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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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Math Virus Formula [10/23/2001]

The virus spreads to all the squares directly touching each other (not including diagonally) and I have found the formula for the number of newly infected cells (although this does not include the first minute)...

Matrix Algebra [08/28/1997]

I am not sure which formula of matrices to use in this situation.

Max and Min of Functions without Derivative [04/22/2003]

Is there a general way to find the maximum and minimum of cubic functions without using derivatives?

Maximizing Horizontal Distance [04/10/1998]

Using algebra, prove that an object needs to be thrown at 45 degrees to travel the greatest possible horizontal distance.

Maximizing Oranges [06/29/2002]

An orchard has 800 orange trees, each of which yields 120 oranges per season. For each new tree that is added to the orchard, the output per individual tree decreases by 2 oranges per season. Determine the number of trees that would maximize the orchard's output.

Maximizing Revenue by Analyzing a Parabola [03/13/2007]

When priced at $30 each, a toy has annual sales of 4000 units. The manufacturer estimated that each $1 increase in cost will decrease sales by 100 units. Find the unit price that will maximize total revenue.

Maximum Number of Intersections of n Distinct Lines [10/07/1998]

Find a pattern for the maximum number of intersections of n lines, where n is greater than or equal to 2.

Meaning of Term in Algebra [09/16/2007]

Why is it that when you multiply or divide two numbers or variables they become one term (such as 2*x becoming 2x), but when you add or subtract two numbers or variables they are still two terms (such as 2 + x)?

The Method of False Position [02/06/2004]

There is a quantity such that 2/3 of it, 1/2 of it, and 1/7 of it added together becomes 33. What is the quantity? Solve the problem by the method of false position.

Method of Finite Differences [10/12/2000]

How can I find the generating equation for the series -3, 2, 13, 30, 53?

Minimum and Maximum Problems Using Algebra [04/05/2000]

Can you show me how to solve these minimum and maximum problems using algebra?

Mixing Alcohol, Cable TV Pricing [8/2/1996]

What amounts of 9 percent and 12 percent alcohol do you mix to get 300,000 gallons of 10 percent alcohol? For each 5-cent increase in the monthly subscription price, 4 people will decide not to subscribe to cable TV...

Mixture Problem [11/11/1997]

How much pure antifreeze should be added to 3 gallons of a 30 percent antifreeze solution to get 65 percent antifreeze?

Modeling Multiplying Two Negatives with Number Lines [11/13/2006]

What is the logic behind the rule of a negative times a negative makes a positive, and how do I demonstrate it on a number line?

Monetary Conversions [01/27/2001]

Given these monetary exchanges: 2 coconuts = 1 banana; 3 bananas = 2 mangos; 4 papaya = 1 coconut, what is the exchange for banana to papaya and for papaya to mango?

Money Puzzle [01/05/1998]

A man goes to the bank and asks for x dollars and y cents.

Monomials, Polynomials [03/02/2001]

Can you explain monomials and polynomials to me?

More on Order of Operations [02/13/2000]

I have found contradictory information on the precedence of the multiplication and division operations. Is there a universally accepted rule for the order of these operations?

More Variables Than Equations in a System [01/21/2002]

I have a problem that uses four variables but only two equations to relate them. I don't seem to have enough information to figure out the value of each variable or answer the question. Can you help?

Mother's Age in Terms of Daughter's [06/27/2001]

The sum of the ages of a father, a mother, and a daughter is 73. When the father is twice as old as the daughter, the sum of their two ages will be 132...

Motion Under Gravity [07/18/2003]

Use the equation s = -16t^2 + vt to determine when the height of an object is 960 feet if the initial velocity is 272 feet per second.

Mowing Half a Lawn [03/31/2002]

Chris and Lee are each responsible for mowing half of their 50-foot by 90-foot rectangular back yard...

Multiple Absolute Value Inequalities/Equalities [08/09/2001]

I can solve inequalities containing absolute values, but not if there are two in the same equation....

Multiplicative Inverse [6/2/1996]

Find the multiplicative inverse of 2+5i.

Multiplying/Adding Fractions Gives Same Answer [03/01/2002]

Find two fractions which, when multiplied and added, give the same answer.

Multiplying and Dividing Fractions [8/18/1996]

Three hard problems, illustrated.

Multiplying Binomials and Other Polynomials [04/16/2004]

I have a hard time multiplying binomials properly, such as (2x + 5)(x + 7). I do not know what order the problem should be solved in.

Multiplying or Dividing by a Negative Number [04/08/1999]

When x(x-4) is less than 0...

Multi-Variable Equations [02/07/1997]

Solve for s in d = (log(f/e) + s * s * 0.5 * t)/(s * s * sqrt(t))

Names of Polynomials [05/22/1999]

Why is an equation having only two roots, one of which is raised to the second power, called a quadratic equation?

Natural Domain of a Function [03/12/1999]

Some inputs don't make sense for some functions.

Natural Numbers Coprime to 6 [02/16/1998]

Let N(x) denote the number of natural numbers less than x which are coprime to 6. Show that lim as x goes to infinity of [N(x)/x] = 1/3.

Negative Exponents [10/23/1996]

I have to simplify this expression with non-negative exponents: x^5.

Negative Numbers Combined with Exponentials [03/09/2001]

Why in the order of operations is negation a multiplication done after exponentiation, rather than as a part of the base? What about polynomials?

Negatives and Inequalities [09/10/1998]

Why when we multiply or divide an inequality by a negative number do we reverse the inequality sign?

Negative vs. Subtraction in Order of Operations [10/30/2002]

I am trying to find some definitive source for treatment of leading negative numbers in simplifying with order of operations.

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.

Non-Linear Simultaneous Equations [12/07/2003]

I have four simultaneous equations with four variables, but each one has a non-linear term in it (e.g., ab + c + d = 3). So none of the usual techniques will work! How can I solve the system?

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