability of a Function Having Complex Roots [Henrik, 05/11/2000]
  What is the probability that the function f(x) = x^2 + px + q = 0 will have complex roots when p and q lie between 0 and 1? ...when p and q lie between 0 and 5? ...when p and q are greater than 0?

• Limits of Difference Equations [Moh, 05/14/2000]
  Find the limit of F and R in the following system of equations: R(x+1) = a*R(x) - b*F(x) and F(x+1) = c*F(x) + d*R(x). This is similar to that of the Lotka-Volterra ecological model.

• Relative Density [Guerra, 05/18/2000]
  A solid object floats in water with three-fourths of its volume beneath the surface. What is the object's density?

• Dividing the Prize Money [Sawbridge, 05/24/2000]
  Mrs. Shoe gave her prize winnings to her children in order... and all the prize money was divided equally amongst her children. How many children were there?

• Solving a Math Poem [Amber, 05/24/2000]
  Take five times which plus half of what, and make the square of what you've got...

• 9 x HATBOX = 4 x BOXHAT [Stribling, 05/30/2000]
  What is the solution to the cryptogram: 9 x HATBOX = 4 x BOXHAT?

• Using the Discriminant [Kemy, 07/19/2000]
  How can I determine the character of the solution of the equation x^2+2x+6=0 in the complex numbers without solving it?

• Delivering a Message [Marshall, 09/02/2000]
  A 25-mile long column of soldiers marches 25 miles. As the march begins, a messenger starts at the rear of the column and goes forward...

• Proof of Convergence [Decroos, 09/29/2000]
  Why does the ratio F(n+1)/F(n) for the Fibonacci numbers converge to the golden ratio?

• Method of Finite Differences [Gillett, 10/12/2000]
  How can I find the generating equation for the series -3, 2, 13, 30, 53?

• Applications of Parabolas [Lau, 10/24/2000]
  How are parabolas used in real life?

• Fermat's Last Theorem with Negative Exponents [Openshaw, 10/26/2000]
  Are there any solutions of Fermat's Last Theorem, x^n + y^n = z^n, for n less than 2?

• Proof of the Rational Root Theorem [Bucksbaum, 11/13/2000]
  How can I prove the Rational Root theorem?

• The Nth Root of N [King, 11/28/2000]
  Is the nth root of n (a whole number other than 1) ever a rational number?

• How Many Points Determine a Parabola? [Ramani, 12/20/2000]
  How can we determine whether or not a given plane curve is a parabola? Under what conditions is a parabola uniquely determined?

• Solutions to X^Y = Y^X [Pelz, 12/21/2000]
  How can I find the solutions to the equation x^y = y^x? I have been told that it involves the Lambert W Relation.

• Factoring 5x^2 + 2x -1 [Doug, 01/22/2001]
  I can't figure out how to factor this: 5x^2 + 2x -1. The best I can do is: (5x+1)^2 + 2(x-1).

• Ant and Rectangle [Li, 01/22/2001]
  Does the ant walk along the diagonals of the rectangle?

• Equation Roots [Sara, 01/22/2001]
  How do you get the real, imaginary, rational, and irrational(roots) of the equation?

• Fundamental Theorem of Algebra [Nataria, 01/25/2001]
  What exactly is the Fundamental Theorem of Algebra?

• Monetary Conversions [Al, 01/27/2001]
  Given these monetary exchanges: 2 coconuts = 1 banana; 3 bananas = 2 mangos; 4 papaya = 1 coconut, what is the exchange for banana to papaya and for papaya to mango?

• Graphing Quadratic Polynomials [Gregory, 02/07/2001]
  Can you give me a simple explanation of how to graph quadratic polynomials like y = x^2 - 8x + 15?

• Functions and Equations [Abby, 02/10/2001]
  When is an equation also a function? How do you recognize a function?

• Increasing the Average [Darbonne, 02/25/2001]
  Five members of a basketball team are weighed and an average weight is recalculated after each weighing. If the average increases 2 pounds each time, how much heavier is the last player than the first?

• Solving Sqrt(x + Sqrt(x + Sqrt(x + ... = 10 [Anjana, 02/26/2001]
  How can I solve the equation sqrt(x+sqrt(x+sqrt(x+...=10 for x if x is known to be a real number?

• Monomials, Polynomials [Heller, 03/02/2001]
  Can you explain monomials and polynomials to me?

• Negative Numbers Combined with Exponentials [Ryno, 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?

• When FOIL Fails [Ryan, 03/22/2001]
  Find the product - (2c-3)3rd power. I can do FOIL on a question to the second power, but I cannot figure out how to do a question to the third power.

• Point on a Line [Chris, 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.

• Digit Reversal Trick Explained [Kouraklis, 03/23/2001]
  Take a 3-digit number and subtract its reverse. Then, take the result and add its reverse. Why is the answer is always 1089, no matter what the initial numbers were?

• Finding Terms in a Binomial Expansion [Jen, 03/27/2001]
  How can I find the fifth term of (-5m+4n^3)^54?

• Order of Operations with Percentages [James, 04/05/2001]
  Why does the order of operations exclude percentage, square roots, etc.?

• Algebra Puzzle [Matias, 04/09/2001]
  If x+y+z = 1 and x^2 + y^2 + z^2 = 2 and x^3 + y^3 + z^3 = 3, what does x^4 + y^4 + z^4 equal?

• Combining Ohm's Laws Formulas [Tony, 04/12/2001]
  In electronics, there are two main formulas, V = I*R and P = V*I. How can I combine these to get formulas like P = I^2*R?

• Finding Focus and Directrix [Brent, 04/12/2001]
  How can you find the focus and directrix when given a formula for a parabola?

• Fourth-Degree Polynomial [Miller, 04/26/2001]
  How can I construct a fourth-degree polynomial that contains all of the following points: (-1,2), (1,-2), (3,7), (2,1) and (0,3)?

• Finding the Equation of a Parabola [Rakesh, 04/28/2001]
  How can I find the equation of a parabola whose zeros are at 0 and 6, and whose minimum value is -9?

• Average Speed [Behringer, 04/29/2001]
  A test track is 1 mile around. A driver drives 1 lap at 160mph. How fast must he drive the second lap in order to average 200mph for the two laps?

• Parabola with Horizontal or Vertical Axis [Jamie, 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?

• Quadratic Function [Trey, 05/04/2001]
  What are the effects of changing the values of a, b, and c in a quadratic function?

• Finding Point of Intersection [Ernst, 05/08/2001]
  Is there a formula to tell if two lines, given by point coordinates, cross and at what coordinates they cross?

• What are Piecewise Functions? [stephanie, 05/13/2001]
  I know piecewise functions are based on expressions between specific intervals, but I do not know how to describe this function family.

• Composition Functions with Added x Value [Eileen, 05/13/2001]
  If x = 1, evaluate g(f(f(x))). I'm confused with this added value of x = 1.

• Cubic Equations [Mehek, 05/17/2001]
  How do you solve cubic equations? Is there a general formula?

• Stairs on an Escalator [Dario, 05/21/2001]
  A woman walks 10 steps down on a downward-moving escalator to reach the bottom. As she reaches the bottom, she runs back up the same escalator at a speed 5 times that which she walked down, covering 25 steps in reaching the top. How many steps are visible on the escalator when it is still?

• Savings on Gasoline [Janet, 05/22/2001]
  Your old car averaged 22 mpg and you new car should average 37 mpg. Suppose you drive 12,500 miles per year and the cost of gas averages $1.85 per gallon. How much will you save on gasoline each year?

• Subtracting Different Types of Units [Herman, 05/26/2001]
  When we subtract equations when solving a word problem, it looks as if we are subtracting the number of items from the cost of the items. How can we subtract different units?

• Subtracting One Equation from Another [Lee, 05/30/2001]
  Why can you subtract one equation from another and get something meaningful that you can use to solve the equations?

• Slope-Intercept Formula [Vittorio, 06/05/2001]
  How come y = mx + b has to be that way?

• Exchanging Seats in a Boat [Beth, 06/08/2001]
  Ten women are fishing in a long, narrow boat. One seat in the center of the boat is empty. The five women in the front of the boat want to change seats with the five women in the back of the boat...

• Floating 2 [Britney, 06/12/2001]
  Start with the number 2 on the far left side, then float the number 2 to the far right side; the new number must be three as large as the old number.

• Hidden Faces of Cubes [Nigel, 06/20/2001]
  My daughter has to produce an equation to show the number of hidden faces when three rows of cubes are placed together on a flat surface.

• How Far Will the Rocket Be from Earth? [Elaine, 06/22/2001]
  A rocket leaves the earth for the sun at a speed of 28,800 mph. At the same time, a photon of light leaves the sun for the earth...

• A Three-Legged Stool [Teri, 06/26/2001]
  Why is a three-legged stool steady, while a four-legged stool can be wobbly?

• Mother's Age in Terms of Daughter's [Claudia, 06/27/2001]
  The sum of the ages of a father, a mother, and a daughter is 73. When the father is twice as old as the daughter, the sum of their two ages will be 132...

• Pumpkin Price [Sharmila, 06/28/2001]
  Peter Peter has 40 pumpkins to sell. He will sell them all if he sets his price at $1.00 each, but will sell one fewer pumpkin for each 5-cent increase in price...

• A Train Breaks Down [Steve, 06/30/2001]
  A train breaks down an hour after starting its journey. After repairs, it can only continue at half its original speed and arrives at its destination two hours late...

• 300 Foul Shots [Roger, 07/11/2001]
  A basketball player shoots 100 foul shots on a given day, and increases the number he shoots by 10 per day...

• Silver Alloy [Milad, 07/12/2001]
  Sterling Silver is 92.5% pure silver. How many grams of pure silver and sterling silver must be mixed to obtain 100g of a 94% Silver alloy?

• Are All Functions Equations? [Maureen, 07/16/2001]
  When my x's are not continuous, would I still have a function since the vertical line test might in fact not touch a point at all?

• Normalization [Michael, 08/01/2001]
  How do I figure out: 90 + 70 + 88 + 94 + x / 5 = 85 ?

• How Far Does C Walk? [Tay, 08/06/2001]
  Three persons A, B, and C, travel from point X to point Y. They leave point X at the same time and follow the same route...

• Multiple Absolute Value Inequalities/Equalities [Karen, 08/09/2001]
  I can solve inequalities containing absolute values, but not if there are two in the same equation....

• Quadratic Formula [Shawn, 08/15/2001]
  How do you solve for b in the quadratic formula?

• Why Factor? [Kevin, 08/18/2001]
  I've been explained the how's, the where's, the what's, but not the WHY. What is the practical use of factoring?

• Graphing Piecewise Functions [Mary, 09/09/2001]
  I do not understand how to graph piecewise functions.

• Distributive Property: (x+2)(x+4) [Lydia, 09/18/2001]
  I'm confused about the distributive property. Example: (x+2)(x+4).

• Open Sentence, Statement [Kristin, 09/18/2001]
  What is an open sentence?

• Man Crossing a Bridge [Eric, 09/27/2001]
  A man is jogging across a bridge at 8 mph. When he is 3/8 of the way across...

• Water Level in a Well [Jason, 10/09/2001]
  A man wishes to determine the water level in a deep well. He drops a stone into the well and hears it hit the water 3 seconds later...

• Distributive Property [Susan, 10/13/2001]
  We are learning the distributive property in school. Why do we have to learn this, and how will we use it, and when?

• Asking Price of a House [Helen, 10/14/2001]
  If a seller wants to clear $50,000 for his house and the real estate commission is 6%, what should be the asking price for the house?

• The Idea behind Simultaneous Equations [Laura, 10/14/2001]
  I'm having a hard time learning the linear combinations method and the substitution method in algebra.

• Etymologies of Algebra, Geometry, Trigonometry [Nikki, 10/22/2001]
  What are the origins and roots of the words geometry, algebra, and trigonometry?

• Math Virus Formula [Victor, 10/23/2001]
  The virus spreads to all the squares directly touching each other (not including diagonally) and I have found the formula for the number of newly infected cells (although this does not include the first minute)...

• Why Flip the Inequality Sign? [Sean, 10/26/2001]
  Please tell me why you flip the inequality sign when dividing by a negative number.

• Looking for Patterns [Amanda, 10/30/2001]
  What would be the answer to: (x-a)(x-b)(x-c)(x-d)(x-e)...(x-y)(x-z)?

• Rate of River Current [Dave, 10/31/2001]
  Ryan is canoeing upstream while his sister Katie sleeps in the back of the canoe...

• Order in Linear Expressions [Candi, 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?

• Exponents as Variables [Bart, 11/20/2001]
  I can solve these problems but I don't know how to prove them: 9^1+x= 27; 2^-x-4=1/32; 243=(1/3)^x+4; 64=0.5)^3-x.

• Substituting Parameters for Numbers [Don, 11/29/2001]
  I don't know what to do with both sides of the equation 17.20X/100 = X-579.59.

• Inverse Function [Trevor, 11/30/2001]
  I got this question wrong: y = (-5x - 2) / (-x + 1).

• Quadratic Model [Erin, 12/03/2001]
  The quadratic model S = -17t^2+45t+2570 approximates the number of suicides by firearms in the U.S. for women, where t represents the number of years after 1985. In what year were there 2370 female suicides by firearms?

• Factoring [Sommer, 12/03/2001]
  This problem is giving me a hard time: 6x^2 + 31x + 5.

• DEFABC Equals 6(ABCDEF) [Vincent, 12/10/2001]
  Let abcdef be a 6-digit integer such that defabc is 6 times the value of abcdef. Find the value of a + b + c + d + e + f.

• Absolute Value and the Distributive Property [Ira, 12/11/2001]
  Is the distributive property applicable to absolute value?

• Finding Line Segment Lengths [Annie, 12/21/2001]
  Can you help me find line segments AB and BC if points A,B,C, and D are collinear with B between A and C and C between B and D...?

• Finding Sets of Integers [Keith, 01/02/2002]
  Without computer assistance, find five different sets of three positive integers such that and k is less than and m is less than n, and 1/k + 1/n + 1/m = 19/84.

• Manipulated and Responding Variables [Katie, 01/13/2002]
  What are manipulated variables and responding variables?

• Roots of Cubic Equations [John, 01/13/2002]
  Can you help me with this? a, b, and c are the roots of the equation x^3 - px^2 + qx - r = 0. Express the following in terms of p, q, and r...

• Don't Multiply by Zero [Richard, 01/23/2002]
  Solve for y: 3y/y-7 - 3/2 = 21/y-7. I get 21/0-3/2 = 21/0.

• Parabolic Golf Shot Equations [Michelle, 01/24/2002]
  Does the ball reach the green?

• Sign Switching [Marielle, 01/28/2002]
  Can you explain sign switching in multiplying and dividing inequalities?

• How Much Popcorn did Paul Sell? [Melissa, 01/28/2002]
  Paul made $44.14 selling 27 items (beer and popcorn). If he made $1.22 selling popcorn and $2.62 selling beer, how many boxes of popcorn were sold?

• Sum of a Number and Its Reciprocal [Rebeka, 01/28/2002]
  The sum of a number and its reciprocal is 5 1/5. What is the number?

• Solving Equations for Variables [Ultra, 02/03/2002]
  How do you solve the following equation for (M) and then (m)? k = M-m/ 1+Mm.

• Area of a Right Triangle [Chris, 02/09/2002]
  Find the area of a right triangle that has a perimeter of length 16 meters and a hypotenuse with length 7 meters.

• Finding a Single Pair of Factors [Lauren, 02/27/2002]
  Factor ax^2 - bx - c.

• Multiplying/Adding Fractions Gives Same Answer [Ryan, 03/01/2002]
  Find two fractions which, when multiplied and added, give the same answer.

• Completing the Square Using a Diagram [Kelvon, 03/06/2002]
  Show x^2 + 3x using a diagram.

• Base e, In, Log [Jerry, 03/08/2002]
  Problems in base e. For example: 3e^(2x-1) = 7, or e^(x+1) = 8.

• Plus or Minus Sign [Kim, 03/08/2002]
  What does this equation mean: y = +- k ? The - sign is directly under the + sign.

• 14b * 20x Rearranged [Josh, 03/11/2002]
  What is 14b times 20x ?

• Setting up Equations [Gideon, 03/10/2002]
  If X^2 is greater than X what can you say about the value of X? If X^2 is less than |X|, what can you say about the value of X?

• Rational Number and its Reciprocal [Nelson, 03/14/2002]
  A rational number greater than one and its reciprocal have a sum of 2 1/6. What is this number? Express your answer as an improper fraction in lowest terms.

• Rule for Completing the Square [Irina, 03/15/2002]
  Which expression should be placed in each set of parentheses in order to solve the equation by completing the square? x^2+6x+(?)=15+(?)...

• Two Values of X [Krystal, 03/20/2002]
  Two numbers differ by 7 and the sum of their squares is 389. Find the two numbers.

• Magic Wheel [GB, 03/20/2002]
  Given a wheel with 16 spokes and a hub, enter the whole numbers 1-17 in the hub and at the end of spokes. The sums of the 3 numbers along the spokes must be equal.

• What We're Doing When We Do Algebra [Mike, 03/25/2002]
  How do you graph x + y = 5 on a graph sheet?

• Mowing Half a Lawn [Jessica, 03/31/2002]
  Chris and Lee are each responsible for mowing half of their 50-foot by 90-foot rectangular back yard...