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Basic Algebra

Measuring and Comparing Earthquakes

What is the formula for measuring earthquakes? Why is a 7.0 earthquake ten times stronger than a 6.0 earthquake? Pick an earthquake in your region of the world. Give the measurement of the earthquake. Explain what this measurement means.

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

Simplifying Expressions

Simplifying Expressions. See attached file for full problem description. Simplify the following expression as much as possible Rewrite the following in simplified radical form Simplify Write in simplified radical form by rationalizing the denominator Solve for Solve for w Write

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

Relation Between Relatively Prime Integers

Modern Algebra Ring Theory (XXXVI) Polynomials over the Rational Field Euclidean Ring Irreducible Polynomial If m and n are relatively prime integers and ( x - m/n ) divides ( a_o + a_1x + ... + a_r x^r ) where the a's are integers, prove that m divide

Prime Polynomials

Give an example of a polynomial of a degree 2 that satisfies the following two conditions: (1) the coefficient of x^2 is 1 and (2) the polynomial cannot be factored. Explain why the polynomial cannot be factored. Give an example of a polynomial with degree 2 that can be factored as the product of two polynomials of degree 1 e

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):

Quadratic Functions and Parabolas : Maximum Height and Maximum Area

(1) Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0 ?16 represents ½g, the gravitational pull due to gravity (measured in feet per seco

Radicals and Rational Exponents

Radical and rational exponent notation are two ways to show the same process. Explain the similarities between radicals and rational exponent notation. Provide at least two other examples of mathematical notation or wording denoting the same process.

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

Algebra Exercises Evaluated

Algebra Exercises. See attached file for full problem description. 1. Evaluate , if possible. 2. Determine whether is rational or irrational. A) Rational B) Irrational 3. Simplify. A) 54 B) C) D) 4. Simplify. Assume all variables represents positive numbers. A) B) C) D)

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

Math Puzzle: Addends and Sums

Fay Ling is not going to pass her second semester math class unless she can supply the missing addends and sums in the following grid. Please help her by filling in the missing information (please see attached).

Arithmetic and Geometric Sequences

Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? Which one of the basic functions (linear, quadratic, rational, or exponential) is related

Synthetic Division and Logarithm and Exponential Functions

A geologist you spoke with is concerned about the rate of land erosion around the base of a dam. Another geologist is studying the magna activity within the earth in an area of New Zealand known for its volcanic activity. One of the shortcuts they apply when doing calculations in the field is to use synthetic division. Use s

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

Algebra Word Problems: Relative Speed

Kim starts to walk 3 mi to school at 7:30 a.m. with a temperature of 0 degrees F. Her brother Bryan starts at 7:45 a.m. on his bicycle, traveling 10 mph faster than Kim. They they get to school at the same time, then how fast is each one traveling?

Finding LCD

Find the LCD for the following rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator. -3/2p^2 +7p-15 , p/2p^2 -11p+12 , 3/p^2 +p-20

GCF

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.

Quadratic Equations Word Problems : Maximizing Area

Amanda has 300 feet of lumber to frame a rectangular patio. She wants to maximize the area of her patio. What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation by using the vertex form to find the maximum. Show the work when computing this equation.

Quadratic Equations

1. Solve using the quadratic equation : 8x^2 - 24x = 9 2. choose from the following a quadratic with solutions of 9 and 3 a. x^2 - 10x + 27 = 0 b. x^2 - 12x + 27 = 0 c. x^2 - 14x + 25 = 0 d. x^2 - 12x + 29 = 0 3. The height h (in feet) of and object is

Quadratic Equations

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. Answer: Show work in this space b) What is the equation for the line of symmetry for the graph of this function? Answer: c) Graph the function using the equation in part a. Explain w

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: