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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Real Numbers Closed under Division [09/24/2002]

Is it true that real numbers are not closed under division because we can't divide by 0?

Rearranging an equation [3/15/1995]

I need this equation solved for V....

Recommended Algebra Software [7/23/1996]

I am looking for math software programs with a focus on algebra.

Recursive Function for Loan Problem [11/13/1997]

What is the recursive function formula for a loan of $100,000, payable at 6 percent, over 20 years?

Reduce Expression of Two Variables [9/4/1996]

How do I reduce (3xy)/(xy+x)?

Redundant Sets of Equations [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?

Reflection Points on a Circle-Shaped Mirror [09/30/2003]

Points A and B are located within a circle. If A were a light emitting point and B a light receiving point, then B would receive light from points P on the circle. How can I find these points?

Relationship Between Commutative and Associative Property? [06/30/2002]

Are both the commutative and associative properties necessary to prove a + b + c = c + b + a?

Relations versus Functions [10/27/1998]

What is the difference between a relation and a function? What about the domain and range of a function?

Relative Density [05/18/2000]

A solid object floats in water with three-fourths of its volume beneath the surface. What is the object's density?

Reversing the Inequality Symbol [03/09/1999]

Why do we reverse the inequality symbol when dividing/multiplying by a negative number?

A Right Triangle of Points [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.

Root-Mean-Square [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.

Roots of Cubic Equations [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...

Rotating Matrices [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???

Rotational Symmetry [11/05/1997]

I am looking for a precise definition of rotational symmetry of a figure in a two-dimensional plane.

Rule for Completing the Square [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+(?)...

Rules of Exponent Manipulation [1/22/1996]

f sub r equals the reciprocal of ...

Running Laps [07/03/2002]

Two dogs run around a circular track at different speeds. How long will it take for them to return to the starting point at the same time?

The Sailor's Reward Problem and Prime Numbers [12/11/2004]

Does the answer to the classic Sailor's Reward problem have to be a prime number?

SAT Algebra Question [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?"

Savings on Gasoline [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?

Set Inclusion Notation [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"?

Sets and Integer Pairs [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).

Sets and Subsets [1/23/1995]

My teacher said that integers are a subset of reals, and whole numbers are a subset of integers, and counting numbers are a subset of whole numbers, and so on and so forth. What does that mean?

Setting up Equations [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?

Sharing the Cost of the Weekend Trip [07/24/2003]

A group of people planned to rent a large beach house for a weekend trip. They were to share the $800 cost equally. However, two people were unable to go and this increased the cost for each person by $20. How many persons were in the original group?

Ships in the Fog [02/01/1999]

Given the locations and speeds of two ships, find whether (and when) they will collide.

Sign Switching [01/28/2002]

Can you explain sign switching in multiplying and dividing inequalities?

Simple Way to Solve an Iterative Equation? [01/09/2009]

Bonuses are paid based on the percentage of projected profitability attained. But the bonus payment in turn reduces the profitability, which reduces the bonus. Through a series of iterations the amounts eventually converge, but is there a simple way to determine the bonus amount without having to go through those iterations?

Simplification [05/04/1997]

Which is more simplified: (1/a) + (1/b) or (a+b)/ab?

Simplification Problems [8/20/1996]

Simplify 2x(4-2x+y) - 5x(y^2+x-y)

Simplifying Algebraic Expressions [6/20/1996]

a-{2b+c2[d-3a+e4]a2b3c5}afg(5a-e3=cd3)2f+4g+f9 = ?

Simplifying Equations [11/7/1995]

Simplifying a fractional equation.

Simplifying Equations [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))

Simplifying with Cube Roots [01/22/1997]

Simplify: cube root(3) / [cube root(6) + cube root(3)]

Simultaneous Equations [11/28/1995]

A student asks about solving simultaneous equations.

Simultaneous Equations [07/01/2002]

A man has a total of 20 dimes and quarters. If the dimes were quarters and the quarters were dimes he would have 90 cents more than he has now. How many of each coin does he have?

Simultaneous Equations and the Addition Method [06/01/1998]

Solving two unknowns in two equations.

Slope and (x, y) Intercept [02/19/1999]

Does slope depend on (x, y) intercept or does (x, y) intercept depend on slope?

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