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Basic Algebra

Classify the Polynomials

Classify the 15 given polynomials as monomials, binomials, trinomials, and polynomials. Use the format given below for categorizing the polynomials. [Note: Simplify wherever possible] (Please see attachment for polynomials)

Laws of Exponents and Opposites of Poynomials

1. Using one of the laws of exponents, prove that any number raised to the power 0 is 1. 2. You are given the following polynomial: 2x7 - 4x3 + 3x. If x were replaced with its opposite in each of the terms of the given polynomial, will it result in the opposite of the polynomial? Explain why or why not and illustrate to supp

Sum of 2 nonnegative numbers is 20 Find the numbers

The sum of 2 nonnegative numbers is 20. Find the numbers if: a)if the product of one number and the square root of the other is to be as large as possible, and b)if one number plus the square root of the other is to be as large as possible.

Important Information about Induction proof

Show that any positive integral power of (√2 - 1) can be written in the form √N - √(N-1) , where N is a positive integer. Hint: Use mathematical induction and consider separately the odd and even powers of (√2 - 1). We need to prove the following statement. Statement : For any positive n, (&#873

Aplication of Algebraic Expressions

3. Lisa is coloring her creation. The blue color used is 50% of the green color used, yellow is 5% of the blue color used, and brown is 7% of the amount of green used. She wants to find the total amount of color used by her. a. Find the total amount of color used by Lisa using an algebraic expression. b. Comment on the kind of

Application of Algebraic Expressions

2. Mr. Pinto is a Web designer. He is trying to put 4 characters on a page. The space occupied by character 2 takes 5 units more than character 1, character 3 takes 7 units less than the character 2, and character 4 takes the same space as that taken by character 2. a. Find the total space occupied by all the characters in an a

Creating algebraic expressions

1. Three prizes are to be distributed in a Creative Design Talent Search Contest. The value of the second prize is five-sixths the value of the first prize, and the value of the third prize is fourth-fifths that of the second prize. a. Express the total value of the three prizes as an algebraic expression. b. Comment on the ki

Compound inequality, Selling Price Range, Retirement pay

Solve each compound inequality and write the solution set using interval notation. 80) 0< 5-2x <=10 -6< 4-x<0 81) -3 < (3x -1)/ 5 < ½ 1/3 < (3-2x)/6 < 9/2 86) Selling Price Range: Renee wants to sell her car through a broker who charges a commission of 10% of the selling price. The book value of the car is $14,900

Clearly identify the variables, coefficients, and constants

Translate the following into algebraic expressions. Clearly identify the variables, coefficients, and constants: a) One fourth of one half of the product of two numbers b) Two-thirds of the quotient of two numbers c) The product of 7 and twice n

Variables

Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours. Form an algebraic equation to express this and identify the variables, coefficients, and constants of the algebraic expression. You are not required to solve the equation.

Linear independence of embeddings

Let E be a finite extension of a field F. Show that any finite set of distinct embeddings of E into the algebraic closure of F is linearly independent over F.

Let G, H be graphs such that G is a subgraph of H. Prove or disprove each of the following: (a) alpha(G) <= alpha(H) (b) alpha(G) >= alpha(H) (c) omega(G) <= omega(H) (d) omega(G) >= omega(H)

The stability number, alpha(G), of a graph G is the cardinality of the largest subset S of V(G), the vertex set of G, such that no two of the vertices in S are connected by an edge of G. The clique number, omega(G), of a graph G is the cardinality of the largest subset S of V(G), the vertex set of G, such that every pair of

ODEs, IVPs

Find the general solution of the ODEs attached (about 10 different problems involving differential equations with constant coefficients) Solve the IVPs attached

Nonnegative Integers

Please see the attachment for problem related to nonnegative integer and my solution (needs to be edited and confirmed)

Proof about congruence modulo 43 (also expressible as equivalence modulo 43)

Let S = Z_43 (where the underscore, "_", indicates that what follows it, in this case 43, is a subscript). Let Q be a subset of S that contains ten non-zero numbers (i.e., that Q contains ten non-zero elements of S). Prove that Q contains four distinct numbers "a," "b," "c," "d" such that ab = cd in Z_43.

Lowest Common Multiple Application Word Problem

Five children collect N pieces of Halloween candy and decide to split it evenly among them. When they try to divide it they have two pieces of candy left over. One of the children leaves, taking the 26 pieces of candy she collected with her. The remaining four children try to split the N-26 remaining pieces of candy and discover

15 Algebra Problems : Find Equation for Line; Describe Graph and Slope

Please see the attached file for the fully formatted problems. Q1. Solve {see attachment} Q2. Solve 9 - 7+15/5 - (6-3)4 Q3. Solve {see attachment} Q4. Find the equation for the line with slope 3/5 and passing through the point (4, 2). Q5. Solve |2x-5| >= 14 Q6. A store issued coupons worth 20% off from any pu

Solve for y

Hello, Stumped on this one. Need to solve for y. 10-6xy = 4y + 8

10 Algebra Questions

1. The width of a rectangle is 8 feet less than the length. If the area is 20 square feet, find the length and the width. 2. Solve the equation: x(x - 4) = 12 3. A boat travels 30 miles upstream against the current in the same amount of time it takes to travel 42 miles downstream with the current. If the rate

Lowest Common Multiple (Prime Factorizations)

Let a and b be integers. A common multiple of a and b is an integer n for which a|n and b|n. We call an integer m the least common multiple of n provided (1) m is positive, (2) m is a common multiple of a and b, and (3) if n is any other positive common multiple of a and b, then n [greater than or equal to] m. The notation fo