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Basic Algebra

Normal subgroups and product of two right cosets

Modern Algebra Group Theory (XXXV) Cosets of Subgroups of a Group Normal Subgroups of a Group A subgroup N of G is a normal subgroup of G if and only if the product of two right cosets of N in G is again a right coset of N in G.

The Order of an Element of a group

Modern Algebra Group Theory (XXXIII) Subgroups of a Group The Order of an Element of a group If in the group G, a^5 = e, aba^(-1) = b^2 for a,b belongs to

College Algebra: Writing Equations from Word Problems

Please help with the following attached questions: 2,8,12,20 2. If 40L of an acid solution is 75% acid, how much pure acid is there in the mixture? 8. Unknown Numbers: Consider the following problem. The difference between six times a number and 9 is equal to five times the sum of the number and 2. Find the number.

Logarithm Problems : Change of Base, Graphing and Solving for X

Find the exact values: 1) log (base 10) 1000 2) ln e^-100 3) log (base 5) (1/25) 4) log (base10) (0.1) 5) log (base 12) 3 + log (base 12) 48 6) 2^(log(base 2) 3 + log(base 2) 5) 7) e^(ln 15) 8) e^(3ln2) 9) log(base 8)320 - log(base8)5 -------------------------------------------------------------------------------

Quadratic Equation Applications

1) Using the quadratic equation x2 - 4x - 5 = 0, perform the following tasks: a) Solve by factoring. b) Solve by completing the square. c) 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 line of s

Problem Set

(See attached file for full problem description) --- ? Identify the document by typing your full name and section number next to the yellow text. ? Rename the file by adding your last name to current file name (e.g., "u1ip_lastname.doc"). ? Type your answers next to the yellow text. ? To show your work, you will need t

Quadratic functions

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. How can I create three unique equations where the discriminant is positive, zero, or negative, and for each case, explain what this value means to the graph of

Putting a function in a form y=

Y = x^2 - 4x - 5 = x^2 - 2*2*x - 5 = ( x^2 - 2*2*x +2^2 ) - 2^2 - 5 = (x-2)^2 - 2^2 - 5 = (x-2)^2 - 4 - 5 = (x-2)^2 -9 y = (x-2)^2 -9 How do I put this in the form y=a(x-H)^2+K, how do I graph this function, and why is it not necessary to plot points to graph when using y=a(x-h)^2+K?

Algebra word problem

If John has 300 feet of lumber to frame a rectangular patio (the perimeter of a rectangle is 2 times length plus 2 times width). He wants to maximize the area of his patio (area of a rectangle is length times width). What should the dimensions of the patio be? How do I set up this equation?

Quadratic equation

Using the Quadratic equation: x2 - 4x - 5 = 0. How do I solve this by factoring? by completing the square? & solve by Quadratic formula?

Problem 12

Select the point which is in the feasible region of the system of inequalities: 4x + y < 8 2x + 5y < 18 x > 0, y > 0 A. (2,4) B. (-1,2) C. (1,3) D. (4,1)

Speed and Distance

Leon drove 270 miles to the lodge in the same time as Pat drove 330 miles to the lodge. If Pat drove 10 miles per hour faster than Leon, then how fast did each of them drive?

Distance and Speed

Janet drove 120 miles at x mph before 6:00 a.m. After 6:00 a.m., she increased her speed by 5 mph and drove 195 additional miles. Write a rational expression for her total traveling time. Evaluate the expression for x = 60.

Prove that if A is a set of positive, finite Lebesgue measure

A point x of a measurable subset A of the reals is called a density point if m( A intersection [x-h, x+h] ) / 2h goes to 1 as h goes to 0 where m is the Lebesgue measure. Prove that if A is a set of positive, finite Lebesgue measure, then almost every point of A is a density point. I would like to note that I can use

Context-fee language

Thank you for taking the time to look at my problem. I cannot make math symbols, thus, I will let ^ denote "raised to the power." For example, a^2 is a squared or a "raised to the power" of 2. Also, I will use the symbol * to denote multiplication. For example, 2*7=14. Okay, here is my problem: Show that the language L={ a

Algebraic Structures, Inverses, Finite Group, Identity

5. Let (A, *) be an algebraic structure, and suppose that A is associative, has an identity, e, and that a &#1028; A has an inverse. Show that if ax = ay, then x = y. 8. Let G be a finite group with identity e, and let . Show that there is an n &#1028; N with a^n = e (Hint: Consider the set {e, a, a2 , ..., am }, where m