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High School Archive

Browse High School Basic Algebra
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Solving simple linear equations.
    Positive/negative integer rules.
    Mixture problems.
    Quadratic equations.
    Absolute value.
    Completing the square.
    Direct and indirect variation.
    Inequalities and negative numbers.

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Distributive Property with Negatives [10/13/2004]

When using the distributive property with negative numbers, I don't understand when, why, and how the operator changes (from addition to subtraction, or the other way). Sometimes it changes, sometimes it doesn't. Can you explain when to change it, and why?

Distributive Property: (x+2)(x+4) [09/18/2001]

I'm confused about the distributive property. Example: (x+2)(x+4).

Dividing Polynomials [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.

Dividing the Prize Money [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?

Divisibility by 37 [11/08/1997]

Take a 3-digit number and add to that its "rotation". Prove that the sum can always be divided by 37.

Division of Polynomials [8/10/1995]

Please send me some examples of polynomial divisions.

Domain of a Function [9/13/1996]

What is the domain of f(x)= x/sqrt(x^2-4)?

Domain/Range of a Function [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.)

Don't Multiply by Zero [01/23/2002]

Solve for y: 3y/y-7 - 3/2 = 21/y-7. I get 21/0-3/2 = 21/0.

Double Quadratic Equation [7/5/1996]

Is there a simple solution to ax^2 + bx + cy^2 + dy + e = 0?

Doubling Opposite Integers [04/19/1998]

On a number line, a certain integer is 24 units away from the double of its opposite. What is the integer?

The Egyptians' Method of False Position [01/16/2003]

How does the method of false position work?

Electrical Relationships [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?

An Ellipse Or A Circle? - Parametric Equations [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?

Empty Set Classification [2/20/1995]

We would like to know if you would classify an empty set as being finite, infinite, or with another classification.

Empty Sets [08/15/1997]

Can you help me understand empty sets?

Enlarging the Penguin Pond [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?

Equal Sum, Product, Quotient of Two Numbers [10/13/2002]

I need to know the sum, product, and quotient, all equal, of two different numbers.

Equation for an Arch [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...

Equation for undefined slope [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.

Equation of a Line in Point-Slope, Slope-Intercept, General Form [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?

Equation of a Parabola [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.

Equation Roots [01/22/2001]

How do you get the real, imaginary, rational, and irrational(roots) of the equation?

Equations for Lines [5/29/1996]

Write an equation of the line containing the point P(1,-3)...

Equation Solving Steps [04/28/1997]

Solve for x in the equation: 4-2(x-2b) = ax+3.

Equations [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)

Equations That Make No Sense [01/15/2003]

Solve for x: x-8/5 = x+2/6.

Equations with Absolute Value [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?

Equations with Two Variables [03/25/1998]

Identify and find solutions to systems of equations or inequalities by graphing.

Equilateral Triangles [6/22/1996]

Draw an equilateral triangle of side n units...

Etymologies of Algebra, Geometry, Trigonometry [10/22/2001]

What are the origins and roots of the words geometry, algebra, and trigonometry?

Examination Puzzle [02/14/2003]

Three students take an examination in N subjects... How many subjects were there, and how many points did each student get?

Examples and Explanations of Basic Properties of Equality [07/31/2004]

Can you explain the substitution, symmetric, and transitive properties of equality in simpler terms?

Exchanging Seats in a Boat [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...

Exponential Equations [01/19/2003]

Is there a mathmatical way to solve 2^x + 3^x = 13?

Exponents as Variables [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.

Exponents in Algebra [8/8/1996]

Evaluate: (2^-3)-(2^-2).

Expressing a Code Algebraically [3/19/1996]

I am to express a code algebraically. The code is the alphabet reversed.. a=z, b=y, etc...

Extraneous Solutions [08/08/2003]

What should an engineer interpret from an equation, or the solutions of that equation, if its solutions prove to be extraneous?

Factor and Multiply to Check [5/21/1996]

Is x to the second power plus 6x plus 5 factorable?

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