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Basic Algebra

Multiplication of Degrees Theorem

Let u be an algebraic element of K (field extension of F) whose minimal polynomial in F[x] has prime degree. If E is a field such that F is contained in E is contained in F(u), show that E = F or E = F(u)

Differentiate between an expression and an equation

How might you graph an equation in two variables in the rectangular coordinate system? What is the relationship between an exponential function, such as y = 2x, and a logarithmic function, such as the logarithm of x to the base of 2? What values does understanding logarithmic functions allow you to solve for? How do you di

polynomial of degree

2. verify that the function f(x) = e^-2x satisfies the hypothesis of mean value theorem on the interval [0, 3] and find all the number c that satisfy the conclusion of the mean value theorem. 3. show that a polynomial of degree two has at most two real roots.

Given positive integers

A dart board has regions worth a points and b points, where a and b are positive integers with no common factors. What is the largest point total that cannot be obtained by throwing darts at the board?

Abstract Algebra: Irrationals

Please provide a proof to the following problem. Thank you for your time, it is greatly appreciated. "Show that the nth-root of m is not rational unless m = k^n for some integer k." Thank you again.

(a) Solve for x. Show all work.

(a) Solve for x. Show all work. x^2 = x (b) If the length of a rectangle is 3 feet longer than its width and the diagonal is 15 feet, find the dimensions (length & width). Show all work.

How do you factor the difference of two squares?

How do you factor the difference of two squares? How do you factor the perfect square trinomial? How do you factor the sum and difference of two cubes? Donâ??t just show a problem; explain how to factor each of these. Which of these three makes the most sense to you? Explain why.

Description of Algebra Questions

3) The profit function for Wannamaker Trophies is P(x) = -0.4x2 + fx - m, where f represents the design fee for a customer's awards and m represents the monthly officerent. Also, P represents the monthly profit in dollars of the small business where x is the number of awards designed in that month. a) If $60 is charged for a

an example of an exponential function

Is the compound interest formula, such as would be used to calculate a car loan, an example of a function? If it is, of what type of function is it an example? Why might you identify it with that type of function?

operations on functions.

Which of the four operations on functions do you think is the easiest to perform? What is the most difficult? Explain why.

Various Basic Algebra Problems: Solving for Variables and Slopes

See the attached file. Show all of your work. Circle your answer(s). Chapter 1 1. Simplify: -12 + 5 - (-4) - 6 2. Simplify:-22(-3)2(5) 3. Simplify: 5/6 - 2/3 - 8/9 4. Simplify: 31.24 - 8.12 + 1.07 5. Simplify: (.8)(-2.4)(-3.8) Chapter 2 6. Solve: -4 = x - 11 7. Solve: 8/15 = x + 2/5 8. Solve: -4/3y

Find the maximum area

Details: When John, decided to renovate his garage, he also wanted to attach it to his house. The only one wall that was available to achieve this was the kitchen wall. The contractor informed him that the area of his new garage will be limited by the cost of the materials he should buy. After some calculations, they decided

The impact today's technology may have on writing and written communication.

Social networks, email and cyberchat have added to the lexicon of English through "coining," blends, clips and replacement. Does this show the development of a pidgin or simply fashionable slang? Is written communication doomed to ever shorter shortcuts, at the expense of expression, or is the technology "additive" in nature, bu

Algebra Questions and FOIL Method

1. Use the FOIL method to find the product (6x^7-2)(x^8-4) 2.If a pro basketball player has a vertical leap of about 20 inches, what is his hang time? Use the hang time function V=48 T^2 ( Simply the answer. Type an integer or a decimal. Round to the nearest tenth) 3.Identify the degree of each term of the polynomia

Quadratic equations

Can you please explain the four-steps for solving quadratic equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make it easier, or to make it easier to understand?

The Degree of Operating Leverage

Grey Products has fixed operating costs of $380,000, variable operating costs of $16 per unit, and a selling price of $63.50 per unit. Please refer to the attached document for the required data. A) Calculate the operating break even point in units. B) Calculate the firm's EBIT at 9,000, 10,000, and 11,000 units, respect

Algebra Example Problem

If the cost of a cell phone has decreased 400% during the past 10 years, does that correspond to a cost decrease of four times? Explain your answer as though you were talking to someone who has never taken algebra.

simple calculus question

1. Evaluate the following limits. (a) lim x^2/(cos9x-cos5x) =_______ x->0 (b) lim x^(1/3) ln x =_______ x->0+ (c) lim ((1/ln x) - (1/x-1)) =_________ x->1+ (d) lim ((1 + (5/x))^(x/2) =__________ x->+infiniti

Specify a rational expression and Calculate the Headwind

. Well, here we are again with that English Channel, which appears to have repeated significance in flying firsts. Louis Bleriot, French aviator and inventor, was the first individual to successfully cross the English Channel in a motorized aircraft. On July 25, 1909, he flew his aircraft, called the Bleriot XI, a three cyli

Addition of square roots

5 outside of the square root symbol then 3 under the square root symbol plus 15 outside of the square root symbol then 3 under the square root symbol plus 12 outside the square root symbol then 3 under the square root symbol plus 32.

Algebra Study Problem

ALGEBRA STUDY PROBLEM Global Warming: If the global climate were to warm significantly as a result of the greenhouse effect or other climatic change, the Arctic ice cap would start to melt. This ice cap contains the equivalent of some 680,000 cubic miles of water More than 200 million people live on land that is less than 3 f

Example Problem: Parseval's Formula

If f(x) = (pi - |x|)^2 on [ -pi, pi], prove that f(x) = (pi^2)/3 + Sum from n= 1 to infinity of (4/n^2)(coxnx) and deduce that the Sum from n=1 to infinity of 1/n^2 = (pi^2)/6 , and the Sum from n = 1 to infinity of 1/n^4 = (pi^4)/90

parameters of quadratic expressions

For our quadratic expression y = x2 + 4 Exhibit that ordered pair which constitutes the vertex Exhibit the y intercept How many zeros does this expression have? What is the range of our quadratic expression?

Algebra Question: Boulders Dropped

All boulders and rocks (large enough not to be buffeted by air current) appear to take the same time to hit bottom. My conjecture, observes Galileo, leader of the team, is that there is a universal gravitational constant which affects all objects, large or small. Knowing, as he does, that if such a constant exists, call it g for

Range of Quadratic Expression

Exhibit the vertex and y-intercept for the quadratic expression y = x^2 - 4 . How many zeros does this expression have? Exhibit those ordered pairs which constitute these zeros. What is the range of this quadratic expression?

discriminant for the quadratic equation

What is our discriminant for the quadratic equation x2 + x + 1 = 0? Do we have a solution to our quadratic formula for the case of a negative discriminant? Note the various possibilities for the discriminant: positive and a perfect square, positive and not a perfect square. zero, and negative. What can we conclude about

The value of linear equations is stressed.

Why is it important to understand linear equations in business? In particular can you provide examples where the relationship between items that can be affected by management and 'items' that management wished to achieve or attain may be 'linear'. Can you think of items for which the relationship in NOT linear?