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    Basic Algebra

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    Algebra Word Problems

    Tom took 16 hours to drive the 1,000 highway miles from Chicago to Boston. He drove the first eight hours at constant speed, and then had to lower his speed considerably by 25 miles per hour for the remainder of his journey to Boston on account of construction. However, he maintained this constant lower speed for another 8 hours

    Twenty questions on algebra

    Identify the letter of the choice that best completes the statement or answers the question. ____ 1. Round off 345.0149 to three decimal places. a. 345.015 b. 345.01 c. 345 d. None of the above For questions 2 through 5 use the following values of X: 1, 7, 0, 8 and -6 ____ 2. ∑Χ a. 28 b. 10 c. 22 d

    Nilpotents and Zero Divisors

    Let x be a nilpotent element of the commutative ring R i.e. x^m for some positive integer m a) Prove that x is either zero or a zero divisor b)Prove that rx is nilpotent for all r in R c)Prove that 1+x is a unit in R d)Deduce that the sum of a nilpotent element and a unit is a unit

    Simplifying Expressions (15 Problems)

    59. x^2 - 3x - 10 * x -2/x^2 - 4x +4 * x - 5 63. 4a^2 * 3a - 6/3a^2 - 12a + 12 * 2a 31. c^2 + 3c / c^2 + 2c - 3 divided by c /c + 1 33. 2y^2 - 7y + 3/ 2y^2 + 3y - 2 divided by 6y^2 - 5y + 1/3y^2 + 5y - 2 35. x^2 - 1 / 4x + 4 divided by 2x^2 - 4x + 2/ 8x + 8 15. x + y/xy^2 plus 3x + y/x^2y 28. 9x/6x - 30 plus 3x

    Using formula to solve algebra

    1) Use the arithmetic sequence of numbers 2, 4, 6, 8, 10... to find the following: a) What is d, the difference between any 2 terms? b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? c) Using the formula for the sum of an arithmetic series, what is the sum of the first 20 terms? d)

    Parallel RC Circuit Problem (Transfer Function)

    See attached file for full problem description. a. Derive the expression for the transfer function of the circuit above. Simplify the expression as far as possible but do not attempt to rationalize it. Refer to the two reactances as Xc1 & Xc2. b. Using the transfer function obtained in part (a) above, derive an expression

    Solving systems of equations by substitution and addition

    -3/x+2 * 5x+10/9 ax+am+3x+3m/a^2-9 / 2x+2m/a-3 solve and write the answer in the lowest term: 5a^2b/12a * 2a^3b/15ab^6 solve the equation x/x-1-3/x=1/2 solve for y: 2(b+y)=b solve by substitution y=3x+11 2x+3y=0 x+2y=1 8x+6y=4 solve by addition -3x+y=3 2x-3y=5 solve by addition:

    Factoring Quadratic Equations Discriminants

    For each given pair of numbers find the quadraticequation with integral coefficients that has the numbers as its solutions. root5,-root5 use the discriminant to determine whether each quadric polynomial can be factored, then factor the ones that are not prime 8x^2-18x-45 6x^2+9x-16 (3a+2)^2-3(3a+2)=10 find all r

    Factoring Equations Root Properties

    A^2- 6a +9=0 Use the even -root property to solve each question x^2= 9/4 (x-3)^2=16 (w-3/2)^2=7/4 (w+2/3)^2=5/9 Find the perfect square trinomial whose first two terms are given. w^2-5w p^2+6/5p factor each perfect square trinomial. y^2-5y+25/4 t^2+3/5t+9/100 solve by complteing the square

    Solving Equations Provided

    3(x-2)+5=7-4(x+3) w/3 +w-4/2=11/2 (X+7)^2=25 0.006x-0.04(x-20)=2.8 3root2+4/root2= xroot18/3root2+2 1/x-1/x-1=1/6

    Simplifying Root Radicals

    Root of 8+ root of 28 root 12x^5-root18x- root 300x^5+ root 98x ^3 root of 54t^4y^3- ^3 root 16t ^4y^3 simplify the the product gives exact answers. (root3+2) (root3-5)

    Simplifying Expressions : Rules of Exponents

    (3^-6)^1/3 simplify each expression assume the variables represent any real #s and use absolute value as necessary (y^3)^1/3 Simplify assume all variables represent positive #s write answer with positive exponents only w^1/3 / w^3 Simplify each expression right your answer with positive exponents assume that all