Explore BrainMass
Share

Explore BrainMass

    Algebra

    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

    where,

    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.

    © BrainMass Inc. brainmass.com December 7, 2019, 2:59 pm ad1c9bdddf

    Categories within Algebra

    Basic Algebra

    Solutions: 7,149

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

    Number Theory

    Solutions: 425

    Number Theory is the examination of integers.

    Graphs and Functions

    Solutions: 2,524

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

    Linear Algebra

    Solutions: 2,116

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

    Group Theory

    Solutions: 234

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

    Boolean Algebra

    Solutions: 90

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

    Combinatorics

    Solutions: 427

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

    Ring Theory

    Solutions: 239

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

    Scientific Notation Problems

    Section 3: Scientific Notation 1. How many one hundred dollar bills would you need to have ten thousand dollars? Explain. 2. How many 1,000 are there in 10 billion? Explain. 3. Explain in your own words: a. How to convert a standard number to scientific notation. b. How to convert a number from scientific notation to

    Examples using Scientific Notation, Proportions, and Per Capita

    Per Capita 1) The National Oceanic and Atmospheric Administration (NOAA) reported that there are 17.8 million feet of Atlantic coastline in the state of North Carolina. If the population of North Caroline is approximately 9.5 million, find the number of feet of coastline per capita in North Carolina. 2) According to the NO

    Finding the probabilities of events

    Boys and Girls A couple plans to have two children. a) Determine the number of sample points in the sample space of the possible arrangements of bous and girls. b) Construct a tree diagram and list the sample space. Assuming that boys and girls are equally likely, determine the probability that the couple has: c) two gir

    Merry-go-round: cyclic equation to model the distance

    Brenna's mom, Mrs. Herstone, is watching Brenna playing at the park. Some children are pushing Brenna around the merry-go-round. Mrs. Herstone decides to take some data, so she started her stopwatch. At 3.5 seconds Brenna is farthest from Mrs. Herstone 26 feet away. When the stopwatch reads 4.2 seconds, Brenna is closest at

    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

    Proving a Time Series is White Noise and Stationary

    Suppose {e_t} and {E_t} are two independent white noise processes with variance sigma^2 and sigma^2_e respectively. (a) Show that {v_t = e_tE_(t-1)} is also a white noise and calculate its variance. (b) Show that y_t = v_t - 0.5_(vt-1) + 3e_(t-1) is stationary.

    Problems of Polynomials

    1. Write a function whose graph is the graph of y = (x+2)^2, but is refelcted about the x-axis. 2. Determine whether the given function is linear or nonlinear? If the function is linear, determine the slope. x y = f(x) 1 -12 2 -7 3 -5 4 -4 5 -5 3. Form a polynomial whose zeros and d

    Finding the Equation of the Exponential Functions

    Find an equation of the exponential function y=g(x) , whose graph passes through the 2 given points. a) (0,5) (3,9) b) (2,24) (4,8) Please show how you got the answer. And find a equation of the linear function y=f(x) for the same points.

    Find the x-intercept or a y-intercept for given function

    Please help answer the following questions: 1. Find all intercepts of the function f(x)=4x^3-7x^2-16x+28 . For each intercept, show your algebra, then state the intercept using correct function notation and as an ordered pair. Clearly state whether the intercept is an x-intercept or a y-intercept. 2. Perform the same ste

    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

    Applied Algebra: Minting Pennies

    6. Owing to the rising cost of copper, in 1982, the US Mint changed the composition of pennies from 95% Copper + 5% Zinc to 2.5% Copper + 97.5% Zinc to save money in minting pennies. Your favourite aunt has a collection of 5,000 pennies minted prior to 1982 and she intends on gifting the collection to you. (a) What is the coll

    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

    Solve the Rational Equation

    Please help solve this rational equation and please explain what a rational equation is. 1/b-5 - 10/b^2-5b+25 = 1/b+5

    Non-dimensionalising Differential Equations

    Two species with populations N1(t) and N2(t) interact according to the model: (dN_1/d_t)=r_1N_1(1-(N_1/K_1) - b_12(N_2/K_1), (dN_2/d_t)=r_2N_2(1-b_21(N_1/K_2), Non-dimensionalise the system (7) so that: (d_u/d_t) = u (1- u - au), (d_u/d_t) = pv (1-Bu), finding explicit formulae for the new constraints p, a, and B

    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

    Solving an example linear programming question

    1. A component has a reliability of 0.75. How many identical components do we have to add n parallel to the frst to increase the overall reliability to 0.95? You may use the following general formulas R_sys = 1-(1-R1)(1-R2)...(1-Ri)...(1-Rn) Ri=e^-(lamda*t) 2. Find both the minimum and maximum values of U=6x1+10x2+7 (grap

    Submodules of polynomial ring K[x]

    Which of the following sets of polynomials n K[x], K commutative are K-modules:(a) all polynomials of degree exactly ; (b) all polynomials of degree at most 4; (c) all monic polynomials; (d) all polynomials of even degree?

    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