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Basic Algebra

Mathematics - Algebra - Discriminants

Determine if the following equation has a solution or not? Justify your answer. √2x^2 - 4x - 7√2 = 0 I figured that you have to multiply both sides by 1/2 to cancel the square roots. The equation then becomes x^2 - 2x - 7 = 0.

Percents and fractions

10. A hamburger costs $1.35 and the price continues to rise at a rate of 11% a year for the next 6 yr. What will the price of a hamburger be at the end of 6 yr? 17. The New Age Savings Bank advertises 4% interest rates compounded daily, while the Pay More Bank pays 5.2% interest compounded annually Which bank offers a bett

Proofs, Diophantine equations, and sequences

See attached 1- Prove by induction, the following result for all n 1- Prove by induction, the following result for all n 2- Prove that , if x2 3- Use induction to prove that (This can be used to show that the infinite har

College algebra study guide

MTH133 Unit 5 Individual Project - A Name: 1) Find the domain of the following: a) Answer: Explain how you obtained your answer here: b) Answer: Show your work or explain how you obtained your answer here: c) Answer: Explain how you obtained your answer here: d) Answer: S

College algebra study guide

MTH133 Unit 4 - Individual Project - A Name: 1) State the domain of the following and provide a brief explanation for your answer: a) Answer: b) Answer: c) Answer: d) Answer: e) Answer: 2) Suppose the graph of is shifted to obtain each the following graphs. What is the equation o

Induction and real numbers

A.prove by induction that (1^3+2^3+...+n^3)= [(1/2)n(n+1)]^2 for all n elements of N b.give an example of two functions f,g on Reals to Reals such that f does not equal g but such that f o g = g o f. c. show that if a,b elements of Real numbers then i. max{a,b} = 1/2(a + b + abs(a-b)) and min{a,b}= 1/2(a+b-abs(a-b))

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

Inequality Sign Change Variables

The inequality signs change because the variable changes from a positive to a negative, or vice versa when multiplied or divided by a negative number. The same type of thing happens to equations when the variable is multiplied or divided by a negative number because of the same situation...what was a positive number becomes a ne

Solving an Inequality and Systems of Inequalities

1. Put the linear inequality into standard form. -2x < 4 2. Determine whether or not the given point satisfies the given inequality. -2x + y > 9, (3, 15) 3. Determine whether the given point (16, 0) is in the feasible set of this system of inequalities. 6x + 3y < 96 x + y < 18 2x + 6y

Interest bearing note

On April 1, Nolton Company borrows $80,000 from West Bank by signing a 6-month, 6% interest bearing note. Instructions Prepare the necessary entries below associated with the note payable on the books of Nolton Company. (a) Prepare the necessary entry on April 1 when the note was issued. (b) Prepare any adjusting entries n

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 proof

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

Algebraic closure

Show that the algebraic closure of Q (rational numbers) in C (complex numbers) (and hence any algebraic closure of Q, once we have the uniqueness statement) is countable.

Inequalities and Change of Direction of Inequality Sign

Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Write an inequality for your classmates to solve. In your inequality, use both the multiplication and addition properties of inequalities.?

Population Growth

Pick a country of your choice that is experiencing population growth. Using the Library, web resources, and/or other materials to find the most recent population count of the country you have chosen and the population growth rate of that country. Use that growth rate to approximate the population in the year 2012. Solve the prob

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

Find the pH of a substance

Part 1: Using the Library, web resources, and/or other materials, find the logarithmic formula that gives the pH of a substance. State what each variable in your equation represents. Find the pH of a substance of your choice that is alkaline (basic). Using this pH, show how to find the hydrogen ion concentration, [H+], of the

Parabolas, Graphing, Translation and Asymptotes...

1) State the domain of the following and provide a brief explanation for your answer: a) Answer: b) Answer: c) Answer: d) Answer: e) Answer: 2) Suppose the graph of is shifted to obtain each the following graphs. What is the equation of the function, g(x), for each graph? Write your answe

Shortest Path Assessment

Please see attached for details. You can use either A* or Floyd-Warshall algorithm to accomplish this. One way that I think might work is to divide the path into 3 sections. Finding the shortest path from node 16 to 3 then from 3 to 11 and then from 11 to 16. We also need to find the shortest path from 16 to 11 then from 11 to 3

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.

An oil drum has a diameter of 0.85m and a length of 1.5m. ...

An oil drum has a diameter of 0.85m and a length of 1.5m. A) What volume of oil can be contained in the drum? B) What is the area of sheet metal used in the drum if it has an open top? ii) The shape of the cross-sectional area of an extrusion is a sector of a circle subtending an angle of 50 degrees. The circle radius is 25mm. W

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

Algebra: Applications of Inequalities

1. Solve using the addition and multiplication principles. 2.4+17.8> 44.5 - 6.5x The solution set{x|x> }. 2. Translate to an inequality. A number is at least 13 The is _ _ _ (use x as the variable.) 3. Translate to an inequality. Use the variable x. The number of people in the chess club is less t

The concentration of a certain drug in a patients body

The concentration(in milligrams per cubic centimeter) of a certain drug in a patients body t hours after injection is given by C(t)= t^2/3t^3+1, 0 greater than t or greater than 5.(0<T) When is the concentration of the drug increasing and when is it decreasing?