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Basic Algebra

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

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?

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,

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?

Various Algebra Questions

Various Algebra Questions. See attached file for full problem description. 1. Simplify: . Show work. 2. Simplify: Show work. Give the exact answer (including a radical). 3. (a) Is the graph of a circle a graph of a function? (Yes or no) (b) Find the center and the radius

Question about Solve an algebraic equation

Details: Your company is considering various locations for expansion. It is your job to check out the various areas and the friendliness for business. One of the factors of interest is the average temperature. As you start your drive, the first electronic sign you see states that the temperature is 22.0 °C. You are not very

Graphing a system of inequalities considering a small home-based company

A small home-based company produces both hand-painted scarves and sweaters. The scarves take 2 hours of labor to produce, and the sweaters take 14 hours. The labor available is limited to 40 hours per week, and the total production capacity is 5 items per week. Write a system of inequalities representing this situation

Algebra Problems

Find all real or imaginary solutions to each equation: 3v^2 + 4v - 1 = 0 Solve the equation 2y^2 - 3y - 6 = 0 (x-10)(x-2) = -20 Determine whether the parabola opens up or down: y = -1/2x^2 + 3 Find the vertex and intercepts for each parabola: g(x) = x^2 + x - 6 Find all real solutions to each equation: x^2 + x +

Algebra Word Problem - Crossing a bridge with a flashlight.

The band U-2 has concert that starts in 17 minutes and they must all cross a bridge to get there. All four men begin on the same side of the bridge. You must help them across to the other side . It is night there is one flashlight. A maximum of two people can cross at one time. Any party who crosses, either 1 or 2 people, m

Factor each of the given polynomials (and/or do what is otherwise indicated).

1. Find the value of "c" such that the expression "(x^2) + 6x + c" is a perfect square. 2. Find the value of "a" such that the expression "(z^2) + 12z + a" is a perfect square. 3. Factor the expression 3*(u^4)*(y^4) - 48*(u^4) completely. 4. Factor the expression 36*(t^3) - 48*(t^2) - 20t completely. 5. Factor the ex

Logarithms : Power Rule

Fill in the blank to make a true statement. To solve 4^x =27, we can take the logarithm of each side of the equation to get log (4^x) = log (27). The power rule for logarithms would then provide a way of moving the variable x from it's position as an _________ to the position of a coefficient. Is the blank, negative value, ba

The C-V-P Equation

The company sells lawnmowers for $895 each. The variable cost per lawnmower is $520. The company's monthly fixed costs are $84,500. Using the C-V-P equation, compute the amount of profit the company will have for a month in which the company sells 375 lawnmowers.

Factor the polynomial f(x) = 2x^3 - 5x^2 - 4x + 3

I am trying to factor the polynomial f(x) = 2x^3 - 5x^2 - 4x + 3. I think it is (x-3)(x+1)(x- 1/2). Am I right? (See work below.) Once I factor f(x), how do I use that to find the answers to the following questions? a) f(x) = 0 b) f(x+2) = 0 c) f(2x) = 0 This is the work that I used to factor f(x):

Exponential and Logarithmic Functions

1. Sketch the graphs of y=5x and y=-5x+2-1 on the same set of axes. Identify the following properties of each graph: a) the domains b) the ranges c) any asymptotes d) the y-intercepts 2. The population of the U.S. doubles approximately every 100 years. In 1980 the population of the U.S. was 200 million. Find the projec

Polynomials : Zeros and Complex Roots

Find the polynomial f(x) of degree three that has zeroes at 1, 2, and 4 such that f(0) = -16. a. f (x) = x3 − 7x2 +14x −16 b . f (x) = 2x3 −14x 2 + 28x −16 c . f (x) = 2x3 −14x 2 +14x −16 d . f (x) = 2x3 + 7x2 +14x +16 Find the third degree polynomial whose graph is shown in the figure

Distance traveled between Chicago and St. Louis

It is approximately 300 miles from Chicago, Illinois, to St. Louis, Missouri. allowing for various traffic conditions, a driver can average approximately 60 miles per hour. a) How far have you traveled after 3 hours? b) How far have you traveled after 4 hours? c) How far have you traveled after 1 hour? ie. write a line

20 algebra problems about quadratic equations

Solve: 1. (4s + 9)^2 = 36 2. f(x) = x^2 + 18x 3. z^2 + 18z + 64 = 0 5. 7n^2 = 10n - 2 6. 5r^2 + 20r = -18 7. -7x^2 - 5x = 9 8. f(x) = 3x^2 - 5x - 1 Find the vertex: 13. f(x) = (x + 6)^2 - 2 Graph: 12. f(x) = -4(x + 7)^2 + 4 15. f(x) = -x^2 + 2x - 7 Find the x and y intercepts: 16. f(x) = 2x^2 + 6x + 1 S


Find the GCF 45m^2n^5, 56a^4b^8

Logarithms explained in this solution

10 Problems Please see the attached file for the fully formatted problems. 1. Find the value of x: . Choose the correct answer from the following: 2. Evaluate the expression . 3. Write the equation in logarithmic form. 4. Evaluate the expression log 2 1. 5. Fill in the blank to make a true statement.

Answering Twenty Algebra Questions

Please see the attached file. (Questions 1, 2) Solve the absolute value inequality: |4x - 4| >= 1 |r - 4.6| < 9 (Question 3) Multiply and simplify: 6y x 4y + 2 12y + 6 5 (Question 4) Find the domain: f(x) = (x2 + 8x)/(x - 8) (Question 5) Find the LCM: 63x, 9x2, yx3 (Question 6) Simplify:

Four questions about systems of inequalities

18. match the system of inequalities to a region in the picture x + 2y <= 8 3x - 2y <= 0 22. solve the system of linear inequalities graphically 3x + 4y <= 12 y >= -3 32. solve the system of linear inequalities graphically, find the coordinates of each corner points, and indicate whether the solution region is bo

Exponential Breakdown

Exponential Model on Growth of Internet Networks 1989- 1996 Internet Network: A global network connecting millions of computers. More than 100 countries are linked into exchanges of data, news and opinions. The Internet is revolutionizing and enhancing the way we as humans communicate, both locally and around the globe. Si