This document presents a system of linear equations involving costs of chicken and cheese sandwiches at a sandwich shop. It can be solved using substitution to determine that chicken sandwiches are $1 more expensive than cheese sandwiches.
Ch 3 test (text) unit 3 test (text) unit 3 handoutRyanWatt
The document discusses the benefits of meditation for reducing stress and anxiety. Regular meditation practice can help calm the mind and body by lowering heart rate and blood pressure. Studies have shown that meditating for just 10-20 minutes per day can have significant positive impacts on both mental and physical health.
This document discusses factors that affect the collection of survey data, including bias, language use, cost, ethics, cultural sensitivity, and timing. It provides examples of good and bad survey questions and identifies issues like influencing responses, understandability, appropriateness, privacy, offense, and influence of survey timing. The purpose is to help readers identify issues with survey questions and create effective surveys.
This document provides a checklist for multiplying and dividing polynomials. It includes modeling multiplication and division using algebra tiles and area models, writing the multiplication and division statements, simplifying expressions without models, and solving word problems involving polynomial operations. Examples are provided for each step, such as modeling -2x(3x - 2) with area and tile models and simplifying 3x(-2x + 4).
The document defines and explains key concepts regarding quadratic functions including:
- The three common forms of quadratic functions: general, vertex, and factored form
- How to find the x-intercepts, y-intercept, and vertex of a quadratic function
- Methods for solving quadratic equations including factoring, completing the square, and the quadratic formula
- How to graph quadratic functions by identifying intercepts and the vertex
Ch 3 test (text) unit 3 test (text) unit 3 handoutRyanWatt
The document discusses the benefits of meditation for reducing stress and anxiety. Regular meditation practice can help calm the mind and body by lowering heart rate and blood pressure. Studies have shown that meditating for just 10-20 minutes per day can have significant positive impacts on both mental and physical health.
This document discusses factors that affect the collection of survey data, including bias, language use, cost, ethics, cultural sensitivity, and timing. It provides examples of good and bad survey questions and identifies issues like influencing responses, understandability, appropriateness, privacy, offense, and influence of survey timing. The purpose is to help readers identify issues with survey questions and create effective surveys.
This document provides a checklist for multiplying and dividing polynomials. It includes modeling multiplication and division using algebra tiles and area models, writing the multiplication and division statements, simplifying expressions without models, and solving word problems involving polynomial operations. Examples are provided for each step, such as modeling -2x(3x - 2) with area and tile models and simplifying 3x(-2x + 4).
The document defines and explains key concepts regarding quadratic functions including:
- The three common forms of quadratic functions: general, vertex, and factored form
- How to find the x-intercepts, y-intercept, and vertex of a quadratic function
- Methods for solving quadratic equations including factoring, completing the square, and the quadratic formula
- How to graph quadratic functions by identifying intercepts and the vertex
The document defines various terms related to circle geometry such as radius, diameter, chord, tangent, arc, and angle. It then lists 10 rules of circle geometry pertaining to angles, chords, tangents, and polygons. Finally, it provides some practice questions and links for additional resources on circle geometry concepts.
Algebra Electronic Presentation Expert Voices F I N A LRyanWatt
This document provides an overview of various algebra topics including absolute values, solving quadratic equations by completing the square, using the quadratic formula, generating equations given roots, determining the nature of roots using the discriminant, solving rational equations, and solving radical equations. Examples and practice problems are provided for each topic along with worked out solutions. Relevant websites with additional resources on these algebra topics are also listed.
This document provides information about various trigonometry concepts including reference angles, trigonometric equations, periodic functions, and ambiguous triangle cases. It defines reference angles as the angle measured from the initial side to the terminal side. It explains how to find reference angles based on the quadrant the main angle is in. It also defines trigonometric equations as equations involving trig functions of unknown angles and provides steps to solve them using factoring or the quadratic formula. The document also discusses periodic functions by defining their equation components and important points over one period. Finally, it reviews formulas for ambiguous triangle cases like the Pythagorean theorem, SOHCAHTOA, and sine/cosine laws.
The document discusses graphs of functions and points of discontinuity. It provides an example of the function h(x) = (x^2 - 4) / (x+2) and instructs the reader to sketch its graph, noting that it will have points of discontinuity where the denominator is equal to zero. The reader is also directed to exercises 1, 4, and 5 on page 125 to complete.
The document discusses graphing rational functions of the form f(x) = a(x)/b(x), where a(x) and b(x) are polynomial functions. It provides examples of how the graphs appear depending on whether the degree of the numerator is even or odd. A 7-step process is outlined for sketching the graphs, which involves finding intercepts, roots, vertical asymptotes, horizontal asymptotes, and the sign of the function to sketch the graph. Two examples applying the 7-step method are shown.
The document discusses the remainder theorem in polynomials, which states that the remainder of dividing a polynomial P(x) by a binomial x - a is equal to P(a). It provides an example of using synthetic division and the remainder theorem to find the remainder, and notes that if the remainder is 0, then the binomial is a factor of the original polynomial. The document also gives an example problem of determining the value of k when dividing a polynomial by a binomial that gives a remainder of 1.
The document describes synthetic division, a shortcut method for dividing polynomials when the divisor is a binomial of the form x ± a. It explains that synthetic division involves arranging the coefficients of the dividend polynomial in descending order of power and using an algorithm to solve for the quotient and remainder. An example is worked through to demonstrate the steps of synthetic division. Readers are instructed to use both long division and synthetic division to find the quotient and remainder of given polynomial divisions, and to check that the same answers are obtained with both methods.
The document discusses composite functions and their domains but provides no actual functions or domains to analyze. It begins discussing composite functions and domains but does not give any examples of specific functions or their domains to examine. The document appears to be incomplete as it does not include the essential information needed to summarize composite functions and their domains.
This document contains multiple math word problems involving scale factors, similarity of shapes, and geometric calculations. Questions ask about determining scale factors used to enlarge or reduce drawings, finding lengths and heights using scale diagrams, calculating total distances given scale information, showing similarity of triangles, and finding missing side lengths of similar shapes. The problems cover a range of geometry and scaling concepts tested on a math assessment.
The document discusses how to sketch graphs of polynomial functions. It explains that for odd degree polynomials, the graph behavior is opposite on the left and right sides, while for even degree polynomials the behavior is similar on both sides. It provides examples of how the graphs of cubic, quartic and quintic polynomials will appear. It outlines steps for sketching a polynomial graph which include finding the y-intercept, roots, sign of the function over intervals, and then sketching the graph. An example problem is given to factor a polynomial and sketch its graph.
The document discusses two theorems for factoring polynomials:
1) The Factor Theorem states that a polynomial P(x) will have a factor (x - a) if P(a) equals 0.
2) The Rational Roots Theorem provides a procedure to find all possible rational roots of a polynomial by considering the factors of the leading coefficient and constant term. The procedure involves listing potential rational roots and using synthetic division or factoring to determine the actual roots.
The document discusses inverse functions. It defines an inverse function as switching the x's and y's in a function's ordered pairs. If this inversion results in another function, it is called the inverse function. The domain of the original function becomes the range of the inverse function, and vice versa. It provides examples of finding the expressions for inverse functions and checking if they are correct inverses. It also discusses the differences between one-to-one and many-to-one functions, and uses the horizontal line test to determine which is being graphed. Exercises are provided to find specific inverse functions.
Polygons are similar when they have equal corresponding angles and proportional corresponding sides. Two polygons are given as examples of similar polygons - a triangle and a square. The document then provides examples of similar and non-similar polygons and asks the reader to identify which are similar by setting up proportions of corresponding sides and finding missing side lengths. The reader is directed to read specific pages and complete selected questions.
This document defines and provides examples of functions. It discusses:
- Functions are relations where each input has exactly one output
- The vertical line test to determine if a relation is a function
- Common operations on functions like addition, subtraction, multiplication, and division
- Composite functions which take the output of one function as the input of another
- Examples of evaluating composite functions and performing operations on functions
The document provides examples of simple interest rate calculations and questions. It defines the simple interest formula as I = Prt, where I is interest, P is principal, r is interest rate as a decimal, and t is time in years. It then gives examples of calculating interest for different principal amounts invested or borrowed at various rates and times. It omits questions 2b, 5, 6, and 8 from the set of exercises.
Sam invests $5000 at an interest rate of 5% compounded annually. Using the compound interest formula, the summary calculates how much Sam's investment will be worth after 5 years. The document also provides an example of Byron borrowing $10,000 from Erick at an interest rate of 3.5% compounded annually, and calculates how much Byron will pay back after 2 months using the same formula. It includes the compound interest formula and defines the terms used.
The document provides reasoning to show that a car was built after 1990 based on the presence of an mp3 player. It does this by:
1) Examining the conclusion that the car was built after 1990.
2) Assuming the opposite, that the car was built before 1990.
3) Developing a contradictory statement using logic - that if built before 1990 it would not have an mp3 player, but it does, so it must have been built after 1990.
The document summarizes inductive and deductive reasoning. Inductive reasoning involves finding general patterns or principles based on specific examples, while deductive reasoning involves drawing logical conclusions based on known statements or facts. It then provides examples of inductive and deductive reasoning, and asks the reader to identify whether each example is valid or not. Finally, it discusses logical statements such as conditionals, converses, inverses, and contrapositives.
1. The document discusses logical statements and their components including conditional statements with hypotheses and conclusions.
2. It provides examples of different types of logical statements including the converse, which interchanges the hypothesis and conclusion; the contrapositive, which reverses and negates both parts; and the inverse, which negates both parts but does not change their order.
3. Not all converses of true statements are necessarily true themselves.
The document defines various terms related to circle geometry such as radius, diameter, chord, tangent, arc, and angle. It then lists 10 rules of circle geometry pertaining to angles, chords, tangents, and polygons. Finally, it provides some practice questions and links for additional resources on circle geometry concepts.
Algebra Electronic Presentation Expert Voices F I N A LRyanWatt
This document provides an overview of various algebra topics including absolute values, solving quadratic equations by completing the square, using the quadratic formula, generating equations given roots, determining the nature of roots using the discriminant, solving rational equations, and solving radical equations. Examples and practice problems are provided for each topic along with worked out solutions. Relevant websites with additional resources on these algebra topics are also listed.
This document provides information about various trigonometry concepts including reference angles, trigonometric equations, periodic functions, and ambiguous triangle cases. It defines reference angles as the angle measured from the initial side to the terminal side. It explains how to find reference angles based on the quadrant the main angle is in. It also defines trigonometric equations as equations involving trig functions of unknown angles and provides steps to solve them using factoring or the quadratic formula. The document also discusses periodic functions by defining their equation components and important points over one period. Finally, it reviews formulas for ambiguous triangle cases like the Pythagorean theorem, SOHCAHTOA, and sine/cosine laws.
The document discusses graphs of functions and points of discontinuity. It provides an example of the function h(x) = (x^2 - 4) / (x+2) and instructs the reader to sketch its graph, noting that it will have points of discontinuity where the denominator is equal to zero. The reader is also directed to exercises 1, 4, and 5 on page 125 to complete.
The document discusses graphing rational functions of the form f(x) = a(x)/b(x), where a(x) and b(x) are polynomial functions. It provides examples of how the graphs appear depending on whether the degree of the numerator is even or odd. A 7-step process is outlined for sketching the graphs, which involves finding intercepts, roots, vertical asymptotes, horizontal asymptotes, and the sign of the function to sketch the graph. Two examples applying the 7-step method are shown.
The document discusses the remainder theorem in polynomials, which states that the remainder of dividing a polynomial P(x) by a binomial x - a is equal to P(a). It provides an example of using synthetic division and the remainder theorem to find the remainder, and notes that if the remainder is 0, then the binomial is a factor of the original polynomial. The document also gives an example problem of determining the value of k when dividing a polynomial by a binomial that gives a remainder of 1.
The document describes synthetic division, a shortcut method for dividing polynomials when the divisor is a binomial of the form x ± a. It explains that synthetic division involves arranging the coefficients of the dividend polynomial in descending order of power and using an algorithm to solve for the quotient and remainder. An example is worked through to demonstrate the steps of synthetic division. Readers are instructed to use both long division and synthetic division to find the quotient and remainder of given polynomial divisions, and to check that the same answers are obtained with both methods.
The document discusses composite functions and their domains but provides no actual functions or domains to analyze. It begins discussing composite functions and domains but does not give any examples of specific functions or their domains to examine. The document appears to be incomplete as it does not include the essential information needed to summarize composite functions and their domains.
This document contains multiple math word problems involving scale factors, similarity of shapes, and geometric calculations. Questions ask about determining scale factors used to enlarge or reduce drawings, finding lengths and heights using scale diagrams, calculating total distances given scale information, showing similarity of triangles, and finding missing side lengths of similar shapes. The problems cover a range of geometry and scaling concepts tested on a math assessment.
The document discusses how to sketch graphs of polynomial functions. It explains that for odd degree polynomials, the graph behavior is opposite on the left and right sides, while for even degree polynomials the behavior is similar on both sides. It provides examples of how the graphs of cubic, quartic and quintic polynomials will appear. It outlines steps for sketching a polynomial graph which include finding the y-intercept, roots, sign of the function over intervals, and then sketching the graph. An example problem is given to factor a polynomial and sketch its graph.
The document discusses two theorems for factoring polynomials:
1) The Factor Theorem states that a polynomial P(x) will have a factor (x - a) if P(a) equals 0.
2) The Rational Roots Theorem provides a procedure to find all possible rational roots of a polynomial by considering the factors of the leading coefficient and constant term. The procedure involves listing potential rational roots and using synthetic division or factoring to determine the actual roots.
The document discusses inverse functions. It defines an inverse function as switching the x's and y's in a function's ordered pairs. If this inversion results in another function, it is called the inverse function. The domain of the original function becomes the range of the inverse function, and vice versa. It provides examples of finding the expressions for inverse functions and checking if they are correct inverses. It also discusses the differences between one-to-one and many-to-one functions, and uses the horizontal line test to determine which is being graphed. Exercises are provided to find specific inverse functions.
Polygons are similar when they have equal corresponding angles and proportional corresponding sides. Two polygons are given as examples of similar polygons - a triangle and a square. The document then provides examples of similar and non-similar polygons and asks the reader to identify which are similar by setting up proportions of corresponding sides and finding missing side lengths. The reader is directed to read specific pages and complete selected questions.
This document defines and provides examples of functions. It discusses:
- Functions are relations where each input has exactly one output
- The vertical line test to determine if a relation is a function
- Common operations on functions like addition, subtraction, multiplication, and division
- Composite functions which take the output of one function as the input of another
- Examples of evaluating composite functions and performing operations on functions
The document provides examples of simple interest rate calculations and questions. It defines the simple interest formula as I = Prt, where I is interest, P is principal, r is interest rate as a decimal, and t is time in years. It then gives examples of calculating interest for different principal amounts invested or borrowed at various rates and times. It omits questions 2b, 5, 6, and 8 from the set of exercises.
Sam invests $5000 at an interest rate of 5% compounded annually. Using the compound interest formula, the summary calculates how much Sam's investment will be worth after 5 years. The document also provides an example of Byron borrowing $10,000 from Erick at an interest rate of 3.5% compounded annually, and calculates how much Byron will pay back after 2 months using the same formula. It includes the compound interest formula and defines the terms used.
The document provides reasoning to show that a car was built after 1990 based on the presence of an mp3 player. It does this by:
1) Examining the conclusion that the car was built after 1990.
2) Assuming the opposite, that the car was built before 1990.
3) Developing a contradictory statement using logic - that if built before 1990 it would not have an mp3 player, but it does, so it must have been built after 1990.
The document summarizes inductive and deductive reasoning. Inductive reasoning involves finding general patterns or principles based on specific examples, while deductive reasoning involves drawing logical conclusions based on known statements or facts. It then provides examples of inductive and deductive reasoning, and asks the reader to identify whether each example is valid or not. Finally, it discusses logical statements such as conditionals, converses, inverses, and contrapositives.
1. The document discusses logical statements and their components including conditional statements with hypotheses and conclusions.
2. It provides examples of different types of logical statements including the converse, which interchanges the hypothesis and conclusion; the contrapositive, which reverses and negates both parts; and the inverse, which negates both parts but does not change their order.
3. Not all converses of true statements are necessarily true themselves.
Temple of Asclepius in Thrace. Excavation resultsKrassimira Luka
The temple and the sanctuary around were dedicated to Asklepios Zmidrenus. This name has been known since 1875 when an inscription dedicated to him was discovered in Rome. The inscription is dated in 227 AD and was left by soldiers originating from the city of Philippopolis (modern Plovdiv).
How Barcodes Can Be Leveraged Within Odoo 17Celine George
In this presentation, we will explore how barcodes can be leveraged within Odoo 17 to streamline our manufacturing processes. We will cover the configuration steps, how to utilize barcodes in different manufacturing scenarios, and the overall benefits of implementing this technology.
Chapter wise All Notes of First year Basic Civil Engineering.pptxDenish Jangid
Chapter wise All Notes of First year Basic Civil Engineering
Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
Beyond Degrees - Empowering the Workforce in the Context of Skills-First.pptxEduSkills OECD
Iván Bornacelly, Policy Analyst at the OECD Centre for Skills, OECD, presents at the webinar 'Tackling job market gaps with a skills-first approach' on 12 June 2024
THE SACRIFICE HOW PRO-PALESTINE PROTESTS STUDENTS ARE SACRIFICING TO CHANGE T...indexPub
The recent surge in pro-Palestine student activism has prompted significant responses from universities, ranging from negotiations and divestment commitments to increased transparency about investments in companies supporting the war on Gaza. This activism has led to the cessation of student encampments but also highlighted the substantial sacrifices made by students, including academic disruptions and personal risks. The primary drivers of these protests are poor university administration, lack of transparency, and inadequate communication between officials and students. This study examines the profound emotional, psychological, and professional impacts on students engaged in pro-Palestine protests, focusing on Generation Z's (Gen-Z) activism dynamics. This paper explores the significant sacrifices made by these students and even the professors supporting the pro-Palestine movement, with a focus on recent global movements. Through an in-depth analysis of printed and electronic media, the study examines the impacts of these sacrifices on the academic and personal lives of those involved. The paper highlights examples from various universities, demonstrating student activism's long-term and short-term effects, including disciplinary actions, social backlash, and career implications. The researchers also explore the broader implications of student sacrifices. The findings reveal that these sacrifices are driven by a profound commitment to justice and human rights, and are influenced by the increasing availability of information, peer interactions, and personal convictions. The study also discusses the broader implications of this activism, comparing it to historical precedents and assessing its potential to influence policy and public opinion. The emotional and psychological toll on student activists is significant, but their sense of purpose and community support mitigates some of these challenges. However, the researchers call for acknowledging the broader Impact of these sacrifices on the future global movement of FreePalestine.
This document provides an overview of wound healing, its functions, stages, mechanisms, factors affecting it, and complications.
A wound is a break in the integrity of the skin or tissues, which may be associated with disruption of the structure and function.
Healing is the body’s response to injury in an attempt to restore normal structure and functions.
Healing can occur in two ways: Regeneration and Repair
There are 4 phases of wound healing: hemostasis, inflammation, proliferation, and remodeling. This document also describes the mechanism of wound healing. Factors that affect healing include infection, uncontrolled diabetes, poor nutrition, age, anemia, the presence of foreign bodies, etc.
Complications of wound healing like infection, hyperpigmentation of scar, contractures, and keloid formation.