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Basic Algebra

Solving Quadratics by Factoring and Graphing

Solve the quadratic equations in questions 1 - 5 by factoring. 1. x2 - 49 = 0 2. 3x3 - 12x = 0 3. 12x2 + 14x + 12 = 18 4. -x3 + 22x2 - 121x = 0 5. x2 - 4x = 5 In questions 6 - 10, solve the quadratic equation by graphing. 11. Write a quadratic equation that will have solutions of x = 3 and x = -7. 12. Write a quadr

Derivatives : Maximum Profit

The total profit (in dollars) for sales of x rowing machines is given by P(x) = -0.2x^2 + 300x - 200. What is the profit if 500 are sold? For what value of x will the profit be at a maximum?

Solving Inequalities

For problems #5 and #6, solve each inequality without graphing 5. x^2 + 3x < 18 6. 2/(a - 2) < 3/(a + 1)

Economics - Exponential and Logarithmic Functions : Rule of 70

The rule-of-70 provides a simple way to calculate the approximate number of years it takes for the level of a variable growing at a constant rate to double. The rule states that if the constant growth rate is r, the variable will double after approximately n years when n = 70/ r. a) Explain how this rule can be derived. b)

Algebra: Solving equations, graphing, inequalities, word problems.

15. A mathematics instructor asked her students to keep track of how much time each spent studying the chapter on percent notation in her basic mathematics course. She collected the information, together with test scores from that chapter's test, in the table below. a). Use the two points reporting data for 9 hours of study

Volume, Interest and Logarithm Questions

1) An open-top box is to be constructed from a 4 foot by 6 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a) Find the function V that represents the volume of the box in terms of x. b) Graph this function

Math Puzzle

Math Puzzle. See attached file for full problem description. 3 - 4(2 - 1)=? For y = -2x - 6 slope = ? y-intercept = ? Solve this system of equations: x + y=5 and 3x - 5y= -9 X=? Y = ? For x/3 - y/6 = 5, what is the Lowest Common Multiple, that is, what do you multiply all terms by to eliminate the denominators?

Factoring Polynomials

9x4 + 4x3 - 27x2 + 12x <------ Factor by finding the GCF x2 + 2x - 15 <--------Factor by grouping For these problems, identify which of the methods from this lesson (GCF, grouping, difference of squares, or perfect squares) could be used to factor the polynomial. 17. x2 + 2x + 1 A This polynomial could b

Synthetic Division

A geologist you spoke with is concerned about the rate of land erosion around the base of a dam. Another geologist is studying the magma activity within the earth in an area of New Zealand known for its volcanic activity. One of the shortcuts they apply when doing calculations in the field is to use synthetic division. After the

Coding Theory : Cyclic Codes

4 (i) Let C be a linear code in IF. Explain what is meant when we say that C is cyclic. Give also the algebraic characterisation of cyclic codes using the ring .... (ii) Explain why the cyclic codes in R are in 1-1 correspondence with the monic polynomials in IFq[xJ that divide ? 1. Give the definition of the generator polynom

Solving Equations

Solving rational exponents a) &#8730; x-2= 1 b) &#8730; x^3 =27 c) 3&#8730;x^2 = 3

Finding Real and Complex Roots of a 6th Degree Polynomial

The 7th degree polynomial x^7 - 3x^6 - 7x^4 + 21x^3 - 8x + 24 has a factor (x - 3) (a) Divide x^7 - 3x^6 - 7x^4 + 21x^3 - 8x + 24 by x - 3 and thus: (b) Express it in the form (x - 3)(ax^6 + bx^3 + c) (c) By putting Z = x^3, find all the factors, real or complex of the 6th degree polynomial and thus: (d) Expres

Constrained Minimization using Lagrange Multipliers

Please see attached PDF file; I'm trying to derive a couple of results involving Lagrange multipliers and a linear algebra equivalence. This makes use of the extension to Lagrange multipliers whereby the constraint is an inequality (see, e.g., section 5.1 of ).

Algebra : Estimation, Word Problems and Optimization

1. Use inductive reasoning to determine the next three numbers in the pattern: 2, 9, 20, 35... 2. Make a conjecture about the relationship between the original number and the final number in the following process. Pick a number Multiply the number by 12 Add 12 to the product Divide the sum by 4 Subtract