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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Finding Howlers [10/25/1999]

Howlers are fractions like 16/64; when you cross out the 6 on the top and the bottom, you are left with 1/4, which is the simplified fraction. How can I find all 2-digit, 3-digit and 4-digit howlers?

Finding Line Segment Lengths [12/21/2001]

Can you help me find line segments AB and BC if points A,B,C, and D are collinear with B between A and C and C between B and D...?

Finding Multiplier of Constants [8/5/1996]

What is a common multiplier of the positive constants a, b, and c such that x/3 = a^2/b^2c?

Finding Point of Intersection [05/08/2001]

Is there a formula to tell if two lines, given by point coordinates, cross and at what coordinates they cross?

Finding Rules for Number Patterns [06/05/2009]

I'm having trouble finding an algebraic expression that generates the pattern 3, 5, 8, 12, 17, 23, 30. Can you help?

Finding Sets of Integers [01/02/2002]

Without computer assistance, find five different sets of three positive integers such that and k is less than and m is less than n, and 1/k + 1/n + 1/m = 19/84.

Finding Solutions to Systems of Equations [10/18/1996]

I need help solving systems of equations, i.e. 3m+5n=21 and 4m+10n=38.

Finding Terms in a Binomial Expansion [03/27/2001]

How can I find the fifth term of (-5m+4n^3)^54?

Finding the Center of a Circle from 2 Points and Radius [01/24/1997]

Given two points on a circle and the circle's radius, find the center coordinates of the circle.

Finding the Center of a Circle from 2 Points [06/01/1999]

How do you find the centre of a circle if you are given 2 points on the circle and the radius?

Finding the Center of a Circle from Three Points [05/22/2000]

How can I find the coordinates of the center of a circle, given the coordinates of three points on its circumference?

Finding the Difference of the Cubes of Two Numbers [9/29/1995]

The difference of two numbers is 1. The product of the two numbers is also 1. What is the difference of the 2 numbers cubed?

Finding the Dimensions of a Room [12/5/1995]

After studying statistical data, Fariba surmises that a club should seat a minimum of 1152 people at tables. The tables will be 3 x 6 feet, and each one will seat 6 customers...

Finding the Equation of a Parabola [04/28/2001]

How can I find the equation of a parabola whose zeros are at 0 and 6, and whose minimum value is -9?

Finding the Inverse Function [04/10/1997]

How do I find the inverse function of f(x)=4x/(x+2), where x does not equal -2? What is the domain and the range?

Finding the Roots of a Cubic [1/27/1996]

Find all the roots of x + y = x^2 + y^2 = x^3 + y^3.

Finding the Square Root of a Quadratic Function [10/30/2002]

Find the square root of 3+4i.

Finding y-intercepts [6/12/1996]

I'm having a problem with finding and graphing y-intercepts of linear equations.

Finding Your Position on a Football Field [11/1/1995]

Write a function F(x) that represents your position on the football field after walking x yards from the goal line. Give the domain and range of this function.

Find the Average Speed [11/27/1997]

A motorist has to travel 160km. His average speed is 8km/h slower than he anticipated and he takes 1 hour longer than intended...

Find Values of x... [9/4/1996]

Determine all values of x for which (x^2-5x+5)^(x^2-2x-48)=1.

First Principle Hyperbolas [01/05/1999]

How do you solve for the standard equation of a hyperbola given its properties?

First Year Algebra [6/19/1996]

What should a person have learned after one year of Algebra I? I want to be prepared for Geometry next year.

Fitting a Picture to a Frame [11/14/1996]

I have a picture frame that needs to have twice as much border on the side of the picture as on the top. If the photo is half the area of the frame, how wide should the borders be?

Floating 2 [06/12/2001]

Start with the number 2 on the far left side, then float the number 2 to the far right side; the new number must be three as large as the old number.

Focus of a Hyperbola [04/06/1998]

When you rotate the focus point of a hyperbola around the center, why does it hit the asymptote with the same x coordinate as the vertex?

Formula for Slope of 3-D Line [03/12/1997]

Is there a formula that gives the slope of a 3-D line?

Formulas for the Equation of a Line [09/28/1998]

Can you explain the meaning behind the point-slope formula? What about other formulas for the equation of a line?

Fourth-Degree Polynomial [04/26/2001]

How can I construct a fourth-degree polynomial that contains all of the following points: (-1,2), (1,-2), (3,7), (2,1) and (0,3)?

The Fourth Dimension [8/24/1995]

What is the fourth dimension mathematically?

Functional Equation [02/18/2008]

If 2f(x) + f(1-x) = x^2 for all x, then f(x) = ?

A Function of a Function [6/19/1996]

Suppose that f(x) is O(g(x)). Does it follow that 2 to the power f(x) is O(2 to the power g(x))?

Functions [11/12/1994]

I'm a first year algebra student having difficulty learning about functions. Exactly how do they work?

Functions and Equations [02/10/2001]

When is an equation also a function? How do you recognize a function?

Functions that are their own inverses [02/28/1998]

Can a function ever be its own inverse?

Fundamental Theorem of Algebra [01/25/2001]

What exactly is the Fundamental Theorem of Algebra?

Gaussian Elimination [01/11/2000]

How can you solve a system of linear equations using Gaussian elimination?

Geometrically Completing the Square [08/07/1997]

What are the steps for geometrically completing the square?

Geometric and Arithmetic Means [5/10/1996]

Find two numbers whose sum is 20 and whose geometric and arithmetic mean is 8.

Given n Points, find a Polynomial Function... [6/27/1996]

Find a polynomial F(x) of degree less than n so that the graph of F passes through all of the points.

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