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# Basic Algebra

### Factor the polynomial f(x) = 2x^3 - 5x^2 - 4x + 3

I am trying to factor the polynomial f(x) = 2x^3 - 5x^2 - 4x + 3. I think it is (x-3)(x+1)(x- 1/2). Am I right? (See work below.) Once I factor f(x), how do I use that to find the answers to the following questions? a) f(x) = 0 b) f(x+2) = 0 c) f(2x) = 0 This is the work that I used to factor f(x):

### Irreducible Polynomials

I need to find the irreducible polynomial in Z3[x]. A) how many irreducible polynomial of degree 2 in Z3[x] B) how many irreducible polynomial of degree 3 in Z3[x]

### Example on the quadratic formula or completing the square

Give an example using either completing the square or the quadratic formula and explain each step as if you were teaching someone who had never used the method before.

### Sequence and Series: Using the index of a series as the domain and the value of the series as the range, is a series a function?

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of the basic functions (linear, quadratic, rat

### Quadratic Functions and Parabolas : Maximum Height and Maximum Area

(1) Suppose a baseball is shot up from the ground straight up with an initial velocity of 32 feet per second. A function can be created by expressing distance above the ground, s, as a function of time, t. This function is s = -16t2 + v0t + s0 ?16 represents ½g, the gravitational pull due to gravity (measured in feet per seco

Radical and rational exponent notation are two ways to show the same process. Explain the similarities between radicals and rational exponent notation. Provide at least two other examples of mathematical notation or wording denoting the same process.

### Proof by Induction : Step-by-step

Let p(n) be the statement that: 1^3 + 2^3 + ... + n^3 = (n (n + 1) /2)^2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive

### Exponential and Logarithmic Functions

1. Sketch the graphs of y=5x and y=-5x+2-1 on the same set of axes. Identify the following properties of each graph: a) the domains b) the ranges c) any asymptotes d) the y-intercepts 2. The population of the U.S. doubles approximately every 100 years. In 1980 the population of the U.S. was 200 million. Find the projec

### Polynomials : Zeros and Complex Roots

Find the polynomial f(x) of degree three that has zeroes at 1, 2, and 4 such that f(0) = -16. a. f (x) = x3 &#8722; 7x2 +14x &#8722;16 b . f (x) = 2x3 &#8722;14x 2 + 28x &#8722;16 c . f (x) = 2x3 &#8722;14x 2 +14x &#8722;16 d . f (x) = 2x3 + 7x2 +14x +16 Find the third degree polynomial whose graph is shown in the figure

### Algebra Exercises Evaluated

Algebra Exercises. See attached file for full problem description. 1. Evaluate , if possible. 2. Determine whether is rational or irrational. A) Rational B) Irrational 3. Simplify. A) 54 B) C) D) 4. Simplify. Assume all variables represents positive numbers. A) B) C) D)

### Distance traveled between Chicago and St. Louis

It is approximately 300 miles from Chicago, Illinois, to St. Louis, Missouri. allowing for various traffic conditions, a driver can average approximately 60 miles per hour. a) How far have you traveled after 3 hours? b) How far have you traveled after 4 hours? c) How far have you traveled after 1 hour? ie. write a line

### Math Puzzle: Addends and Sums

Fay Ling is not going to pass her second semester math class unless she can supply the missing addends and sums in the following grid. Please help her by filling in the missing information (please see attached).

### Arithmetic and Geometric Sequences

Using the index of a sequence as the domain and the value of the sequence as the range, is a sequence a function? Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic sequence? Which one of the basic functions (linear, quadratic, rational, or exponential) is related

### Synthetic Division and Logarithm and Exponential Functions

A geologist you spoke with is concerned about the rate of land erosion around the base of a dam. Another geologist is studying the magna 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. Use s

### Algebra Questions: Please solve these equations related to arithmetic sequence and geometric sequence

1) Use the arithmetic sequence of numbers 1, 3, 5, 7, 9,...to find the following: a) What is d, the difference between any 2 terms? Answer: Show work in this space. b) Using the formula for the nth term of an arithmetic sequence, what is 101st term? Answer: Show work in this space. c) Using the formula for the su

Solve: 1. (4s + 9)^2 = 36 2. f(x) = x^2 + 18x 3. z^2 + 18z + 64 = 0 5. 7n^2 = 10n - 2 6. 5r^2 + 20r = -18 7. -7x^2 - 5x = 9 8. f(x) = 3x^2 - 5x - 1 Find the vertex: 13. f(x) = (x + 6)^2 - 2 Graph: 12. f(x) = -4(x + 7)^2 + 4 15. f(x) = -x^2 + 2x - 7 Find the x and y intercepts: 16. f(x) = 2x^2 + 6x + 1 S

### Algebra Word Problems: Relative Speed

Kim starts to walk 3 mi to school at 7:30 a.m. with a temperature of 0 degrees F. Her brother Bryan starts at 7:45 a.m. on his bicycle, traveling 10 mph faster than Kim. They they get to school at the same time, then how fast is each one traveling?

### Finding LCD

Find the LCD for the following rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator. -3/2p^2 +7p-15 , p/2p^2 -11p+12 , 3/p^2 +p-20

### GCF

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.

### Quadratic Equations Word Problems : Maximizing Area

Amanda has 300 feet of lumber to frame a rectangular patio. She wants to maximize the area of her patio. What should the dimensions of the patio be, and show how the maximum area of the patio is calculated from the algebraic equation by using the vertex form to find the maximum. Show the work when computing this equation.

1. Solve using the quadratic equation : 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

2) For the function y = x2 - 4x - 5, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. Answer: Show work in this space b) What is the equation for the line of symmetry for the graph of this function? Answer: c) Graph the function using the equation in part a. Explain w

Please see the attached file. (Questions 1, 2) Solve the absolute value inequality: |4x - 4| >= 1 |r - 4.6| < 9 (Question 3) Multiply and simplify: 6y x 4y + 2 12y + 6 5 (Question 4) Find the domain: f(x) = (x2 + 8x)/(x - 8) (Question 5) Find the LCM: 63x, 9x2, yx3 (Question 6) Simplify:

### 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

### Algebra Word Problems

3. You buy a new piece of equipment for \$11,778 and you receive a cash inflow of 2,000 per year for 10years. What is the internal rate of return? 4. The firm is in a 30% tax bracket and has a 14% cost of capital. Should Propulsion Labs purchase the equipment? Use the net present value method. 5. Propulsion Labs will acquir

### Motivation Concepts Analysis

Explain the theory below. Facial feedback hypothesis by Laird (1974) - Describe how this theory would AND would not be applicable if applied to one workplace situations. In the instance in which the selected theory of motivation was not applicable to your workplace experience, assess the need to develop and create n

### 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

### Simplifying Expressions and Radical Equations - MTH209

Please help me with Pg.390#64 and Pg.594 #40 See attached file for full problem description. MTH 209 Week 3

### 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