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Basic Algebra

Algebra Word Problems : 'Together and Alone' Problems

Problem 1:Suppose one painter can paint the entire house in twelve hours, and the second painter takes eight hours . How long would it take the two painters together to paint the house? Problem 2: Two trains leave the same train station at the same time , but in opposite direction. The faster train travels at an average ra

Logarithms and Exponents

For problems 1 -3, use the algebraic definition of the logarithm to evaluate (simplify) the expression by hand and state the property number used. All work must be shown. 1. log8 (8^(x-1) 2. log4 ((1/16)^7) 3. log (0.0001) For problems 4 - 6, solve for x exactly by hand. 4. log5 (x - 1) = 1 5. log2 (1/8) = x 6. lo

Integers and Real Numbers

Draw the real line and label from about -5 to 5 in increments of 1. There are an infinite amount of integers on the real line. Based on your sketch you'll also agree with me that there are twice as many total integers as there are positive integers, right? But how many positive integers are there? That's it... an infinite am

Word Problems : Solving Equations

1. It takes a passenger 5 hours less time than it takes a cargo plane to make the trip from Los Angeles to London. If the passenger plane averages 700 miles per hour on the trip while the cargo plane averages 450 miles per hour, how far is it from Los Angeles to London? 2. The molecular formula for Acetone. How many hydro

Graphs of Inequalities

If the inequality involves only x, then graph the vertical line x = k. x > k is the region to the right of the line. x = k is the line itself. x < k is the region to the left of the line. Could there be a horizontal line? What would be it's equation/inequality? How do you decide on a so

Algebra Word Problems

1. Three consecutive even integers are such that the square of the third is 76 more than the square of the second. Find the three integers. 2. A photo is 3 inches longer that it is wide. A 2-inch border is placed around the photo making the total area of the photo and border 108in2. What are the dimensions of the photo?

Similarity Classes of 6x6 Polynomials

Abstract Algebra II - Modules. This is for the second problem #11 Find all similarity classes of 6x6 matrices over C with caracteristic polynomial (x^4 - 1)(x^2 - 1).

Should We Purchase That New Copier?

Campus Print Shop is thinking of purchasing a new, modern copier that automatically collates pages. The machine would cost $22,000 cash. A service contract on the machine, considered a must because of its complexity, would be an additional $200 per month. The machine is expected to last eight years and have a resale value of $4,


Is it possible to use the inclusive brackets [ or ] with -infinity or infinity? Why or why not?

Algebra Word Problems

The owner of a hobby store bought a case of 9-volt batteries for $26.00. He marked the price up such that his profit was $1.74 per battery. After selling 13 batteries, the store owner had recovered his cost. How many 9-volt batteries are in a case?

Absolute Values

I know that the two bars | | around the expression 2-x and x-2 stand for 'absolute value'. But how does using | | differ from using simple brackets such as: ( ) or [ ] ?