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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.

Rate of River Current [10/31/2001]
Ryan is canoeing upstream while his sister Katie sleeps in the back of the canoe...

Rates of Paddling [04/25/2000]
I can travel 12 miles downstream in six hours less than it takes me to travel the same distance upstream... How fast is this river's current?

Rational Equations [06/07/1997]
How do you solve 1/(x+1) - 1/(x+2) = 1/2?

Rational Inequality [2/15/1996]
Find the sum of all values of x such that 6x is an integer and (x-4)/(x-2) >= 3.

Rationalizing Denominators [07/12/1997]
How can I rationalize a denominator with odd power radicals?

Rational Number and its Reciprocal [03/14/2002]
A rational number greater than one and its reciprocal have a sum of 2 1/6. What is this number? Express your answer as an improper fraction in lowest terms.

Rational Root Test [10/28/1996]
How do you solve the system that consists of the equations xy+6=0 and x^2+y^2-6y-1=0?

Rational Root Theorem [08/27/1998]
List all possible rational zeros of the each function, then determine the rational zeros: f(x) = x^3 - 4x^2 + x + 2.

Ratio of Ratios [06/05/2002]
In a community, 3/5 of the men are married to 2/3 of the women. What fraction of the residents are married?

The Ratio of the Speed of a Colonel to his Soldiers [11/7/1995]
A colonel leads a column of soldiers. He marches to the rear of the column at a speed different from the column's and then at the same speed marches back to the front of the column. During this time the column marches a distance equal to its length. What is the ratio of the speed of the faster to the slower?

Real Life Uses of Quadratic Equations [06/13/2002]
When would you solve a quadratic equation in real life?

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?

Remaining Confusion [09/10/2011]
A programming student wonders where she has gone wrong interpreting modulus among the order of operations. Doctor Peterson shows how to proceed, offering up three ways to evaluate the remainder, before anticipating (correctly, it turns out) where the student might have erred.

Reversing the Inequality, Explained to a Teacher with an Antigravity Metaphor [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.

Root Propagation and Loss [10/05/2016]
A teen seeks to get a handle on the ways that extraneous roots arise and valid solutions get destroyed. With multiple variations on a single example, the student and Doctor Peterson explore the range of ways algebraic manipulations can lead problem-solvers astray — and how they can keep the big picture in sight.

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?

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