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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Probate Puzzle [12/15/2003]

A will specifies that every son should receive three times as much as a daughter and every daughter should get two times as much as their mother. What is the mother's share?

Proof of Convergence [09/29/2000]

Why does the ratio F(n+1)/F(n) for the Fibonacci numbers converge to the golden ratio?

Proof of the Rational Root Theorem [11/13/2000]

How can I prove the Rational Root theorem?

Proof That 3 = 0? [10/28/2006]

Starting with x^2 + x + 1 = 0 and using algebraic manipulations, I seem to be showing that 3 = 0. Where am I going wrong?

Proof That All Numbers Are Equal? [12/06/2005]

I saw a proof that all numbers are equal, which makes math pointless. There must be something wrong with the proof. Can you tell me what?

Proof That Equation Has No Integer Roots [05/09/2000]

How can I prove that if p is a prime number, then the equation x^5 - px^4 + (p^2-p)x^3 + px^2 - (p^3+p^2)x - p^2 = 0 has no integer roots?

Proof Using Pell's Equation [09/18/1999]

Given Pell's equation for sqrt(D) and p/q = [a1;a2;...;an], can you prove that p^2 - D.q^2 = (-1)^n.k?

Proof with Inequalities [10/10/1999]

1. How can I prove that a^6 + 4*b^6 >= 4 if ab = 1? 2. At each vertex of a polygon, a number is written... How many sides does the polygon have?

Prove Triangle of Sides with Length... [8/1/1996]

Let a, b and c be the lengths of the sides of a triangle. Prove that the square root of (a+b-c) plus the square root of (b+c-a) plus the square root of (c+a-b) is equal to or less than the sum of the square roots of a, b and c. Determine when equality occurs.

Pumpkin Price [06/28/2001]

Peter Peter has 40 pumpkins to sell. He will sell them all if he sets his price at $1.00 each, but will sell one fewer pumpkin for each 5-cent increase in price...

Quadratic Equation [6/22/1996]

What is a quadratic equation used for?

Quadratic Equation [8/28/1996]

What is the formula for the quadratic equation?

Quadratic Equation [04/08/1997]

The sum of two numbers is 15 and their product is 54. Find the numbers...

Quadratic Formula [10/01/1999]

Could you give me some ideas for how to use the quadratic formula, and some practice problems?

The Quadratic Formula [12/12/2005]

We've been studying the quadratic formula as a way to solve quadratic equations, but I'm a little confused by it. Can you give me a summary of what the formula is, how and when you apply it, and why it's important?

Quadratic Formulas, Equations, Parabolas, Graphing [6/16/1996]

Given 6x^2 + x - 1 = 0, how do I find the roots, the vertex, some coordinates, and from these graph it?

Quadratic Formula: Solve for b [08/15/2001]

How do you solve for b in the quadratic formula?

Quadratic Function [05/04/2001]

What are the effects of changing the values of a, b, and c in a quadratic function?

Quadratic Inequalities [03/18/2003]

When I solve (x^2 + 1)/4 greater than or equal to (x + 2)/2 , of my final two answers, only one works.

A Quadratic Inequality [4/27/1996]

Solve the inequality: (3x+1)(5-10x)>0

Quadratic Model [12/03/2001]

The quadratic model S = -17t^2+45t+2570 approximates the number of suicides by firearms in the U.S. for women, where t represents the number of years after 1985. In what year were there 2370 female suicides by firearms?

Quadratic Problem [7/12/1995]

Find the quadratic functions with vertex (3,-1) and one x-intercept at x=1.

Quadratic Trinomials [8/14/1995]

How do you factor quadratic trinomials as the product of linear binomials?

Quadrilateral Patterns [03/06/1997]

What is the formula that gives the number of quadrilaterals within a square grid when you increase the square grid by one unit on each side?

Quarter Circles [12/20/1996]

Find a function that graphs a quarter of a circle in quadrants II and IV.

Radical Equation [04/12/1997]

How do I solve the radical equation 3x+(5x^(1/2))-28=0?

Radioactive Decay of an Isotope [01/05/1998]

I know the decay of the 226Ra isotope involves the use of logarithms (an exponential function ae^x), but I'm having trouble fitting my information to my equation...

Raising Sides of an Equation to the 0 Power [12/04/1997]

If you raise both sides of an equation to the 0 power, will both sides then be equal to one?

Raising Sqrt(2) [10/14/1997]

What is the value of x in the following equation: x^x^x^x^x ... = 2 ?

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?

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