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Basic Algebra

Simplifying Expressions

Do the addition: 7a^3 + 8a^2 + 3 + -2a^3 + 9a - 6 4a^3 - 3a^2 + 3a + 6 ___________________________


Multiply: (x2 + 5x - 4)(x2 - x + 2)


Use FOIL to multiply: (3x - 4)(3x - 5)

Simplifying Expressions

Simplify the expression. Assume a and b are positive real numbers and m and n are rational numbers. See attached file for full problem description.


Factor out the GCF in the expression -6h^5 t^2 +3h^3 t^6


Find the GCF 45m^2n^5, 56a^4b^8

Logarithms explained in this solution

10 Problems Please see the attached file for the fully formatted problems. 1. Find the value of x: . Choose the correct answer from the following: 2. Evaluate the expression . 3. Write the equation in logarithmic form. 4. Evaluate the expression log 2 1. 5. Fill in the blank to make a true statement.

20 algebra problems involving square roots

See attached file for full problem description. 1. for g(x) = sqrt(x^2 - 20), find g(5) 2. find the domain of f(x) = sqrt(x) + 6 3. the cost of making clocks is c = 121sqrt(n + 36). what is c when no clocks are made? 4. find the following: sqrt((14y)^2) 5. simplify: y^(4/3)/y^(5/6) 6. graph: f(x) = -sqrt(2 - x)

Abstract Algebra

Determine the degree of the extension. See attached file for full problem description.

Completing the square

1.Solve by completing the square: x2 + 4x + 2 = 0 2. Solve using the square root property: (x + 3)2 = 36 3.Solve by factoring: x2 - 9x = -8

Quadratic Equations

1. 8x^2 - 24x = 9 2. choose from the following a quadratic with solutions of 9 and 3 a. x^2 - 10x + 27 = 0 b. x^2 - 12x + 27 = 0 c. x^2 - 14x + 25 = 0 d. x^2 - 12x + 29 = 0 3. The height h (in feet) of and object is dropped from the height of s fe

Quadratic Formula and Vertex Form

Using the quadratic equation x2 - 4x - 5 = 0, perform the following assignment; Solve by factoring and solve by using the quadratic formula 2) For the function y = x2 - 4x - 5, Put the function in the form y = a(x - h)2 + k.

Logarithmic and Exponential Functions

I need clear solutions to problems d,e, and f on the attached PDF. I also need help with this problem: The number of e-coli present in a given culture after t hours is given by the formula: N=1000e^(.69t) The doubling time is five hours a. What is the continuous growth rate? b. What is the annual growth rate?

Four questions about systems of inequalities

18. match the system of inequalities to a region in the picture x + 2y <= 8 3x - 2y <= 0 22. solve the system of linear inequalities graphically 3x + 4y <= 12 y >= -3 32. solve the system of linear inequalities graphically, find the coordinates of each corner points, and indicate whether the solution region is bo

Exponential Breakdown

Exponential Model on Growth of Internet Networks 1989- 1996 Internet Network: A global network connecting millions of computers. More than 100 countries are linked into exchanges of data, news and opinions. The Internet is revolutionizing and enhancing the way we as humans communicate, both locally and around the globe. Si

Systems of Equations Word Problems

1. You are hiking along the California coast and wonder about the height of a particular Giant Redwood tree. You are 5 feet and nine inches tall and your shadow is 5 feet long. The shadow of the tree is 195 feet long. How tall is the tree? 2. The next two problems are examples of "simple Hindu Algebra", quoted on page 528 of

Factoring Equations and Simplifying Expressions

1. Factor. 8m4n - 16mn4 A) 8m4n(1 - 16mn4) B) 8m4n(1 - 2n3) C) 8m4n4(m - 2n) D) 8mn(m3 - 2n3) 2. Factor completely. b2 - ab - 6a2 A) (b - 3a)(b + 2a) B) (b + 3a)(b - 2a) C) (b - 6a)(b + a) D) (b + 6a)(b - a) 3. Factor completely. 3(x - 2)2 - 3(x - 2) - 6 A) 3(x - 4)(x - 1) B) 3(x - 4)(x + 1) C) 3(x

Fields and Ideals

Let F be a field and f(x), g(x) be elements of F[x]. Show that f(x) divides g(x) if and only if g(x) is an element of < f(x) >. Note that < f(x) > is an ideal. Below is a problem from an undergraduate course in Abstract Algebra. The book we use is titled "A First Course in Abstract Algebra" by John B. Fraleigh. We have

Writing Equations from Word Problems

Translate to an algebra statement; do not solve: Nine times the difference of a number and twelve yields the same result as triple the same number increased by seven.

Factoring Polynomials

12 Problems. Please see the attached file for the fully formatted problems. Section 4.1 Find the greatest common factor for each of the following sets of terms. Exercise 14 , , Exercise 42 Factor each of the following polynomials. Exercise 60 Find the GCF of each product. Exercise 62 T