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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Acid Concentration, Heating Bill [7/6/1996]

1) A pharmacist has 8 liters of a 15 percent solution of acid. How much distilled water must she add.... 2) By installing a $120 thermostat, a family hopes to cut its annual heating bill...

Adding and Subtracting Polynomials [12/08/1996]

How do you add and subtract polynomials?

Algebra and Trig Equation [4/20/1996]

How can I solve this equation: 1 = sin(3x) - cos(6x) ?

All About Functions [11/06/1996]

Could you please explain functions?

Completing the Square [09/08/1997]

Please explain 2x^2 = x + 5 .

Derfs and Enajs: Algebra and Venn Diagrams [03/09/2003]

All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derfs nor Sivads?

Diagonals and Tiles [11/17/2001]

Jay tiled a 15x21' rectangular ballroom with 1 ft. sq. tiles. Then he drew diagonals connecting opposite corners of the room. How many tiles did the diagonals pass through?

Direct/Indirect Variation [6/12/1996]

Please explain direct and indirect variation.

Distributive Property [04/25/2002]

What's the best and simplest way to teach pupils that a-b = -(b-a)?

Distributive Property, Illustrated [09/28/2001]

How can I show (12*2) + (12*3) using the distributive property?

Doubling Sequence [8/24/1996]

On Jan 1st it snowed one centimeter; on Jan 2, 2cm; on Jan 3, 4 cm...

Equation of a Line Parallel to an Axis [06/19/2003]

How can I get the equation of a line if the line passes through a point and is parallel to the x- or y-axis?

Equations of a Line given Two Points [8/31/1996]

How do you find the equation of a line going through two points if you only know the two points?

Equations: the "Elimination" Method [11/20/1996]

Is there an easier way to solve a system of two equations than by the substitution method?

Explaining Algebra Concepts and FOIL [08/04/1998]

Some ideas for learning algebra that may help prevent frustration.

Exp, Log, and Ln Functions Explained [7/31/1996]

What is the exp function? When is it needed? Also, how do I calculate Log and Ln functions with basic arithmetic and logic?

Factoring Polynomials [11/14/1996]

Is there a logic behind the factorization of polynomials?

Factoring Polynomials [11/07/2001]

Factoring polynomials like 12x^3y^9 + 20x^5y^4.

Factoring to Solve a Problem [7/31/1996]

I have problems understanding the solution I get when I factor an expression to solve: x (x + 1) = 132...?

Finding the Equation of a Line [01/08/1997]

Given either a point and a slope or two points, how do you find the equation of a line in both point-slope and standard form?

Geometric Objects and Properties using Algebra [06/29/1998]

Why does y = mx+b, and what does it mean?

Graphing Coordinates [1/15/1997]

How can you tell if you have a straight line just by looking at the numbers?

Horizontal and Vertical Asymptotes [12/5/1995]

I am confused about horizontal and vertical asymptotes. Please tell me how to find them, and their definition.

An Introduction to Parabolas [02/04/1999]

What is a parabola? What are some of its properties? What are some examples of parabolas in real life?

Linear Expressions [08/17/1999]

What are linear expressions, and how will I use them in my life?

Linear Programming [01/30/1997]

Maximize the profit of a nutrition center given information about the energy trail mixes they sell.

Locus and Equations of Lines [01/10/1999]

Describe the locus of points that are 3 units from the line x = -1...

Long Division of Polynomials [6/26/1995]

How do you use long division to solve polynomials with remainders?

Loosening the Earth's Belt [1/18/1996]

The earth has a belt around the equator that is perfectly fit. If a measurement of 1 foot is added to the belt, theoretically the belt will no longer touch the earth at any point. What is the new distance between the surface of the earth and the belt?

Man and Train on a Bridge [2/1/1996]

When a man is 3/8 of the way across a railroad bridge that goes from point A to point B, he hears a train approaching at 60 mph. If he runs back he will meet the train at A, and if he runs forward the train will overtake him at B. How fast can the man run?

Meaning of Irrational Exponents [03/17/1997]

y^x is the product of x factors of y. Where do irrational exponents fit in this? How can you have an irrational number of factors?

Mixing Milk and Butterfat [09/04/2001]

Milk that has 5% butterfat is mixed with milk that has 2% butterfat. How much of each is needed to obtain 60 gallons of milk that has 3% butterfat?

Negative Ratios and Dividing by Zero [6/8/1995]

How can 1 : -1 = -1 : 1 ? Is x divided by 0 = infinity? Are there different infinities?

No Solution, Infinite Solutions [01/03/2002]

Solve: 8(2x-3) = 4(4x-8); -3(x-3) is greater than or equal to 5-3x.

Order of Operations Puzzle [09/22/2002]

What is _ + _ x _ - _ = 22? We're given the numbers 2, 3, 4, 8.

The Particular and the General Case [11/06/2001]

If a+b+c=3 and a(^2)+b(^2)+c(^2)=5 and a(^3)+b(^3)+c(^3)=7 what is a(^ 4)+b(^4)+c(^4)? And how is it done?

Polynomial Inequality Problem [2/7/1996]

A student asks for help with solving algebraic inequalities.

Proof by Induction [07/13/1997]

Prove by induction on n that |A^n|=|A|^n.

Purpose of Algebra [10/15/1996]

What is the purpose of algebra and who came up with the idea?

Pythagorean Theorem Proof: Four Right Triangles [10/7/1996]

I don't understand the Pythagorean Theorem.

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