Explore BrainMass

Explore BrainMass

    Basic Algebra

    BrainMass Solutions Available for Instant Download

    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

    Quadratic equations, discriminant, and graph

    When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx +

    Quadratic Equations - Discriminant

    When using the quadratic formula to solve a quadratic equation (ax2 + bx + c = 0), the discriminant is b2 - 4ac. This discriminant can be positive, zero, or negative. Create three unique equations where the discriminant is positive, zero, or negative. For each case, explain what this value means to the graph of y = ax2 + bx +

    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 hydroge

    Graphs of Exponential and Logarithmic Functions

    Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer. y = 2x y = log2x Plot the graphs of the following functions. Scan the graphs and post them to the Facilitator along with your response. f(x)=6x f(x)=3x - 2 f(x)=(1/2)x f(x)= log2x

    Quadratic Equations : Vertex Form

    1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 4x - 5, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for the line of symmetry for the grap

    Evaluating Functions: Example Problem

    Evaluate each of the functions below at x = 1, 2, 4, 8, and 16. Plot the graph of each function. Classify each as linear, quadratic, polynomial, exponential, or logarithmic, and explain the reasons for your classifications. Compare how quickly each function increases, based on the evaluations and graphs, and rank the functions f

    Use polynomial, rational, exponential and logarithmic functions.

    Human populations can be modeled using an exponential growth function. Use the Library for research or other resources to find the following: current world population current U.S. population current growth rate of the world population current growth rate of the U.S. population Starting in the current year, determine th

    Modeling Exponential Functions

    Many different kinds of data can be modeled using exponential and logarithmic functions. For example, exponential functions have been used by Thomas Malthus to describe the growth of human populations. Exponential growth has also been used to indicate how property values grow in strong real estate markets. Create a set of dat

    Graphs of Inequalities Horizontal Lines

    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

    Graphing and Word Problems

    Please see the attached file for the fully formatted problems. IP Unit 1 1) a) Given the above graph, identify the graph of the function (line, parabola, hyperbola, or exponential), and give the domain and range as shown in the graph. Graph Type Explanation of why you chose that graph type: Domain Rang

    Quadratic Equations

    1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 4x - 5, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for the line of symmetry for th

    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,

    Factoring: Binomials, Trinomials and Polynomials

    Please see the attached file for the fully formatted problems. Find the greatest common factor for each of the following sets of terms. Factor each of the following polynomials (see attachment).

    Create a set of data that can be modeled as a polynomial function.

    Details: Many different kinds of data can be modeled using polynomial functions. An example of a polynomial function would be gas mileage for an automobile. If we compare gas mileage at two different speeds, V1 and V2, the gas required varies as (V1/V2), raised to the third power, (V1/V2)3. Rational functions are also usefu

    In the real world, where might these so-called imaginary numbers be used?

    1. When solving a quadratic equation using the quadratic formula, it is possible for the b2 - 4ac term inside the square root (the discriminant) to be negative, thus forcing us to take the square root of a negative number. The solutions to the equation will then be complex numbers (i.e., involve the imaginary unit i). Questio

    Find the mass and radius of three of the nine planets in our solar system.

    A simple pendulum, such as a rock hanging from a piece of string or the inside of a grandfather clock, consists of a mass (the rock) and a support (the piece of string). When the mass is moved a small distance away from its equilibrium point (the bottom of the arc), the mass will swing back and forth in a constant amount of tim