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Basic Algebra

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

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

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

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

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(-

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

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

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

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

Algebra : Estimation, Word Problems and Optimization

1. Use inductive reasoning to determine the next three numbers in the pattern: 2, 9, 20, 35... 2. Make a conjecture about the relationship between the original number and the final number in the following process. Pick a number Multiply the number by 12 Add 12 to the product Divide the sum by 4 Subtract

What is the maximize the area of a rectangular patio?

I have 400 feet of lumber to frame a rectangular patio. I want to maximize the area of the patio. What should the dimensions of th patio be. Show how the maximum area of patio is calculated from the algebraic equation. Use the vertex form to find the maximum area.

Quadratic Equations

1) Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: a) Solve by factoring. b) Solve by using the quadratic formula. 2) For the function y = x2 - 6x + 8, perform the following tasks: a) Put the function in the form y = a(x - h)2 + k. b) What is the equation for the