Explore BrainMass


Algebra is a branch of Mathematics which deals with structures utilizing letters and symbols to represent specific values and their relations to each other. Basic Algebra deals with natural numbers, which are generally positive integers, and their arithmetical operation, while the more complex rules and properties of these mathematical structures are explored in Number Theory. Thus, it can be seen that Algebra is essentially a study of arithmetic computations with non-numerical mathematical objects.

Consider the following equation:

3x+4 = 9


x is the unknown

3, 4 and 9 are the known natural numbers

Through the use of algebra, the unknown value in the above equation can be solved. One important rule to remember is that an algebraic equation represents a scale, so an operation done to one side must be done to the other. Thus, for the above equation, we can isolate x by subtracting 4 from both sides, then divide both sides by 3:

3x+4(-4) = 9(-4)

3x = 5

x = 5/3

Thus, it can be seen that by understanding algebra and its operations is extremely important for all facets of mathematics.

Categories within Algebra

Basic Algebra

Postings: 7,131

Basic Algebra, also known as Elementary Algebra, deals with the arithmetic operations of unknown variables and natural numbers.

Number Theory

Postings: 423

Number Theory is the examination of integers.

Graphs and Functions

Postings: 2,518

A function is a relationship between inputs and outputs with a specific property that one input is related to only one output.

Linear Algebra

Postings: 2,111

Linear Algebra is the study of systems of linear equations, with applications in vector spaces and linear mapping.

Group Theory

Postings: 233

Group Theory refers to the study of algebraic structures known as groups.

Boolean Algebra

Postings: 90

Boolean Algebra is a sub-discipline of algebra which deals with the truth values of specific variables.


Postings: 422

Combinatorics is a sub-discipline of Algebra which is concerned with the study of combination, enumeration and permutation of sets of elements.

Ring Theory

Postings: 238

Ring Theory is the study of abstract algebraic structures in which addition/multiplication operations are well defined.

Emile's Inheritance

Emile got a letter in the mail saying that a wealthy relative had left him an inheritance. At a meeting the next week, a lawyer read the following statement. To Emile, because he likes math problems, I leave a choice. He can have one of two inheritances. He must make his choice before leaving the office today. Optio

Simple volume of a cylinder with unit conversion.

Since this module focuses on measurement it will be very important that mathematical conversions be clearly demonstrated throughout your problem write-up. For example, if you are converting 28 yards to meters, you must track your calculations with cancellation of units as seen below: 28 yards times (0.9144 meters / 1 yard)

Parking Option Best for the Employee on a Monthly Basis

A downtown employee is looking for the best option for parking a car during a 5 day work week. One parking garage offers unlimited parking at a flat rate per month. Another garage offers an hourly rate for parking. Which option is best for the employee on a monthly basis? Consider that the employee works standard 8 hours a da

Vector Calculus and Linear Algebra

Question 4 Find the work done by the force F (x,y,z) = -x^2y^3 i + 4j + xk on moving charged electric particle along the path given by the equation r (t) = 2cos t i + 2sintj + 4k, where the parameter t varies from pi/4 to 7pi/4. Question 5 Displacement of the spring system with friction is described by the differenti

Variance on Shelter Sample Data

You want to make a statement about the variability in the costs of personnel shelters. After collecting sample data (cost in $K) on 9 shelters you perform some preliminary calculations. Given the information provided: The coefficient of variation is about 17.64% The variance is about $61.72K The stand

Algebra: Elimination and Substitution Methods

1. Solve the following system of equations using the Substitution method: 5X-7Y= - 18 4X+3Y= 20 2. Solve the following system of equations using the elimination method: 2X-3Y=12 -2X+3Y=12 Solution: Computation of the Equations 2X-3Y =12 -2X+3Y =12 3. A total of $80,000 is invested in two funds paying 2.3% and 3.1

Graph rational equation

A. Graph the function  =  f(x) = x-2/x^2 - 3x + 2 B. Find the domain and range of , showing all work. C. Find the → , showing all work, or explain why the limit does not exist. D. Find the → , showing all work, or explain why the limit does not exist. E. Apply the definition of continuity to

Bank reconciliations and horizontal models for interest

Prepare a bank reconciliation as of August 31 from the following information: a. The August 31 balance shown on the bank statement is $9,810. b. There is a deposit in transit of $1,260 at August 31. c. Outstanding checks at August 31 totaled $1,890. d. Interest credited to the account during August but not recorded on the co

Algebra Calculations

Can you please explain how to do these problems? 1. Evaluate 3x-4y/ 2z when x= -2, y=3, z=4 . Express your answer as a fraction. 2. Use the order of operations to simplify the following expression. (-2)2 -3 2 3. Write the statement as an algebraic equation: 'The difference between x and 2 is 4 more than twice x' 4

Several Statistics Example Questions

6. Why can't you obtain a correlation coefficient greater than ±1? 8. As the value of r approaches ±1, what does it indicate about the following: a) The consistency in the X-Y pairs b) The variability of the Y scores at each X c) The closeness of the Y scores to the regression line d) the accuracy with which we can pred

Accounting: Liabilities and Shareholders' Equity

Liabilities and Shareholders' Equity Accounts payable............................................... $5,520 $4,970 Accrued expenses............................................... 8,572 4,310 Non-current liabilities......................................... 4,450 1,535 Common stock, no par value..........

Calculating new table factors for investments

To determine the compound amount of an investment of $10,000 with an interest rate of 6% compounded monthly after 4 years requires you to use a table factor that goes beyond the Compound Interest Table. Calculate the new table factor for this investment. (Points : 2.5) 5. Now, using the new table factor from

Algebra, Geometry Problems

Check attachment for cleaner version of the questions below. Solve the following equations algebraically. Must show work. 1a) (t^{frac{2}{3}}) =4 b)√(5&x) + 1 = 3 = 3 c) =2- (frac{2}{3}) (frac{5x -3}{x-1}) 2)Solve algebraicaly a) (sqrt{x+2}-x=0) b) (4- frac{x}{x-2} = frac{-2}{x-2}) The volume of a cube is gi

Solving equations and finding intercepts

Find an equation of the line that passes through the given point and has the given slope. Express your answer in slope-intercept form: 28) (8,0), m = -3 Find an equation of the line passing through the pair of points. Write the equation in slope intercept form 36) (4, 8) and (-3, 8) Find an equation at the line sati

Under or overapplied costs for Arts & Co.

Arts & Co. applies manufacturing overhead to jobs based on machine hours used. At the beginning of the year, the company estimated that overhead costs would total $86,000 for the year, and that the machine would run for 4,000 hours during the year. 1. Determine the pre-determined overhead rate for the year. 2. One jo

Contribution margin and break-even points

The following cost information is available for a single product manufactured and sold by Forever You Company: Variable costs: Direct materials $ 10 Fixed costs (in total): (Per unit) Direct labor 12 Fixed overhead $ 540,000 Variable overhead 3 Fixed selling 360,000 Variable selling 2

Activity Costing

See the attachment. The purchasing department of a manufacturing firm has decided to apply its costs to jobs using an activity based costing system. Its costs of $490,000 are split among the three major activities: Activity Cost Allocation Measure Total Activity Finding suppliers $ 300,000 N

5 Simple Algebra and Function Questions

See the attached file. 1. Determine whether the graph of y = 3 + x2 is symmetric with respect to the x-axis, the y-axis, or the origin. 2. A salesperson earns a base salary of $2,000 per month and a commission of 5% on the amount of sales made. If the salesperson has a paycheck of $3,006 for one month,

Differential Analysis Report on Changes in Selling Price

Please help in preparing a differential analysis report on the case study mentioned, dated April 21 of the current year, on the proposal to sell at the special price. 'FDE Manufacturing Company has a normal plant capacity of 37,500 units per month. Because of an extra large quantity of inventory on hand, it expects to produce

Loan Interest and Maturity Value

1. Using the exact interest method (365 days), find the amount of interest on the following loan Principal Rate (%) Time (days) Exact Interest $1,700 12½ % 33 (Points : 2) 2. What is the maturity value of the following loan? Use MV = P(1 + RT) to find the maturity. Principal Rate (%) Time Maturity Value $120,740 11

Defining functions and calculating circles

Six Questions Show Work 1. The number of representatives N that each state has varies directly as the number of people P living in the state. If New York, with 19,254,630 residents has 29 representatives, how many representatives does Colorado, with a population of 4,665,177, have? 2. Find the center and radius of th

Assume the project variance is 4 weeks. i. What is the probability that all the activities are completed within 19 weeks? ii. When is the due date if there is a 90% of completing all the activities?

I want assistance with c(i) and c(ii) only in following question. The project of building a backyard swimming pool consists of eight major activities and has to be completed within 19 weeks. The activities and related data are given in the following table: Activity Immediate predecessor Activity time (weeks) A - 3 B - 6

Monthly Analysis using a Linear Programming Model

"A northern hardware company is studying a plan to open a new distribution center in southeast. The company plans to rent a warehouse and an adjacent office, and distribute its main products to the local dealers. The company has decided to initially start with four of its main products: Pressure washers, Go karts, Generators, an

Solving Age Related Problems.

Please help solve the following age-related problems. Problem 1 Barbie's father's age is 45. He is 15 more than than twice the age of Barbie. How old is Barbie? Problem 2 Brenda's age is 3 times Layton's age. In 4 years, she will be twice as old as Layton by then. What are their present ages?

Algebra: Buying Office Max Furniture

You have decided to buy some office furniture. Please respond to all of the following prompts: 1. First, go to Find the price of a conference table you would like to buy. 2. If you need to buy 6 chairs additionally for the table and have a $2000 budget, what is the highest price you can pay for a