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Basic Algebra

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

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

Factoring Quadratic Equations

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

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

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 Radicals

Rewrite each expression with a rational denomination ^4root 2/^4root 27 radical expression in simplified form root 1/2 root 3/8

Simplifying 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

Simplifying Radicals

^3 root of 1/a^2 evaluate expression below 27^-4/3 use the rules of exponents to simplify each eXpression 3^1/3 3^-1/3

Nilradicals and Prime Ideals

Assume R is commutative ring. Prove that the following are equivalent: a) R has exactly 1 prime ideal b) Every element of R is either nilpotent or a unit. c) R/N(R) is a field Here N(R) denotes the nilradical of R. The set of nilpotent elements form an ideal called the nilradical of R

Revenues Using Logarithms

Equation - R=12log10Days In 10 days revenue = $12 million how long will it take to reach $36m Answer is 1,000 days but I cannot figure out how this happened. I tried 36=12log10days 36/12 = log10days 3 = log10days 3 = days Incorrect

Coefficients of Quadratic Equations

Quadratic Equations Write three quadratic equations, with a, b, and c (coefficients of x2, x, and the constant) as: 1. Integers 2. Rational numbers 3. Irrational numbers See attached file for full problem description.

Solving Equations

(m-7)^2 = 25 (w+4)^2=16 √x^2 + 3x +6 =4 √x - √x-1 = 1 1+ √x+7 = √2x + 7

Simplifying Radicals

Simplify each radical expression. Assume all variables represent positive real numbers. Here are six problems. √48 √20n^25 4√32m^11 Find the domain of each radical expression. Use interval notation 4√-5x-1 Simplify the expressions involving rational exponents. Assume all variables re

Tangent Lines and Logarithmic / Exponential Functions

Tangent Line and Logarithmic/Exponential Functions This project is going to consider the relationship between a point (a, b) on the natural logarithmic and exponential functions and its relationship to the intercept of the tangent line to the respective functions at the point (a, b). Hint: Recall the distance between two

Fermat and Wilson's Theorem

1. If and are distinct primes prove that for any integer a, Use Fermat's theorem 2. Show that if and are both primes, then 4[ (mod Use Wilson's theorem. 3. Let be an odd prime. Prove that if g is primitive root modulo and (mod is not Use the binomial expansion See attached file for full