The document discusses linear sequences and how to determine the algebraic rule that defines each sequence. It explains that linear sequences can be represented by the general form y=mx+b, where m is the slope (gap between terms) and b is the y-intercept. Through examples of finding the patterns and calculating m and b for different sequences, it illustrates how to write the rule for any linear sequence in order to determine future terms quickly without having to list all previous terms.
I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...
I have added to the original presentation in response to one of the comments.... the result of 'x' is correct on slide 7, take a look at the new version of this ppt to clear up any confusion about why...
* Find zeros of polynomial functions
* Use the Fundamental Theorem of Algebra to find a function that satisfies given conditions
* Find all zeros of a polynomial function
* Evaluate a polynomial using the Remainder Theorem.
* Use the Factor Theorem to solve a polynomial equation.
* Use the Rational Zero Theorem to find rational zeros.
* Find zeros of a polynomial function.
* Use the Linear Factorization Theorem to find polynomials with given zeros.
* Use Descartes’ Rule of Signs.
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
The Indian economy is classified into different sectors to simplify the analysis and understanding of economic activities. For Class 10, it's essential to grasp the sectors of the Indian economy, understand their characteristics, and recognize their importance. This guide will provide detailed notes on the Sectors of the Indian Economy Class 10, using specific long-tail keywords to enhance comprehension.
For more information, visit-www.vavaclasses.com
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
3. Sequences Terms: 4, 5, 6, 7, 8 … Each number is a term of the sequence. Each term of the sequence is associated with the counting numbers. The counting number represent the terms location: First, second, third, etc. 1 2 3 4 5 … 4 5 6 7 6 …
4. Since each sequence can be thought of and viewed as an ordered pair, they can be graphed. 1 2 3 4 5 … 4 5 6 7 8 … 1 2 3 4 5 … 4 5 6 7 8 … x y # of term Term Value
5. As you can see the sequence is a line of integer values. Hence we call it a linear sequence. We can find the succeeding points by graphing or just visually recognizing the pattern. However, graphing is very time consuming.
6. 1 2 3 4 5 … 4 5 6 7 8 … x y # of term Term Value Recognizing the pattern is not efficient for finding the 50 th term because you need to find the first 49 terms to compute the 50 th term. Therefore, it would be quicker if we could come up with a simple algebraic rule.
7. 1 2 3 4 5 … 4 5 6 7 8 … x y # of term Term Value Let’s look at the change in each term or gap between terms. 1 1 1 1 Note that the change in y is 1. The change in x is also 1.
8. 1 2 3 4 5 … 4 5 6 7 8 … x y # of term Term Value 1 1 1 1 Since the sequence is linear it has the following form: Y = mX + b m = 1 or the gap between terms.
9. 1 2 3 4 5 … 4 5 6 7 8 … x y # of term Term Value 1 1 1 1 Since the sequence is linear it has the following form: Y = mX + b m = 1 or the gap between terms. The slope will always be the gap between terms because the change in x will always be 1.
10. 1 2 3 4 5 … 4 5 6 7 8 … x y # of term Term Value 1 1 1 1 Y = (1)X + b To find the value of b, use the first term and substitute 1 for x and substitute 4 for y. 4 = (1)(1) + b 4 = 1 + b 3 = b The rule is y = x + 3
11. 1 2 3 4 5 … 4 5 6 7 6 … x y # of term Term Value 1 1 1 1 It works. Look at each term. The rule is y = x + 3 5 = 2 + 3 6 = 3 + 3 7 = 4 + 3 8 = 5 + 3
12. 1 more time. That was the first try. Let’s do another. 1 2 3 4 5 … 6 11 16 21 26 … x y # of term Term Value 5 5 5 5 Since each sequence can be thought of and viewed as an ordered pair, they can be graphed.
13. As you can see the sequence is a line of integer values. Hence we call it a linear sequence. We can find the succeeding points by graphing or just visually recognizing the pattern. However, graphing is very time consuming.
14. Recognizing the pattern is not efficient for finding the 50 th term because you need to find the first 49 terms to compute the 50 th term. Therefore, it would be quicker if we could come up with a simple algebraic rule. 1 2 3 4 5 … 6 11 16 21 26 … x y # of term Term Value 5 5 5 5
15. 1 2 3 4 5 … 6 11 16 21 26 … x y # of term Term Value 5 5 5 5 Let’s look at the change in each term or gap between terms. Note that the change in y is 5. The change in x is also 1.
16. 1 2 3 4 5 … 6 11 16 21 26 … x y # of term Term Value 5 5 5 5 Since the sequence is linear it has the following form: Y = mX + b m = 5 or the gap between terms.
17. 1 2 3 4 5 … 6 11 16 21 26 … x y # of term Term Value 5 5 5 5 Since the sequence is linear it has the following form: Y = mX + b m = 1 or the gap between terms. The slope will always be the gap between terms because the change in x will always be 1.
18. 1 2 3 4 5 … 6 11 16 21 26 … x y # of term Term Value 5 5 5 5 Y = 5X + b To find the value of b, use the first term and substitute 1 for x and substitute 6 for y. 6 = 5(1) + b 6 = 5 + b 1 = b The rule is y = 5x + 1 This is usually done mentally by multiplying the term # by the gap and figuring out what else is needed to make the term value.
19. 1 2 3 4 5 … 6 11 16 21 26 … x y # of term Term Value 5 5 5 5 The rule is y = 5x + 1 11 = 5(2) + 1 It works. Look at each term. 16 = 5(3) + 1 21 = 5(4) + 1 26 = 5(5) + 1
20. Let’s see if we can do these quickly 1 2 3 4 5 … x 9 13 17 21 25 … x y # of term Term Value 4 4 4 4 y = mx + b y = 4x + b 9 = 4(1) +b 5 = b y = 4x + 5 4x + 5
21. Again 1 2 3 4 5 … x 5 8 11 14 17 … x y # of term Term Value 3 3 3 3 y = mx + b y = 3x + b 5 = 3(1) +b 2 = b y = 3x + 2 3x + 2
22. And Again 1 2 3 4 5 … x 4 11 18 25 32 … x y # of term Term Value 7 7 7 7 y = mx + b y = 7x + b 4 = 7(1) +b -3 = b y = 7x - 3 7x - 3
23. One more time ! 1 2 3 4 5 … x 8 15 22 29 36 … x y # of term Term Value 7 7 7 7 y = mx + b y = 7x + b 8 = 7(1) +b 1 = b y = 7x + 1 7x + 1
24. Linear sequences must be done quickly. The speed should be almost as fast as you can write. The rule is in the form of m x + b . where x is the number of the term.
25. Let’s try a few more ! 1 2 3 4 5 … x 5 7 9 11 13 … x y # of term Term Value 2 2 2 2 y = mx + b y = 2x + b 5 = 2(1) +b 3 = b y = 2x + 3 2x + 3
26. And Another ! 1 2 3 4 5 … x 8 18 28 38 48 … x y # of term Term Value 10 10 10 10 y = mx + b y = 10x + b 8 = 10(1) +b -2 = b y = 10x - 2 10x -2
27. Let’s try tricky ones ! 1 2 3 4 5 … x 7 7 7 7 7 … x y # of term Term Value 0 0 0 0 y = mx + b y = 0x + b 7 = 0(1) +b 7 = b y = 7 7
28. And Another ! 1 2 3 4 5 … x 17 14 11 8 5 … x y # of term Term Value -3 -3 -3 -3 y = mx + b y = -3x + b 17 = -3(1) +b 20 = b y = -3x + 20 -3x + 20
29. Let’s find the 20 th Term 3 13 18 23 28 8 5 5 5 5 y = 5x + b 3 = 5(1) + b -2 = + b 5x - 2 5(20) - 2 98 x 1 2 3 4 5 6 … x … 20 y GAP
30. Again 3 7 9 11 13 5 2 2 2 2 y = 2x + b 3 = 2(1) + b 1 = + b 2x + 1 2(20) + 1 41 x 1 2 3 4 5 6 … x … 20 y GAP
31. And Again 3 11 15 19 23 7 4 4 4 4 y = 4x + b 3 = 4(1) + b - 1 = + b 4x - 1 4(20) - 1 79 x 1 2 3 4 5 6 … x … 20 y GAP
32. One Last Time 3 13 18 23 28 8 5 5 5 5 y = 5x + b 3 = 5(1) + b - 2 = + b 5x - 2 5(20) - 2 98 x 1 2 3 4 5 6 … x … 20 y GAP
33. C’est fini. Good day and good luck. A Senior Citizen Production That’s all folks.
