Category: Algebra

El álgebra es una rama de las matemáticas que estudia las estructuras, las relaciones y las cantidades. Utiliza letras y símbolos para representar variables y cantidades desconocidas, permitiendo así resolver ecuaciones y expresar generalizaciones sobre patrones numéricos y relaciones entre números. El álgebra abarca conceptos fundamentales como ecuaciones.
El álgebra es una parte fundamental de las matemáticas que se centra en el estudio de las estructuras algebraicas, que son conjuntos provistos de operaciones que satisfacen ciertas reglas. Aquí hay algunos aspectos clave y conceptos importantes relacionados con el álgebra: 1. **Expresiones algebraicas**: Son combinaciones de números, letras (llamadas variables) y operadores matemáticos como suma, resta, multiplicación y división. Ejemplos simples incluyen ( 3x + 5 ) o ( 2a^2 – 3ab + b^2 ). 2.

What is one thing that you found interesting about future value and present value for compound interest? Has this chapter changed how you thought about investing and saving?
Respond to at least two of your classmate’s posting.
150 words

Policia moderna, societas, et futurus convergent, auxilia technology et scientia.”
In this phrase, we’re discussing the convergence of modern policing, society, and the future, and how they’re aided by technology and science.
– “Policia moderna” refers to modern policing, which encompasses the latest strategies, tactics, and tools used by law enforcement agencies to maintain social order and combat crime.
– “Societas” represents society, which includes the communities, cultures, and individuals that police agencies serve and interact with.
– “Futurus” denotes the future, which is shaped by the evolving relationships between policing, society, and technology.
– “Auxilia” means “aided by” or “assisted by,” highlighting the supportive roles of technology and science in modern policing.
– “Technology” (technologia) encompasses the various tools, systems, and platforms used in policing, such as forensic analysis, surveillance systems, and communication networks.
– “Scientia” represents science, which includes the application of scientific methods, research, and expertise to improve policing practices and address complex social issues.

You are a financial advisor helping a client plan for retirement. Your client has a certain amount of money to invest in two different types of investment products: bonds and stocks. The bonds yield a fixed annual return of 4% interest, while the stocks yield a variable annual return of 8% interest. Your client wants to invest a total of $50,000.
Setting up Equations for Investments (15 points):
Define two variables to represent the amount invested in bonds and stocks, respectively.
Write a system of linear equations to represent the total amount invested and the total annual interest earned from both types of investments.
Use the given information to set up the equations.
Solving the System of Equations (20 points):
Solve the system of linear equations using an appropriate method (substitution, elimination, or matrices).
Determine the amount invested in bonds and stocks to maximize the total annual interest earned.
Optimizing the Investment (15 points):
Calculate the total annual interest earned when the investment is optimized.
Discuss the significance of optimizing the investment in terms of maximizing returns for retirement planning.
Linear Programming (25 points):
Formulate a linear programming problem to maximize the total annual interest earned subject to the constraint that the total investment does not exceed $50,000.
Use graphical or algebraic methods to find the optimal solution.
Interpret the solution in the context of the problem.
Reflection (10 points):
Write a reflection on the process of solving the financial planning problem.
Discuss the relevance of systems of linear equations and linear programming in financial decision-making.
Reflect on how this assignment has enhanced your understanding of mathematics in finance.
Submission Guidelines:
Present your solutions in a well-organized format.
Clearly label each step of your calculations.
Submit your assignment as a PDF document, including any necessary graphs or diagrams.

Hello! Please let me know if you have any questions. Attached are the questions on the first page. There is no other necessary materials before starting. Please make sure to have clear handwriting. Make sure the number nine does not look like the letter g. Make sure the variable x looks like an x and not some other type of symbol. Overall, please have neat and legible handwriting. Please only use the indicated methods asked for in the directions. If you have any questions please message me. I will be happy to clear anything up. Their are example problems in the PDF as well, the pages attached have titles at the top to what question they refer to. Again, please feel free to contact me with any questions. MUST complete the problems using the specific method asked. Please refer to other example questions for more guidance, and please solve them the exact way mentioned and showed in the examples.

apply relevant economic principles and formulas to arrive at the solutions. 
algebraic manipulations and understand Keynesian macroeconomic theory required to complete it.
There is no formal word limit.  As is usual for an exam, for this assessment you are not expected to include full referencing, but are
encouraged to cite the sources of key theories, models, case studies, statutes etc . 
This is an individual assessment: do not copy and paste work from any other source or work with any
other person during this exam. Text-matching software will be used on all submissions.
I will include another quesstion that we are required to pick one from. So pick whichever you find you could go more in detail and are able to make it human-like with the solving as well

This assignment assesses your skills/knowledge on identifying polynomial and rational functions, the domain, using the graphical representation of these functions, and hence you will study the behavior- discontinuities, increasing, decreasing and extrema.
In real life situations the growth need not be smooth and always increasing or decreasing. The functional values may be having different turnings and may be disappearing at some points. These kinds of situations are represented by polynomial and rational functions. This assignment will enable you to identify such functions and interpret them mathematically and graphically.
You are required to complete all the 5 tasks in this assignment, answer the following questions, and show stepwise calculations. When you are instructed to make a graph in this assignment, please use GeoGebra graphing tool.
Task 1. Interpret the following graph in detail:(I) Identify the turning points, zeros, and x-intercepts.
(ii) Do you find any point or zero which has a multiplicity in the graph? If so, specify them with multiplicity and explain the reason.
(iii) Identify the degree and the polynomial as well as identify the domain in which the polynomial is increasing and decreasing.
(iv) Do we have local maximum/minimum here? If yes, find them.
(v) Find the remainder when the polynomial is divided by x-4.
Task 2. Given a polynomial: f(x) = x4 – 8×3 -8×2 +8x +7
(i)Use rational theorem and synthetic division to find the zeros of the polynomial
(ii) Draw the graph using GeoGebra graphing tool.
(iii) Identify its end behavior
Task 3. Given a function ” src=”https://my.uopeople.edu/filter/tex/pix.php/6a632a9cf828e20f00570b5551673896.png”>
(i) Find the horizontal and vertical asymptotes.
(ii) Find the domain of rational function. Show all steps.
(i) Identify the horizontal and vertical asymptotes (if any). Explain how you would find horizontal and vertical asymptotes of any rational function mathematically.
(ii) Identify the zeros of the rational function.
(iii) Identify the rational function.
Task 5. Before working on this task 5, please read the following reading:
Read page 238 of the following textbook will help you in understanding the concepts better.
Stitz, C., & Zeager, J. (2013). College algebra. Stitz Zeager Open Source Mathematics. https://stitz-zeager.com/szca07042013.pdf
An online courier service is ready to transport a diverse range of items to ensure efficient delivery. The agency requires boxes of various dimensions. Let’s now focus on creating open boxes that have fixed height for storing these items. Take a cardboard of length thrice of the width and cut the edge of all 4 corners with 15cms, then fold the cardboard to get an open box. Based on that information, answer the following questions:
(i) Find the volume of the open box, explain whether the resultant function is a polynomial or any other.
(ii) Find the possible domain for the volume function
(iii) If we wish to put a flexible item that has a volume of 12500 cubic cm, what dimensions of the box would be appropriate?
Submission Settings: Please complete all the 5 tasks in this assignment.
You may use a word document that addresses the questions mentioned above. The word document should be double-spaced in Times New Roman font, which is no greater than 12 points in size.      
Use APA citations and references if you use ideas from the readings or other sources. For assistance with APA formatting, view the Learning Resource Center: Academic Writing. The document should be double-spaced in Times New Roman font, which is no greater than 12 points in size. Use high-quality, credible, relevant sources to develop ideas that are appropriate for the discipline and genre of writing.

Hello! Please let me know if you have any questions. Attached are the questions on the first page. There is no other necessary materials before starting. Please make sure to have clear handwriting. Make sure the number nine does not look like the letter g. Make sure the variable x looks like an x and not some other type of symbol. Overall, please have neat and legible handwriting. Please only use the indicated methods asked for in the directions. If you have any questions please message me. I will be happy to clear anything up. Their are example problems in the PDF as well, the pages attached have titles at the top to what question they refer to. Again, please feel free to contact me with any questions. MUST complete the problems using the specific method asked. Please refer to other example questions for more guidance, and please solve them the exact way mentioned and showed in the examples.

Watch the videos available at: The Cornell Note Taking System – Learning Strategies CenterFill out and upload the Cornell Notes corresponding to Section 1.4. Quadratic Equations.We strongly recommend you creating Cornell Notes for all the sections we will cover in classes.