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Basic Algebra

Reduce answers to lowest terms.

Reduce answers to lowest terms. 4/ (a-b) + 4 /(b-a) 1/(x^2-4) - 3 / (x^2-3x-10) 2x /(x^2-9) + 3x /(x62+4x+3) (Complete problem found in attachment)

College Mathmatics (check Homework)

1. In the number 351,472, which digit tells the number of thousands? ____a. 5 ____b. 4 ____c. 3 _x__d. 1 2. Write expanded notation for 7205. ____a. 7 thousands + 2 hundreds + 5 tens __x_b. 7 thousands + 2 hundreds + 5 ones ____c. 7 thousands + 2 tens + 5 ones ____d. 2 thousands + 7 hundreds + 5 ones 3.

Simplify the exponential expressions.

#6 Assume that the variables represent non-zero real numbers. - Simplify the exponential expressions. Please see the attached file for the fully formatted problems.

Quadratic formula - error analysis

Improving the Quadratic Formula. Show that these roots can be calculated with the equivalent formulas... (See attachment for full question including Hint)

Equations and word problems

1- suppose you have 45 muffins. how many muffins are left after you give a friend 1/5 of them? 2- a baker at rod's bakery misread the directions and used 5 3/4 cups of flour in a recipe. it was 1 3/4 times too much flour. how much flour should the baker have used? 3- solve the equation. check the solution: x/3=

Word Problems, Simplify, Area, LCM, Solve for X and Hypotenuse

Divide (12a squared - 25a -7 divided by (3a-7) (x cubed - 6x squared + 7x -2 divided by (x-1) A circle has a radius of 10 inches. Find the increase in area that occurs when the radius is increased by 2 in. Round to the nearest hundredth. An object is released from the top of an building 320 ft high. The initial velocity

Equation Given Two of the Complex Conjugate Roots

The equation x^4 - 18x^3 + 121x^2 - 368x + 420=0 has complex conjugate roots (4+j2) & (4-j2). By a process of division and solving a quadratic equation, find all the roots and hence write down all the factors of : x^4

Congruences : Primes, Inverse Modulo, GCD and Wilson's theorem

Please assist me with the attached congruence problems (hint: use Wilson's Theorem) a)Prove if a,b,c Z, N and gcd (c, ) = , then ac bc(mod ) if and only if a b (mod ). b) Let a Z, N, and p > 2 be a prime. Prove that a is its own inverse modulo p if and only if a 1 (mod p ). C) Let a,b Z, N .prove that ax

Find the Vertex and Intercepts of a Function

See attached file 1. Write the polynomial in descending order and find the degree: x2 - x5 + 2x4 - 1 2. Subtract 3x -5 + 2x3 from 3x3 - 1 3. Multiply: (9x - 2) (x + 4) 4. Multiply (5x - 6y) (5x + 6y) 5. Simplify 6. Divide:

Quadratic function

Questions (also attached): Graph each equation and state its domain and range. 27) g(x)= x 2 + 2 28) f(x)= x 2 - 4 32) y= 2x 2 + 3 Graph each square root and state its domain and range. __ 34) g(x) = √ x - 1 _____ 36) f(x) = √x + 1

Modern algebra - Extension field

Please see attachment. P/S: To show subfield please show a) closed under addition, and multiplication b) additive identity and additive inverse c) closed under reciprocal

Word Problem : How much will each party pay?

The Gooch family, the McCoy family, a bachelor and a couple without children have decided to buy a summer home together. They will divide the purchase price according to the size of each family. The house costs $264,000. The smaller of the two families- the McCoys - have 2 children and will carry one third of the cost. The large

Important information about Quadratic Inequality

A person's revenue "R" (in dollars) on the sale of "X" fruitcakes is determined by the formula R = 50x - x squared. Her cost "C" in dollars for producing "X" fruitcakes is given by the formula C = 2x + 40. For what value of "X" is the person's profit positive? (Profit = revenue - cost).

Convergence of series

Please help with the following problem. This problem is from Advanced Calculus II class. It is also an introduction to real analysis. Consider the series n = 1 to infinity 1/( 1 + n^2 x) (a) For what values of x in R does the series converge absolutely? (b) On what intervals of R does it converge uniformly? (c) On wh

Finite Extension Field and Isomorphism

Argue that every finite extenstion field of R is either R itself or is isomorphic to C. Note: R is set of all real numbers C is set of all complex numbers

Economy's Lorenz Curve

Author's explanation of a Lorenz curve: Economists use a cumulative distribution called a Lorenz curve to describe the distribution of income between households in a given country. Typically, a Lorenz curve is defined on [0,1] with endpoints (0,0) and (1,1) and is continuous, increasing, and concave upward. The points on this cu

Newton-Cotes formula

Derive all the weights for closed Newton-Cotes formula. Please see attached for full question.