See also the
Dr. Math FAQ:
order of operations
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.
Completing the square.
Direct and indirect variation.
Inequalities and negative numbers.
- Asking Price of a House [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?
- Associative Property [5/22/1996]
What is the associative property in algebra?
- Associative Property of Multiplication and Grouping Symbols [10/22/2006]
Does the Associative Property of Multiplication make grouping symbols
unnecessary, since (a x b) x c = a x (b x c) = a x b x c?
- Asymptote for (x-4)/x^2 [04/10/2002]
For the function (x-4)/x^2 there is a horizontal asymptote at y=0;
however, at x=4 y=0 the graph of the function does intersect the line
that is supposed to be the asymptote. How can this be if by definition
the asymptote is a line that the function gets close to but does not
- 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 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
- Comparison of On-line Rates [5/20/1996]
Jack is interested in two on-line companies, Easy Comp and Destruct
- 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
- 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
- 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, Coping with Complicated Coefficients [10/25/2017]
A teen struggles to solve a quadratic by completing the square. Doctor Peterson
outlines one way to prepare ax^2 + bx + c when a ≠ 1; steps
through the method with an equation where a = 1; and links to another approach.
- Completing the Square: How Does it Work? [01/20/1999]
Can you explain why completing the square works? How exactly do you do
- 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?