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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Asymptote of a Function [06/02/2002]

Determine the value of A so that y = (Ax+5)/(3-6x) has a horizontal asymptote at y = -2/3.

Asymptotes [6/3/1996]

When do asymptotes occur?

Average Speed [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?

Avoiding Careless Mistakes [01/30/2002]

How can I avoid careless mistakes?

Ballista Equation [09/30/2002]

I have to create an equation for how a ballista, an ancient weapon in the form of a giant crossbow, which fires bolts and grapeshot, would accurately hit its target.

Ball Thrown between Trains [10/15/2003]

Two trains A and B each of length 100m travel in opposite directions in parallel tracks. The speeds are 20m/s and 30m/s respectively. A boy sitting in the front end of train A throws a ball to a boy sitting in the front end of train B when they are at the closest distance. The speed of the ball is 2m/s. The ball, instead of reaching the boy, hits the rear end of the train. Find the distance between the parallel tracks.

Base Conversions: Trial and Error or Formula? [11/26/2002]

Find base x of a given number that is equivalent to a number in any base.

Base e, In, Log [03/08/2002]

Problems in base e. For example: 3e^(2x-1) = 7, or e^(x+1) = 8.

Binomials: Completing the Square [08/01/1997]

Find two binomials whose product is X ^ 2 - 25 and two binomials whose product is X ^ 2 - 6X + 9.

Burning 300 Calories [10/15/1997]

Liam burns 8.3 Cal/min when using a rowing machine, and 5.9 CAl/min when using an exercise bike...

Buying Cows, Pigs, and Chickens [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?

Calculate Gross Salary From Net Salary [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?

Can an Imaginary Number Be a Valid Answer? [01/12/2006]

The solution to x^2 + 1 = 0 is +/- SQRT(-1) or +/- i. But if i does not exist, how can it be an answer?

Cancelling Exponents [03/02/1997]

How did they turn 2^29/2 x 3^16 / 2^32 x 3^15 into 3 / 2^3?

Cars Leaving at Different Times [09/28/2003]

Two cars leave a garage traveling in opposite directions. One car leaves at 8 am and averages 60 mph. The other car leaves at 9 am and averages 50 mph. At what time will they be 225 miles apart?

Challenging Algebra Age Problem [02/29/2004]

A man has nine children whose ages are at an exact interval. The sum of the squares of the ages of each is the square of his own age. What is the age of each child and the man?

Circle Center's Cartesian Coordinates [03/24/1999]

How do you find the Cartesian coordinates of a circle's centers if you know two points on its perimeter?

Closure Axiom [06/12/1997]

What is the closure axiom?

Combining Ohm's Laws Formulas [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?

Combining Positive and Negative Exponents [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?

Comparison of On-line Rates [5/20/1996]

Jack is interested in two on-line companies, Easy Comp and Destruct Comp...

Competition Questions [2/25/1995]

We are trying to prepare students for competitions and have two problems we cannot solve....

Complete the Square and Factor [01/14/1997]

How do you complete the square? Can you use this to factor polynomials?

Complete This Square: x^2 + y^2 - 6x + 2 = 0 [03/16/2003]

I thought completing the square only involved quadratic functions, such as f(x) = ax^2 + bx + c = 0. This question relates to the equation of a circle...

Completing the Cube [11/28/1996]

Is there some method analogous to completing the square for higher dimension polynomials?

Completing the Square: a Diagram [03/06/2002]

Show x^2 + 3x using a diagram.

Completing the Square: Alternate Method [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...

Completing the Square and the Quadratic Formula [09/30/1997]

I really need help with this problem: 1 + 7/x + 2/x^2 = 0.

Completing the Square: How Does it Work? [01/20/1999]

Can you explain why completing the square works? How exactly do you do it?

Completing the Square in Vertex Form [01/13/1998]

Put y = 10x^2 + 10x + 1 into vertex form (y-k = a(x-h)^2.

Completing the Square of a Polynomial [5/22/1996]

How do you complete the square of a polynomial?

Completing the Square to Solve Quadratic Equations [12/21/1998]

Steps for solving quadratic equations.

Completing the Square to Solve Two Equations [5/30/1996]

I have to solve two equations by completing the square...

Completing the Square Using a Diagram [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 [11/09/1999]

How are imaginary numbers used in solving quadratic equations? How can solutions of this type be represented graphically?

Complex Roots of a Quadratic Equation [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?

Composition Functions with Added x Value [05/13/2001]

If x = 1, evaluate g(f(f(x))). I'm confused with this added value of x = 1.

Compound Inequalities [09/10/1997]

Can you write compound inequalities that use "or" the same way you write compound inequalities that use "and"?

Compound Inequality [9/15/1996]

5x-1 > 4 and 6x+3 < 4x-1

Concept of Factoring [03/22/1997]

Could you explain the concept of factoring and give examples of its practical uses?

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