Ask Dr. Math

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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Go for the Gold! [1/28/1996]

Your job is to prepare the women's athletes for the Olympic 1,500-meter race.

Graphing [8/18/1995]

I've got questions concerning graphing.

Graphing a Function with Asymptotes [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?

Graphing an Equation [4/4/1996]

How do you graph 2x-y = 10?

Graphing an Equation [11/08/1997]

Please explain how to graph this equation: y = a + b(x) + c(x^2) + ...

Graphing an Equation with Absolute Value [10/15/1995]

How would you approach graphing negative 2 times the absolute value of x plus 2?

Graphing Intercepts [11/06/1997]

How would I find the intercept for a problem such as 3x-2y = 12?

Graphing Parabolas [01/16/1997]

How do you know how to graph a parabola from looking at its equation?

Graphing Piecewise Functions [09/09/2001]

I do not understand how to graph piecewise functions.

Graphing points [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.

Graphing Quadratic Polynomials [02/07/2001]

Can you give me a simple explanation of how to graph quadratic polynomials like y = x^2 - 8x + 15?

Graphing Slope Intercept [02/13/1999]

When given the slope intercept form, how do you know whether you rise or drop when looking at the slope?

Hands of a Clock [10/10/1997]

How many times do the hour and minute hands cross in a 12-hour period of time?

Height of the Ball [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?

Help with a Proof [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+....

Hidden Faces of Cubes [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.

Hiking Up and Down [04/24/1999]

How many kilometers is it from the base to the top of the mountain?

Hints for Algebra 101 [7/31/1995]

Do you have any helpful hints for algebra 101?

Horner's Method of Solving Irrational Roots [01/29/1998]

Can you give a method, formula, and answer for this equation? x^3 - 3x^2 - 2x + 5 = 0

How Far Does C Walk? [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...

How Far Will the Rocket Be from Earth? [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...

How Long Did She Walk? [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...

How Many Factor Pairs Does a Given Number Have? [03/19/2004]

I'm wondering if there is a formula or algorithm that will tell me exactly how many pairs of factors a number has?

How Many Mice, Cats, and Dogs? [01/13/2003]

You must spend $100 to buy 100 pets, choosing at least one of each pet. The pets and their prices are: mice @ $0.25 each, cats @ $1.00 each, and dogs @ $15.00 each. How many mice, cats, and dogs must you buy?

How Many Points Determine a Parabola? [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?

How Many Valentines? [02/10/2003]

If everyone in your class gave a Valentine to everyone else in your class, how many valentines would be exchanged?

How Much Money Entering the First Store? [09/26/2002]

Timothy spent all of his money at five stores. At each store, he spent $1 more than half of the amount he had when entering the store. How much money did he have when he entered the first store?

How Much Popcorn did Paul Sell? [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?

The Idea Behind Simultaneous Equations [10/14/2001]

I'm having a hard time learning the linear combinations method and the substitution method in algebra.

Identity and Inverse Properties for Zero [01/07/2004]

If we subtract 0 from a number and get the same number, doesn't that make 0 an identity for subtraction? Also, can't a number be its own inverse for subtraction?

If 1/x+x=5, what does 1/x^2+x^2 equal? [08/16/2002]

A complex and an easy solution to the problem.

Implied Multiplication and TI Calculators [05/02/2008]

If I type 36/6(25-11*2) into my TI-85, I get an answer of 2. If I include a multiplication symbol to have 36/6*(25-11*2), I get an answer of 18. I thought that when the 6 is written right up against the parenthesis, the multiplication is implied. Why am I getting two different answers?

The Importance of Defining Variables Clearly in Algebra [11/01/2007]

A sample of dimes and quarters totals $18.00. If there are 111 coins in all, how many are there of each coin?

Increasing the Average [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?

Inequalities [08/01/1997]

How do I deal with an equation with a greater than or less than sign?

Inequalities and Absolute Value [8/28/1996]

How do I find the solution set for problems like |X| > X and |X + 2| - X >= 0?

Inequalities and Absolute Value [10/17/1997]

What's the definition of absolute value?

Inequalities and Absolute Value - Case Method [09/01/1998]

What is the case method? How does it apply to inequalities with absolute values?

Inequality with Absolute Value: What Does |x| Mean? [06/14/1999]

Why can't I just write the inequality |x| > a as (-a) > x > a?

Infinite Geometric Progression [10/02/1997]

How do you go about solving .27 repeating into a fraction?

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