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# Basic Algebra

### 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

### 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

### Creating a Function Command in SQL

I need a simple SQL program demonstrating the use of CREATE FUNCTION command in SQL. A create table can be used to generate a simple record of items such as name, title, age. The Create Function command will be used to retrieve one specific value. The program should demonstrate and show how you can pass a variable in and outp

### Simplifying and Solving Polynomial Equations

Pg 317 Factor the GCF in each expression. #64 Pg 324 Factor each polynomial completely #64 Pg 331 #90 Pg 339 Factor the polynomial completely #98 Pg 345 Factor the polynomial completely. If a polynomial is prime, say so. Pg 353 Solve each equation #16 Pg 353 #54 MTH 2

### Polynomial Factorize, Solve equation, Prime Polynomial, GCF

Section 5.1 #50 Complete the factoring of each monomial. = -12 ab3c3(8a2bc2) #58 Factor out the GCF in each expression. 6wz + 15wa =3w(2z+5a) Section 5.2 #52 Factor each polynomial. =5(y2+4) #56 =4(3a2-4a-8) #70 Use grouping to factor each polynomial completely 3x+3z+ax+az =3(x+z)+a

### Basic Algebra

25 Algebra problems. 1. Which number is prime? A) 4 B) 43 C) 39 D) 121 2. Find the GCF for 14 and 21. A) 1 B) 6 C) 7 D) 42 3. Find the LCM for 13 and 78. A) 1 B) 13 C) 78 D) 1014 4. Convert to a fraction. A) B) C) D) 5. Convert 0.4 to

### Polynomial: linear, quadratic, cubic, or quartic

Determine if possible whether f(x)=3x^3-2x^2-7x+5 has a zero between a=1 and b=2. (e answer will be yes or cannot say Determine if possible whether f(x)=x^3+3x^2-9x-13 has a zero between a=1 and b=2. (The answer will be either "yes", or "cannot". Classify the polynomial as linear, quadratic, cubic, or quartic. Determine t

### Prove by contradiction that there does not exist a largest integer.

Prove by contradiction that there does not exist a largest integer. Hint: observe that for any integer n there is a greater one, say n+1. So begin the proof "Suppose for contradiction that there is a largest integer. Let this integer be n...."

### 29 algebra problems: polynomials, rational functions, exponents

See attached file for full problem description. 1. Use the five properties of exponents to simplify the expression 2. - 5x - 6, x = -3 and x = -2 3. What expression raised to the fourth power is 81x12y8z16? 4. The cost in dollars of manufacturing w wing nuts is given by the expression 0.07w + 13.3. Find the cost w

### Solve logarithms for x

Solve following for x, expressing answers as compound fractions and integers where appropriate: a) log (5x - 4) - log (5x - 4) = 2 b) log (5x - 4) + log (5x - 4) = 2 The logarithms are base 3.

### Studying Statistics : Law of Large Numbers and Sampling Techniques

1. Explain in your own words the law of large numbers. Provide an example to illustrate. 2. Explain in your own words, using the definition of probability why: a) the probability of an event that cannot occur is 0; b) the probability of an event that must occur is 1. 3. Why is expectation important? Explain what the expect

### Sets and Functions : The symmetric difference of two sets

The symmetric difference of two sets and , denoted by , is defined by ; it is thus the union of their differences in opposite orders. Show that A &#916; &#966; = A ; A &#916; A = &#966;

### Algebra Word Problems : Relative Speed

Susan and her husband John bicycled cross-country together. One morning, Susan rode 30 miles. By traveling only 5 miles per hour faster and putting in one more hour, John covered twice the distance Susan covered. What was the speed of each cyclist? (Give all possible answers)

### How many lines are possible?

Jemma and Gareth are playing a board game on a 7 X 7 square grid. They take turns to place a black counter in an empty square on the grid. The winner is the person who completes a line of three counters. * * * * * In this game, Win

### Functions of Functions

1. If f(x)=2x-3 and g(x)=x2+1, find each of the following: a) f(g(2)) b) g(f(3)) 2. Let f(x)=x2+2 and g(x)=square root of 1-x2. a) Find the domain and range of f and g. b) Are the functions of f g and g f defined? 3. Given F(x)=cubed root of x+5, find functions f and g such that F=f g. Explain the answer.

### Manipulating Algebraic Expressions

See attached file for full problem description. 1. Write each intervals in absolute value notation. a) xE(0,9) The midpoint of the interval (0+9)/2. Since 9-4.5=4.5, each point in the interval is 4.5 units or less from the number 4.5. Thus the interval can be described as: I x-4.5I less than or equal to 4.5. b) xE(-

### Algebra / Statistics (50 Problems) : Sets, Word Problems and Systems of Inequalities and Equations

1. Convert 0.58 to a fraction and write your answer in lowest terms. 2. Evaluate. | 16 | - | -11 | A) -27 B) -5 C) 5 D) 27 3. Simplify: -(-(-27)). 4. Determine the maximum and minimum values for the following set. 5, -50, 30, 20, -18, -6 5. Express 76% as a fraction. 6. Subtract. 14.318 - 10

### Graphing, inequalities, absolute value, solving equations

1. Find the solution sets for the following: |5x - 7| > 12 2. Find the equation of the line satisfying the following: The line with x-intercept 7 and y-intercept -5. 3. Graph the functions L(x) = -3x + 17 and Q(x) = 2x2 + 7x - 22 on the same set of axes. 4. Determine the x-intercepts of g(x) = x2 - x - 20 5. De

### Algebra : Simplifying Expressions using the Remaider Theorem and Solving Equations

1. Divide, then write the result as a division statement. a) (x3-3x2+5x-4)/(x-2) X not equal to 2 ___________ x-2)x3-3x2+5x-4 x3-2x2 -x2+5x -x2+2x 3x-4 3x b) (x3-3x-2)/(x+3) 2. Use the Remainder Theorem to determine the remainders ( do not divide). a) (x3-7x2+2x-4)/(x+2)

### 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

### Cutting the Corners from a Rectangle to form an Open-top Box

Thomas is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?

### For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?

A company uses the formula C(x) = 0.02x^2 - 3.4x + 150 to model the unit cost in dollars for producing x stabilizer bars. For what number of bars is the unit cost at its minimum? What is the unit cost at that level of production?

### 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?

### 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?

### Questions regarding 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

### Earthquakes and the Richter Scale

The intensity level of an earthquake is based on the Richter scale. Using logarithms, the Richter scale measures an earthquake relative to (as a ratio of) the weakest possible tremor. What is the formula for measuring earthquakes? Why is a 7.0 earthquake ten times stronger than a 6.0 earthquake? Pick an earthquake in you

### 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