You've seen that many quantities are related to each other. However, not all of them are directly related. Now you will explore quantities that vary inversely. In inverse variation, one quantity decreases as the other increases.
This powerpoint presentation discusses or talks about the topic or lesson Direct Variations. It also discusses and explains the rules, concepts, steps and examples of Direct Variations.
You've seen that many quantities are related to each other. However, not all of them are directly related. Now you will explore quantities that vary inversely. In inverse variation, one quantity decreases as the other increases.
This powerpoint presentation discusses or talks about the topic or lesson Direct Variations. It also discusses and explains the rules, concepts, steps and examples of Direct Variations.
Mathematics 9 Lesson 4-C: Joint and Combined VariationJuan Miguel Palero
This powerpoint presentation discusses or talks about the topic or lesson Joint and Combined Variations. It also discusses and explains the rules, concepts, steps and examples of Joint and Combined Variation
May this presentation could help you, the pictures here is not mine I get it from YouTube videos, I upload this ppt because
most the ppt here help me a lot in my teaching mathematics. This topics is different kinds variation direct variation, inverse variation, joint variation and combined variation.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
The simplified electron and muon model, Oscillating Spacetime: The Foundation...RitikBhardwaj56
Discover the Simplified Electron and Muon Model: A New Wave-Based Approach to Understanding Particles delves into a groundbreaking theory that presents electrons and muons as rotating soliton waves within oscillating spacetime. Geared towards students, researchers, and science buffs, this book breaks down complex ideas into simple explanations. It covers topics such as electron waves, temporal dynamics, and the implications of this model on particle physics. With clear illustrations and easy-to-follow explanations, readers will gain a new outlook on the universe's fundamental nature.
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
MATATAG CURRICULUM: ASSESSING THE READINESS OF ELEM. PUBLIC SCHOOL TEACHERS I...NelTorrente
In this research, it concludes that while the readiness of teachers in Caloocan City to implement the MATATAG Curriculum is generally positive, targeted efforts in professional development, resource distribution, support networks, and comprehensive preparation can address the existing gaps and ensure successful curriculum implementation.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
it describes the bony anatomy including the femoral head , acetabulum, labrum . also discusses the capsule , ligaments . muscle that act on the hip joint and the range of motion are outlined. factors affecting hip joint stability and weight transmission through the joint are summarized.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
2. Warm Up Solve for y . 1. 3 + y = 2 x 2. 6 x = 3 y Write an equation that describes the relationship. 3. y = 2 x y = 2 x – 3 4. 5. y = 3 x 9 0.5 Solve for x .
5. A recipe for paella calls for 1 cup of rice to make 5 servings. In other words, a chef needs 1 cup of rice for every 5 servings. The equation y = 5 x describes this relationship. In this relationship, the number of servings varies directly with the number of cups of rice.
6. A direct variation is a special type of linear relationship that can be written in the form y = kx , where k is a nonzero constant called the constant of variation.
7. Example 1A: Identifying Direct Variations from Equations Tell whether the equation represents a direct variation. If so, identify the constant of variation. y = 3 x This equation represents a direct variation because it is in the form of y = kx . The constant of variation is 3.
8. 3 x + y = 8 Solve the equation for y. Since 3x is added to y, subtract 3x from both sides. This equation is not a direct variation because it cannot be written in the form y = kx. Example 1B: Identifying Direct Variations from Equations Tell whether the equation represents a direct variation. If so, identify the constant of variation. – 3 x –3 x y = –3 x + 8
9. – 4 x + 3 y = 0 Solve the equation for y. Since –4x is added to 3y, add 4x to both sides. Since y is multiplied by 3, divide both sides by 3. Example 1C: Identifying Direct Variations from Equations Tell whether the equation represents a direct variation. If so, identify the constant of variation. +4 x + 4 x 3 y = 4 x This equation represents a direct variation because it is in the form of y = kx . The constant of variation is .
10. Check It Out! Example 1a 3 y = 4 x + 1 This equation is not a direct variation because it is not written in the form y = kx. Tell whether the equation represents a direct variation. If so, identify the constant of variation.
11. Check It Out! Example 1b 3 x = –4 y Solve the equation for y. – 4 y = 3 x Since y is multiplied by –4, divide both sides by –4. Tell whether the equation represents a direct variation. If so, identify the constant of variation. This equation represents a direct variation because it is in the form of y = kx . The constant of variation is .
12. Check It Out! Example 1c y + 3 x = 0 Solve the equation for y. Since 3x is added to y, subtract 3x from both sides. This equation represents a direct variation because it is in the form of y = kx . The constant of variation is –3. Tell whether the equation represents a direct variation. If so, identify the constant of variation. – 3 x –3 x y = –3 x
13. What happens if you solve y = kx for k ? y = kx Divide both sides by x (x ≠ 0). So, in a direct variation, the ratio is equal to the constant of variation. Another way to identify a direct variation is to check whether is the same for each ordered pair (except where x = 0).
14. Example 2A: Identifying Direct Variations from Ordered Pairs Tell whether the relationship is a direct variation. Explain. Method 1 Write an equation. y = 3 x This is direct variation because it can be written as y = kx, where k = 3. Each y-value is 3 times the corresponding x-value.
15. Example 2A Continued Tell whether the relationship is a direct variation. Explain. Method 2 Find for each ordered pair. This is a direct variation because is the same for each ordered pair.
16. Method 1 Write an equation. y = x – 3 Each y-value is 3 less than the corresponding x-value. This is not a direct variation because it cannot be written as y = kx. Example 2B: Identifying Direct Variations from Ordered Pairs Tell whether the relationship is a direct variation. Explain.
17. Method 2 Find for each ordered pair. This is not direct variation because is the not the same for all ordered pairs. Example 2B Continued Tell whether the relationship is a direct variation. Explain. …
18. Check It Out! Example 2a Tell whether the relationship is a direct variation. Explain. Method 2 Find for each ordered pair. This is not direct variation because is the not the same for all ordered pairs.
19. Tell whether the relationship is a direct variation. Explain. Check It Out! Example 2b Method 1 Write an equation. y = –4 x Each y-value is –4 times the corresponding x-value . This is a direct variation because it can be written as y = kx, where k = –4.
20. Tell whether the relationship is a direct variation. Explain. Check It Out! Example 2c Method 2 Find for each ordered pair. This is not direct variation because is the not the same for all ordered pairs.
21. Example 3: Writing and Solving Direct Variation Equations The value of y varies directly with x , and y = 3, when x = 9. Find y when x = 21. Method 1 Find the value of k and then write the equation. y = k x Write the equation for a direct variation. 3 = k (9) Substitute 3 for y and 9 for x. Solve for k. Since k is multiplied by 9, divide both sides by 9. The equation is y = x . When x = 21 , y = (21) = 7.
22. The value of y varies directly with x , and y = 3 when x = 9. Find y when x = 21. Method 2 Use a proportion. 9 y = 63 y = 7 Use cross products. Since y is multiplied by 9 divide both sides by 9. Example 3 Continued In a direct variation is the same for all values of x and y.
23. Check It Out! Example 3 The value of y varies directly with x , and y = 4.5 when x = 0.5. Find y when x = 10. Method 1 Find the value of k and then write the equation. y = k x Write the equation for a direct variation. 4.5 = k (0.5) Substitute 4.5 for y and 0.5 for x. Solve for k. Since k is multiplied by 0.5, divide both sides by 0.5. The equation is y = 9 x . When x = 10 , y = 9 (10) = 90. 9 = k
24. Check It Out! Example 3 Continued Method 2 Use a proportion. 0.5 y = 45 y = 90 Use cross products. Since y is multiplied by 0.5 divide both sides by 0.5. The value of y varies directly with x , and y = 4.5 when x = 0.5. Find y when x = 10. In a direct variation is the same for all values of x and y.
25. Example 4: Graphing Direct Variations A group of people are tubing down a river at an average speed of 2 mi/h. Write a direct variation equation that gives the number of miles y that the people will float in x hours. Then graph. Step 1 Write a direct variation equation. distance = 2 mi/h times hours y = 2 x
26. Example 4 Continued A group of people are tubing down a river at an average speed of 2 mi/h. Write a direct variation equation that gives the number of miles y that the people will float in x hours. Then graph. Step 2 Choose values of x and generate ordered pairs. x y = 2 x ( x, y ) 0 y = 2 (0) = 0 ( 0 , 0 ) 1 y = 2 (1) = 2 ( 1 , 2 ) 2 y = 2 (2) = 4 ( 2 , 4 )
27. A group of people are tubing down a river at an average speed of 2 mi/h. Write a direct variation equation that gives the number of miles y that the people will float in x hours. Then graph. Step 3 Graph the points and connect. Example 4 Continued
28. Check It Out! Example 4 The perimeter y of a square varies directly with its side length x . Write a direct variation equation for this relationship. Then graph. Step 1 Write a direct variation equation. perimeter = 4 sides times length y = 4 • x
29. Check It Out! Example 4 Continued Step 2 Choose values of x and generate ordered pairs. The perimeter y of a square varies directly with its side length x . Write a direct variation equation for this relationship. Then graph. x y = 4 x ( x, y ) 0 y = 4 (0) = 0 ( 0 , 0 ) 1 y = 4 (1) = 4 ( 1 , 4 ) 2 y = 4 (2) = 8 ( 2 , 8 )
30. Step 3 Graph the points and connect. Check It Out! Example 4 Continued The perimeter y of a square varies directly with its side length x . Write a direct variation equation for this relationship. Then graph.
31. Lesson Quiz: Part I Tell whether each equation represents a direct variation. If so, identify the constant of variation. 1. 2 y = 6 x yes; 3 2. 3 x = 4 y – 7 no Tell whether each relationship is a direct variation. Explain. 3. 4.
32. Lesson Quiz: Part II 5. The value of y varies directly with x, and y = –8 when x = 20. Find y when x = –4. 1.6 6. Apples cost $0.80 per pound. The equation y = 0.8 x describes the cost y of x pounds of apples. Graph this direct variation. 2 4 6
