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Dr. Math FAQ:
order of operations
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.
Completing the square.
Direct and indirect variation.
Inequalities and negative numbers.
- 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
- 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
- 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.
- Go for the Gold! [1/28/1996]
Your job is to prepare the women's athletes for the Olympic 1,500-meter
- Graphing [8/18/1995]
I've got questions concerning graphing.
- Graphing a Function with Asymptotes [07/05/1998]
How do you find the asymptotes of f(x) = (2x + 1)/(x - 3)? How do you use
the asymptotes to graph the function?
- Graphing an Equation [4/4/1996]
How do you graph 2x-y = 10?
- Graphing an Equation [11/08/1997]
Please explain how to graph this equation: y = a + b(x) + c(x^2) + ...
- Graphing an Equation with Absolute Value [10/15/1995]
How would you approach graphing negative 2 times the absolute value of x
- Graphing Intercepts [11/06/1997]
How would I find the intercept for a problem such as 3x-2y = 12?
- Graphing Parabolas [01/16/1997]
How do you know how to graph a parabola from looking at its equation?
- Graphing Piecewise Functions [09/09/2001]
I do not understand how to graph piecewise functions.
- Graphing points [4/13/1996]
Given f(x)=4 and g(x)=2, which is the Y axis and which is the X axis?
f(x)=x-2(3)+4 ; g(x)=x-2(3)+4.
- Graphing Quadratic Polynomials [02/07/2001]
Can you give me a simple explanation of how to graph quadratic
polynomials like y = x^2 - 8x + 15?
- Graphing Slope Intercept [02/13/1999]
When given the slope intercept form, how do you know whether you rise or
drop when looking at the slope?
- Hands of a Clock [10/10/1997]
How many times do the hour and minute hands cross in a 12-hour period of
- Height of the Ball [01/05/1998]
A football player kicked a 41-yard punt. The path of the ball was modeled
by y= -0.035x(squared) + 1.4x + 1, where x and y are measured in yards.
What was the maximum height of the ball?
- Help with a Proof [4/6/1995]
I'm trying to figure out how to prove that a is less than b implies that
a*a is less than b*b is true in R+....
- Hidden Faces of Cubes [06/20/2001]
My daughter has to produce an equation to show the number of hidden faces
when three rows of cubes are placed together on a flat surface.
- Hiking Up and Down [04/24/1999]
How many kilometers is it from the base to the top of the mountain?
- Hints for Algebra 101 [7/31/1995]
Do you have any helpful hints for algebra 101?
- Horner's Method of Solving Irrational Roots [01/29/1998]
Can you give a method, formula, and answer for this equation? x^3 - 3x^2
- 2x + 5 = 0
- How Far Does C Walk? [08/06/2001]
Three persons A, B, and C, travel from point X to point Y. They leave
point X at the same time and follow the same route...
- How Far Will the Rocket Be from Earth? [06/22/2001]
A rocket leaves the earth for the sun at a speed of 28,800 mph. At the
same time, a photon of light leaves the sun for the earth...
- How Long Did She Walk? [06/12/1999]
A woman usually takes the 5:30 p.m. train, arriving at her station at
6:00, and her husband picks her up and drives her home...
- How Many Factor Pairs Does a Given Number Have? [03/19/2004]
I'm wondering if there is a formula or algorithm that will tell me
exactly how many pairs of factors a number has?
- How Many Mice, Cats, and Dogs? [01/13/2003]
You must spend $100 to buy 100 pets, choosing at least one of each
pet. The pets and their prices are: mice @ $0.25 each, cats @ $1.00
each, and dogs @ $15.00 each. How many mice, cats, and dogs must you
- How Many Points Determine a Parabola? [12/20/2000]
How can we determine whether or not a given plane curve is a parabola?
Under what conditions is a parabola uniquely determined?
- How Many Valentines? [02/10/2003]
If everyone in your class gave a Valentine to everyone else in your
class, how many valentines would be exchanged?
- How Much Money Entering the First Store? [09/26/2002]
Timothy spent all of his money at five stores. At each store, he spent
$1 more than half of the amount he had when entering the store. How
much money did he have when he entered the first store?
- How Much Popcorn did Paul Sell? [01/28/2002]
Paul made $44.14 selling 27 items (beer and popcorn). If he made $1.22
selling popcorn and $2.62 selling beer, how many boxes of popcorn were
- The Idea Behind Simultaneous Equations [10/14/2001]
I'm having a hard time learning the linear combinations method and the
substitution method in algebra.
- Identity and Inverse Properties for Zero [01/07/2004]
If we subtract 0 from a number and get the same number, doesn't that
make 0 an identity for subtraction? Also, can't a number be its own
inverse for subtraction?
- If 1/x+x=5, what does 1/x^2+x^2 equal? [08/16/2002]
A complex and an easy solution to the problem.
- Implied Multiplication and TI Calculators [05/02/2008]
If I type 36/6(25-11*2) into my TI-85, I get an answer of 2. If I
include a multiplication symbol to have 36/6*(25-11*2), I get an
answer of 18. I thought that when the 6 is written right up against
the parenthesis, the multiplication is implied. Why am I getting two
- The Importance of Defining Variables Clearly in Algebra [11/01/2007]
A sample of dimes and quarters totals $18.00. If there are 111 coins
in all, how many are there of each coin?
- Increasing the Average [02/25/2001]
Five members of a basketball team are weighed and an average weight is
recalculated after each weighing. If the average increases 2 pounds each
time, how much heavier is the last player than the first?