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This document discusses polynomial functions, including their end behavior depending on whether the degree is even or odd. It also covers factored form, standard form, and how to solve polynomials using box and diamond steps or synthetic division. The key steps for synthetic division are listed as writing down coefficients in order, drawing a box and line while switching signs of the number dividing, dropping the first number down, and repeating multiplication.
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Day 5 examples u3f13
Polynomial functions are algebraic expressions with variables raised to whole number powers. They can be classified based on their degree as linear, quadratic, cubic, quartic, or quintic. The graph of a polynomial is smooth and continuous without sharp corners. Polynomials can also be described based on having an odd or even degree, which determines their end behavior as the variable approaches positive or negative infinity. The key characteristics used to identify a polynomial function include its degree, leading coefficient, even/odd classification, number of x-intercepts, and number of local maxima and minima points.
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This document contains notes from math lessons on linear functions and slope. It includes examples of finding the slope and y-intercept of linear functions from graphs, equations, and real-world contexts. Key points covered are:
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División de Polinomios.
División de Polinomios:
1. División de Polinomio entre un Monomio.
2. División entre Polinomios.
3. División Sintética (Ruffini).
Solving all equations
The document provides instructions for solving various types of one-step and two-step equations. It explains that to isolate the variable, the opposite operation should be applied to both sides of the equal sign. For one-step equations, this involves using subtraction to cancel out addition or division to cancel out multiplication. For two-step equations, the same operations are used after first cancelling out any addition or subtraction. The document also provides guidance on combining like terms and solving equations with variables on both sides.
Limits!
This document defines and explains key limits concepts in mathematics including intended height, approaching a limit from the right or left, holes, asymptotes, vertical asymptotes, horizontal asymptotes, and slant asymptotes. It states that the sign after the number being approached indicates the side of the graph and discusses factors that do and do not cancel in determining asymptotes or holes.
Two step equations
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- The document provides examples of setting up two-step equations like 2x = -2 and -3y - 5 = -20 in a do/undo box, with the "do" side showing the operations on the same side as the variable and the "undo" side showing the inverse operations to solve step-by-step for the variable.
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Slope-intercept form is represented by the equation y=mx+b, where m is the slope and b is the y-intercept. There are three methods to find the slope: rise over run, change in y over change in x, and point-slope formula. The slope tells the rate of change, while the y-intercept is the initial value when x=0. To graph a line in slope-intercept form, you plot the y-intercept and then use the slope to trace successive points on the line by calculating the rise over run at each interval of x. Word problems can be modeled using this form by identifying the independent and dependent variables and finding their relationship through calculating slope from ordered pairs of known values.
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Day 5 examples u3f13
Polynomial functions are algebraic expressions with variables raised to whole number powers. They can be classified based on their degree as linear, quadratic, cubic, quartic, or quintic. The graph of a polynomial is smooth and continuous without sharp corners. Polynomials can also be described based on having an odd or even degree, which determines their end behavior as the variable approaches positive or negative infinity. The key characteristics used to identify a polynomial function include its degree, leading coefficient, even/odd classification, number of x-intercepts, and number of local maxima and minima points.
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This document provides examples for solving 16 inequality word problems by adding or subtracting the number being added or subtracted from both sides of the inequality. It explains that for problems where a number is being subtracted, that number should be added to both sides since it is negative, and for problems where a number is being added, that number should be subtracted from both sides since it is positive. The document works through each problem as an example, showing the steps to solve it and obtain the simplified inequality. It concludes by reminding students of the rules for adding and subtracting positive and negative numbers.
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This document contains notes from math lessons on linear functions and slope. It includes examples of finding the slope and y-intercept of linear functions from graphs, equations, and real-world contexts. Key points covered are:
- The slope-intercept form of a linear function is y=mx+b, where m is the slope and b is the y-intercept.
- Slope can be positive, negative, zero, or undefined, depending on the steepness and direction of the line from left to right.
- To find the slope of a line from its graph, students select two points on the line, calculate the rise over run between those points, and determine if the slope is positive, negative,
División de Polinomios.
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1. División de Polinomio entre un Monomio.
2. División entre Polinomios.
3. División Sintética (Ruffini).
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The document provides instructions for solving various types of one-step and two-step equations. It explains that to isolate the variable, the opposite operation should be applied to both sides of the equal sign. For one-step equations, this involves using subtraction to cancel out addition or division to cancel out multiplication. For two-step equations, the same operations are used after first cancelling out any addition or subtraction. The document also provides guidance on combining like terms and solving equations with variables on both sides.
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This document defines and explains key limits concepts in mathematics including intended height, approaching a limit from the right or left, holes, asymptotes, vertical asymptotes, horizontal asymptotes, and slant asymptotes. It states that the sign after the number being approached indicates the side of the graph and discusses factors that do and do not cancel in determining asymptotes or holes.
Two step equations
- Two-step equations can be solved using a do/undo box method where the operations on the "do" side represent the mathematical operations relating to the variable, and the "undo" side represents the inverse operations in reverse order to solve for the variable.
- The document provides examples of setting up two-step equations like 2x = -2 and -3y - 5 = -20 in a do/undo box, with the "do" side showing the operations on the same side as the variable and the "undo" side showing the inverse operations to solve step-by-step for the variable.
- Using this method of a do/undo box with the operations written in order on one side
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Slope-intercept form is represented by the equation y=mx+b, where m is the slope and b is the y-intercept. There are three methods to find the slope: rise over run, change in y over change in x, and point-slope formula. The slope tells the rate of change, while the y-intercept is the initial value when x=0. To graph a line in slope-intercept form, you plot the y-intercept and then use the slope to trace successive points on the line by calculating the rise over run at each interval of x. Word problems can be modeled using this form by identifying the independent and dependent variables and finding their relationship through calculating slope from ordered pairs of known values.
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Slope-intercept form is represented by the equation y=mx+b, where m is the slope and b is the y-intercept. There are three methods to find the slope: rise over run, change in y over change in x, and point-slope formula. The slope tells the rate of change, while the y-intercept is the initial value when x=0. To graph a line in slope-intercept form, you plot the y-intercept and then use the slope to trace successive points on the line by calculating the rise over run at each interval. Word problems can be modeled using this form by identifying the independent and dependent variables and finding their relationship through calculating slope from ordered pairs of known values.
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This document outlines a 5-step method for converting units of measure: 1) rewrite the problem leaving out numbers, 2) write conversion factors, 3) multiply to solve one side of the equation, 4) multiply both sides of the equation equally, and 5) solve the equation. An example problem converts 4 meters to centimeters and another converts 60 inches to feet using this method.
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This document discusses how to graph linear inequalities on a coordinate plane. It explains that less than and greater than signs are represented by dashed lines, while less than or equal to and greater than or equal to signs use solid lines. It notes that inequalities must be written in slope-intercept form before graphing and that the shading depends on whether the inequality involves less than or greater than. Specifically, y greater than inequalities are shaded above the line and y less than inequalities are shaded below the line. Practice graphing many problems to fully understand how to determine the shading direction.
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Module Four Lesson 2 Remediation Notes - Slope intercept form
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Frequently the terms NoSQL and Big Data are used as synonyms. While both technologies divert from the traditional RDBMS data model and spread data across clusters of servers, the “problems” these technologies address are quite different. Hadoop, is focused on data analysis – gleaning insights from large volumes of data. NoSQL databases, focus on interactive applications – delivering high-performance, cost-effective data management for massive number of users. In this session, we share how IBM BigInsights and Couchbase Server can used together to build better applications.
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The document discusses Couchbase Server and document-oriented data management. It highlights key benefits of Couchbase Server such as easy scalability, consistent high performance, and high availability. It compares relational and document data models, showing how Couchbase Server uses a flexible document model to store data. The architecture of Couchbase Server 2.0 is also summarized, focusing on new features like indexing and querying capabilities.
Navigating the Transition from relational to NoSQL - CloudCon Expo 2012
For more deep NoSQL content from Couchbase, check out http://www.couchbase.com/webinars
NoSQL databases have emerged as a better match than relational systems for modern interactive applications, offering cost-effective data management at “Big Data” scale. But there are significant differences between structured and schema-less database technology. What should architects and technical managers know as they explore NoSQL solutions for their teams?
In this workshop you will learn:
- How to evaluate NoSQL (both technical advantages and limitations) as a potential data management approach
- Critical differences between NoSQL and RDBMS for designing, building and running production applications
- Ideal use cases for NoSQL technology and sample reference architectures
How companies use NoSQL and Couchbase
This document discusses how companies use NoSQL and Couchbase. Couchbase is an open-source, distributed document-oriented database that supports both key-value and document data models. It offers features like easy scalability, high performance, flexible data modeling with JSON documents, and 24/7 availability. Common use cases for Couchbase include mobile apps, caching, session stores, user profiles, content management, and real-time analytics. The document provides examples of companies using Couchbase for applications in social gaming, advertising targeting, and education.
API TEST
The document discusses the benefits of exercise for mental health. Regular physical activity can help reduce anxiety and depression and improve mood and cognitive function. Exercise causes chemical changes in the brain that may help protect against mental illness and improve symptoms for those who already suffer from conditions like depression and anxiety.
Bank system presentation
The document discusses plans to improve a bank's information system. It analyzes the current system's strengths, weaknesses, opportunities, and threats. It then outlines goals of increasing customer satisfaction by allowing all operations to be done remotely via online and mobile banking. This would help the bank penetrate new international markets and rural areas in a faster, safer, and more cost-effective manner. A task plan is proposed to implement necessary changes to the system through tasks like requirement analysis, design, testing, and deployment.
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Part 2 of the webinar - Which freaking database should I use?
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Merchandise, store and financial planning with Targetta
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Couchbase Server and IBM BigInsights: One + One = Three
Couchbase Server and IBM BigInsights: One + One = Three
Go simple-fast-elastic-with-couchbase-server-borkar
Go simple-fast-elastic-with-couchbase-server-borkar
Navigating the Transition from relational to NoSQL - CloudCon Expo 2012
Navigating the Transition from relational to NoSQL - CloudCon Expo 2012
Bingo
- 1. Polynomial Fuctions Aquarius washington
- 2. End Behavoir Even Multipicity: it bounces off
- 3. odds Right- is positive infinity A: is negative left- positive infinity A: is positive left- negative infintiy Right is negative infinity.
- 4. evens A: is positive: left positive infinity. A: is negative: negative infinity Right- positive infinity Right – negative infinity
- 5. Factored form You use factor form to get to standard form. Y=(X+4)(X-1)^2(x=4)
- 6. Standard Form Y=1x^3+1x^2-4x+8 How to solve- use box and diamond sequence.
- 7. Polynomial Long Steps! 1) Devide 2) Multiply 3) subtract
- 8. Synthetic divison 1) write the coeffientsdown in order. 2) Draw a box & line while switching the signs of what you devide by. 3) drop your first number down. 4) multiply then repeat.