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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.
 Nested Negative Exponents [8/2/1996]

How do I deal with nested negative exponents?
 Net Result of Consecutive Percentage Increases [12/11/2003]

Suppose a quantity is increased by some percentage, and then is later
increased again by another percentage. How can I calculate the
overall percentage increase?
 Nonlinear Factors [10/12/1998]

I have been told that factoring the sum of two squared numbers is not
possible, but factoring x^4 + 4 is possible. Please explain.
 NonLinear Simultaneous Equations [12/07/2003]

I have four simultaneous equations with four variables, but each one
has a nonlinear term in it (e.g., ab + c + d = 3). So none of the
usual techniques will work! How can I solve the system?
 Normalization [08/01/2001]

How do I figure out: 90 + 70 + 88 + 94 + x / 5 = 85 ?
 The Nth Root of N [11/28/2000]

Is the nth root of n (a whole number other than 1) ever a rational
number?
 Number of Equations Needed in a Simultaneous Linear System [10/29/2003]

Could you tell me why we need the same number of equations as
variables in order to get a unique solution to a system of
simultaneous linear equations?
 Number * Sum of Remaining Four Numbers [04/03/2003]

Find 5 numbers such that when each number is multiplied by the sum of
the remaining 4 numbers, the following values will result: 152, 245,
297, 320, 360.
 Objects in a Pyramid [7/8/1996]

Objects are stacked in a triangular pyramid... how many objects are in
the nth layer from the top?
 Old Test Questions Answered [1/23/1995]

I am studying for my midterm, and I've come across two questions that I
got wrong and don't understand why....
 One Variable Equations with Decimals [02/11/1997]

How do you solve 8.25x + 3 = 17.5 + x?
 Open Sentence, Statement [09/18/2001]

What is an open sentence?
 Operator Precedence [08/13/2003]

Since the following statement is true: (1+1)**(52) is 8, why is the
following statement true and not false: 2**1+1 is 3 and not 4, and
3*1**3 is 3 and not 27...' ?
 Ordering Exponents and Variables [04/08/2000]

Is there a rule for putting terms in descending order if the variables
have the same exponent? What about negative exponents and descending
order?
 Ordering Products, Powers, and Parameters of Trigonometric Functions [10/31/2010]

A student wants to know how to unambiguously interpret strings of trigonometric
functions, multiplication, and exponentiation. Doctor Peterson digs into a history book
 as well as another math doctor's conversation  to illuminate the vagaries of the
notation.
 Order in Linear Expressions [11/20/2001]

Can you give me a convincing argument as to why, in an equation such as
y=137x, where y is a function of x, it should be written as y=7x+13?
 Order of Operations [05/19/1999]

Given a, b, x, and y, find ax/by.
 Order of Operations with Percentages [04/05/2001]

Why does the order of operations exclude percentage, square roots, etc.?
 Other Ways to Get the Quadratic Formula [02/19/2010]

Doctor Jacques shares two ways to derive [b +/ SQRT(b^2  4ac)]/2a
without explicitly completing the square.
 Pairs of Odd Integers [09/24/1997]

Find all pairs of odd integers a and b that satisfy the equation: a +
128b = 3ab.
 Parabola with Horizontal or Vertical Axis [05/03/2001]

How can I find the focus and directrix of a parabola whose axis is either
horizontal or vertical, like 2x^2 = y?
 Parabolic Golf Shot Equations [01/24/2002]

Does the ball reach the green?
 Parallel and Perpendicular Lines [01/14/1999]

How do you tell without graphing whether the graphs of these equations
are parallel, perpendicular, or neither?
 Parallel Lines [12/31/1998]

What are some ways of proving lines parallel  geometrically and
algebraically?
 Parametric Form for Equation of a Line [6/30/1996]

How can you convert an equation such as y = 3x/4 + 7/2 to parametric
vector form?
 Parity [8/2/1996]

How do I determine if the given function is odd, even or neither? What's
the symmetry of the graph?
 Partial Fractions [01/29/1998]

How do I express 3/1(x^3) in partial fractions?
 Pascal's Triangle Pattern [04/22/1999]

What pattern does multiplying each entry by 1, 2, 3, 4, 5... in order,
and adding the products yield?
 Perfect Square: Solving Two Equations [6/14/1996]

x^2 + 5 is a perfect square, and x^2  5 is a perfect square.
 Perimeter Equals Area in a Triangle [4/2/1996]

When will the area and perimeter of a right triangle be numerically
equal?
 Picture Frame, Triangle Measurements [5/20/1996]

My teacher gave us ten questions to answer and I could do all except two:
1) A framed rectangular picture is 35cm long and 25cm wide... 2) The base
of a triangle is 9cm more than the perpendicular height...
 Plus or Minus Sign [03/08/2002]

What does this equation mean: y = + k ? The  sign is directly under the
+ sign.
 Point Equidistant from 3 Other Points [04/11/1999]

How do you find a point that is equidistant from three other points?
 Point on a Line [03/23/2001]

Can you please tell me a formula to find if a point exists on a line?
Both are in x,y form.
 Polynomial BrainTwisters [12/4/1995]

I'm stumped on some similar polynomial problems...
 Polynomial Degrees and Definition of a Field [03/02/1998]

The degree of polynomials added together, and definition of a field.
 Polynomial Factoring Rules [04/02/1997]

How do I apply the polynomial factoring rules to t^21+1 and 25y^2144 =
0?
 Polynomial Problem [3/11/1995]

A remainder of 9 results when the polynomial p(x) is divided by x2, a
remainder of 3 when p(x) is divided by x+2, and a remainder of 3 when
divided by x1. Find the remainder when p(x) is divided by (x2)(x+2)(x
1).
 Population and Percentage [03/07/1999]

Given population data, find the number of women in two different years.
 Positive Unit Fractions [10/02/2002]

Find five different positive unit fractions whose sum is 1. (A unit
fraction is a fraction whose numerator is 1. All denominators must
also be natural numbers.)
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