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Basic Algebra

Rational Expressions

1 For the rational expression S = ( an+1 - 1 ) / ( a - 1), the value of S for a = 2 and n = 5 is: A) 31 B) 127 C) 63 D) 15 E) None of the above. 2 For the rational expression in question 1 above, the value of S for a = 1 and n = 2 is: A) 1 B) 2 C) 3 D) undefined, since the denominator of S is zero fo


Basic Concept of groups in Algebra with example.

Inequalities, domain and Intersections of Lines

#1 The largest possible domain of the function f(x) = sqrt{[x-1]/[x+2]} is the set (A) all x except x=-2 (B) x < -2 or x greater or = 1 (C) none of the above. #2 The solution of the inequality (x-3)(x^2-3x+2) > 0 is (A) 1 < x < 2 and x > 3 (B) x > 3 (C) none of the above. #3 In the triangle whose sides are 3 , 4 , and

Transcendence basis

Suppose that L has transcendence degree n over K and that L is algebraic over K(&#945;1, . . . , &#945;n). Show that &#945;1, . . . , &#945;n is a transcendence basis for L over K. Might help: Theorem - Definition: Let L be an extension of K, A a subset of L. The following are equivalent: (1) A is a maximal algebraically

Prime Factorization and Greatest Common Factor ( GCF )

The table below contains ten questions. Please read through the set of possible answers and determine the best answer to each question. In the yellow answer column of the quiz, type the letter (A, B, C, D, or E) that corresponds to the answer you've chosen. Each question has only one answer. Place only one letter into each ans


Two Cyclists Yan and Clancy are in a race. Yan is better on shorter courses and Clancy is better on longer courses. Yan's average speed is given by 30 ?x/10 mph and Clancy's average speed is given by 28 ?x/20 mph, where x is the distance of the race in miles and 0<x less than or equal to 200. What distances could the race be for

Inequalities : When do you flip the inequality sign?

1.The inequality sign changes when both sides are multiplied by a negative number. This happens because it needs to read true. If you do not flip the sign it will not be a true inequality. However, if you multiply by a positive number you do not need to change the inequality sign. You do not change the sign in regular equations.

Finding the Value for a Function

The average (mean) cost for a service club to publish a directory of its members is given by the rational function f(x)=1.95x+900/x Where x is the number of directories printed. Find the average cost per directories printed. Find the average cost per directory for x=4000.

Algebra Operations with Polynomials

1. For each polynomial listed below, determine i the degree of the polynomial ii the coefficient of the leading term iii the constant term a. P(x) = x + 1 b. Q(x) = 3x + 2 c. R(x) = x2 + 2x + 1 d. W(x) = 4x2 + x + 3 e. Z(x) = 3x3 + 2x2 + x

There are 12 golf balls ...

There are 12 golf balls...all the same size. Eleven of the golf balls are the same weight. One of the golf balls weighs a little less OR a little more than those eleven. Using the scale no more than three times, how can you find the one that weighs a little less OR a little more than the other eleven?

The tallest structure in the ...

The tallest structure in the United States is the Blanchard TV tower in North Dakota. Find the height of the tower if the angle of elevation of its top from a point on the ground 400.2 ft from its base is 79.02 degrees.

The equation ax^2+bxy+cy^2+dx+ey+f=0, where ...

The equation ax^2+bxy+cy^2+dx+ey+f=0, where a, b, and c are not all zero, defines a conic section. Find the unique conic section through the points (-1,1), (3,2), (4,1/2), (1,0), and (-2,2).

A property management company manages 200 apartments renting for ...

A property management company manages 200 apartments renting for $800.00 each with all the apartments rented. For each $10.00 pre month increase in rent there will be 2 vacancies with no possibility of filling them. what rent per apartment will maximize the total monthly revenue?

A couple of I think quick questions . . .

Hi! I'm using old tests to study for an abstract algebra exam and of course the old exams do not come with solutions. This means that I need help. I tend to struggle with proofs because I forget some steps or I am not as rigorous as I should be. Thus I need to see actual complete rigorous proofs so that I can make sure that I re

Formulas, equations, substituion methods, inequalities

Please see attachment. I've been working on this for the last few days. Some of the problems I understand and some I do not. 1. Perform the indicated operation: 2 &#61485;&#61480;&#61485;3&#61472;&#61481; 3 5 2. Use order of operations to simplify: 25 - 3(22 + 1) = 3. Simplify:

Algebra: equations and inequalities

1. Evaluate: 7 -|(-3)(2) - 2| 2. Simplify: 7x - (4 - 2x) 3. Ross jogs at a rate of one mile every 0.25 hours. At what rate is he jogging in miles per hour? 4. Solve for x: 5(2x-3) =x+3 5. Solve for x: (1/2) x - 1/3 = (1/4) x+ 1/6 6. Solve for x: 2x- 3 = ax 7. Solve: |3x-9|=3 8. Solve the in