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Basic Algebra

Find x value in quartic equation

To solve the quartic equation, one of the approaches is to seek squares on both sides. For example, to find x, in ax^4+bx^2+cx=d. One way is to convert the equation to the following format: (square root of a x^2+e)^2=(gx+h)^2. However, when a, e, g and b becomes irrational number, it is difficult to apply this strategy. Here, I

Asymptotic Behaviors of Various Functions

1) Determine the order of the following expressions as ??0: ?(?(1-?) ), (4?)^2 ?, 1000?^(1?2), ln?(1+?), (1-cos??)/(1+cos?? ), ?^(3?2)/(1+sin?? ), ?^(3?2)/(1-cos?? ), sech ^(-1) ?, exp?(tan?? ), ln[1+(ln?(1+2?))/(1-2?)], ln[1+(1+2?)/(?(1-2?))], ?_0^? exp?(-s^2)ds. 2) Arrange the following in descending order for ??0.

Word problem

A girl is celebrating her seventh birthday. Each guest is served one large slice of chocolate cake, a hamburger, French fries, and some oranges. Identify the food groups mentioned above. If one slice of chocolate cake contains 35g of carbohydrate, 15g of fat and 5g of protein, calculate the kilocalories that each slice

Scale factor after dilation

find the scale factor after a dilation centered at the origin if H(4*square root of 2, -3 square root of 5), P (-2 * square root of 2, 2 * square root of 5) and H(square root of 128, - square root of 180) P(- square root of 32, square root of 80)

Congruent Modulo m

Please submit solution as a PDF or MS Word file. Prove proposition 4. Proposition 4: If m?2 is a fixed integer and a,b,c?Z then: (1) a?a mod m (2) If a?b mod m then b?a mod m (3) If a?b mod m and b?c mod m, then a?c mod m Much thanks!

How to calculate net income

Company reports the following operating results for the month of August: Sales $350,000 (units 5,000); variable costs $210,000; and fixed costs $90,000. Management is considering the following independent courses of action to increase net income. 1. Increase selling price by 10% with no change in total variable costs. 2. R

Two Proofs for a Modern Algebra Class

Please help me learn how to write these two proofs correctly for my Modern Algebra class. Please submit all work as either a PDF or MS Word file. ** Please see the attached file for the complete problem description **

Samples of Basic Algebra

1. If a bag contains 15 marbles, how many samples of 2 marbles can be drawn from it? How many samples of 4 marbles can be drawn? 2. Seven workers decide to send a delegation of 2 to their supervisor to discuss their grievances. a. How many different delegations are possible? b. If it is decided that a certain employe

Concept Checks for Binomial Coefficients

1. Determine the binomial coefficient for the fifth term in the expansion of (x+y)^9 Write the binomial expansion for each expression: 1. (a-b)^7 Write the indicated term of each binomial expansion: 1. Twelfth term of (2x+y^2)^16

Slopes, Lines and Graphs

An airplane climbs from sea level to a cruising altitude of 31,500 feet at a rate of 6300 ft/min. After cruising for 20 minutes, the airplane begins its descent at a rate of 3500 ft/min. If we were to sketch a graph of the airplane's flight pattern, which measurement would the x-axis represent? Which measurement would the y-axis

Properties of Logarithms and Simplification of Expressions

Use the properties of logarithms to rewrite each expression. Simplify the result if possible. 1. log2 ((2*square root 3)/5) Given log10 (2) = 0.3010 and log10 (3) = 0.4771, find each logarithm without using a calculator. 2. log10 (20/27)

Variation Problems

Solve each variation problem: 1. If m varies jointly as z and p, and m=10 when z=2 and p=7.5, find m when z=5 and p=7. 2. Current in a circuit: The current in a simple electrical circuit varies inversely as the resistance. If the current is 50 amps when the resistance is 10 ohms, find the current if the resistance is 5

College Algebra: Polynomial Functions

For each polynomial function, find all zeros and their multiplicities: 1. f(x)=(x+1)^2(x-1)^3(x^2-10) Find a polynomial function of degree 3 with real coefficients that satisfies the given conditions: 1. Zeros of 2, -3, and 5; f(3)=6 2. Zero of 4 having multiplicity 2 and zero of 2 having multiplicity 1; f(1)= -18

Problems in Galois Theory Involving a Cubic PolynomialK

Let f be a cubic monic polynomial and char K not 3. a. Show how to make a change of variables x' = x - lamda in f (x) = 0 to reduce to a monic equation where the coefficient of x^2 is zero b. Suppose K = R. Let D be the discriminant of f. Prove that f has one real root if D < 0 and three real roots if D > or equal to 0. c. Le

Forward Rate for the Japenese Yen

Use the information below to answer the following questions. (Do not include the dollar signs ($). Round your answers to 4 decimal places, (e.g., 32.1616)) CURRENCY PER U.S. $ Japan Yen 115.76 6-months forward 112.91 Canadian Dollar

Double angular formula

Find the exact value of a) sin a/2, b) cos a/2, C) tan a/2 tan a= 4/3, a lies in quadrant 3 sin a/2 = cos a/2 = tan a/2 = (type an exact answer, using radicals as needed. simplify answer)

Applications of rational expressions

Look at the example application of rational expressions on page 315 of your textbook. Then, using the Internet, locate a Web site that has an additional example that interests you. (Use the search words "rational expressions applications.") Following the example of problems 51-54 on page 315, formulate two to three values for yo

Expected value of certainty in investments

What is expected value under certainty of the following investments, and the expected value of perfect info In a good market in a bad market Houses +10 -5 Dogs +7 -4 Cats +5 -2 Chances of bad market 60%

Half angle formulas

Use the given information to find the exact value of a) sin alpha/2 = b) cos alpha/2 = c) tan alpha/2 = when sec alpha = -17/8, alpha lies in quadrant 2 (Type an exact answer, using radicals as needed. simplify answer)

Solving and graphing Quadratic equations

Some homework practice I would like your assistance to prepare for exam. 1. Y^2-6y+9=8 ( exact solutions to three decimal places) Y=_______ 2. Solve 7x+x(x-4) = 0 the solution is x = _________ Find the x intercepts of f(x) = 7x+x(x-4) the x intercepts are _____ 3. F(x) = -1/2x^2 The vertex is _______

Factor the following expression completely.

Please explain how to solve the given problems. Factor the following expression completely. 1. 81m^3-63m^4+8m^5 Solve each quadratic equation by whatever method you choose. Round the answer to the nearest tenth, if necessary. If there is no answer, mention that clearly. 2. 56-y^2 = 0 3. 5x^2+13x-1=0 4. x^2+3x=-6

Prove the arithmetic-geometric mean inequality.

Prove the arithmetic-geometric mean inequality by using an elementary method (no use of calculus, derivative or limit), that is, (X1...Xn)^1/n <= (X1+...+Xn)/n for non-negative real numbers X1, X2, ..., Xn.

Homework problem

Solve each system of inequalities by graphing. Name the coordinates of the vertices of the polygonal convex set using a matrix. Y is greater than or equal to -.5x = 1 Y is less than or equal to -3x + 5 Y is less than or equal to 2x + 2 *Please show how you find the vertices, I am unsure how to do so by hand and do not h

Algebra problem

Problem: John and his son are hauling Christmas trees to market. The market is 420 miles from the tree farm. John's truck averages 32 MPH and leaves at 8 am. Owen's truck averages 46 MPH and leaves at 9 am. At what time will the two trucks be in the same location?

Break-even analysis: A look at profit and loss

I recently opened a specialty pizza business. I can sell my specialty pizzas for $15. The cost for making the pizzas includes a fixed cost of $55. And a labor cost of $4.00 per pizza. 1. Create an equation to determine revenue. 2. Create an equation to determine total cost. 3. How many pizzas must be sold to break even (i.e.,

M&M Restaurant Bowls

3 guys walked out a restaurant and saw a bowl of M&Ms. Guy 'A' took a third and returned 4. Guy 'B' took a quarter of what's left and returned 3. Guy 'C' took half of the rest and returned 2. How many M&Ms was in the bowl if 17 is left?

Monetary question

1. Nick is one-forth his grandfatherâ??s age. Five years ago, he was one-fifth his grandfatherâ??s age. How old are Nick and his Grandfather now? 2. Eloise bought new clothes for school. In the first store, she spent half the money she had, plus $10. In the second store, she spent half of what was left, plus $5. In th

Real - World Math Algebra: solving equations and problems

In general, the area of a rectangular shape is found by multiplying the length of the area by the width of the area. This can be represented by the formula area = length x width or A = L x W. If you were to measure the length and width in feet, then the result of this equation will be in square feet (ft^2). The resulting number

Nearest tenth the median of these attendance numbers

The table below gives the total spectator attendance for various U.S. sports in 1997. Sport Attendance (millions) Pro Baseball 64.9 College Basketball (Menâ??s) 27.7 College Basketball (Womenâ??s) 6.7 Pro Basketball (Menâ??s) 21.7 College Football 36.9 Pro Football 14.