The document shows the step-by-step solution to a system of two linear equations with two unknowns, x and y. The system is 20x+58y=176 and -10x-12y=-54. By substitution, the solution is found to be x=3 and y=2.
This document contains 5 math problems involving multiplication and distribution. The first 3 problems ask the student to calculate expressions like 23 × 102, 15 × 98, and 12 × 99. The next problem asks the student to calculate 23 × 8.5 + 23 × 1.5. The final problem is 4.25 × 12 - 4.25 × 2. The second half of the document shows the step-by-step workings and solutions to each of the 5 problems.
This PowerPoint presentation discusses mathematical operations and properties involving addition, multiplication, and exponents. It provides examples of solving equations like 3×12+7×12 using the distributive property. It also reviews solving equations with negative numbers and provides an example reviewing exponent rules for negative one. It concludes with a follow up activity involving another equation to solve.
The document summarizes how to graph linear equations. It discusses:
1) The standard form of a linear equation is Ax + By = C, where A and B are integers with greatest common factor of 1.
2) Linear equations can also be written in y-intercept form as y = mx + b, where y has a coefficient of +1.
3) Examples are given of converting between standard and y-intercept form.
4) The document shows how to graph linear equations by plotting points in a table using the equation to relate x and y values.
The document contains solutions to 5 problems related to computer and network security concepts:
1. It finds the greatest common divisor (GCD) of several pairs of numbers using Euclid's algorithm.
2. It calculates several numbers modulo other numbers.
3. It uses Fermat's theorem to calculate 3201 modulo 11.
4. It performs encryption and decryption of messages using the RSA algorithm with sample public and private keys.
5. Given a cipher text and public key, it decrypts the plain text message using the RSA algorithm.
Pembahasan soal un matematika smp tahun 2014 paket 1-www.olimattohir.blogspot...Mathematics Sport
- The document contains step-by-step solutions to various mathematics problems involving algebra, geometry, trigonometry, and statistics.
- Examples of problems solved include simplifying algebraic expressions, finding missing values in equations, calculating lengths and angles in geometric shapes, determining median and mean of data sets, and calculating probabilities.
- The solutions are presented clearly and systematically with the work shown at each step.
This document provides solutions to 20 problems involving finding patterns in number sequences and calculating sums of sequences. Each problem is presented along with the solution steps. The solutions involve recognizing patterns in the terms and using formulas such as the sum of consecutive integers or the formulas for arithmetic and geometric sequences.
pedagogy of mathematics part ii (numbers and sequence - ex 2.7), numbers and sequences, Std X samacheer Kalvi, Geometric progression, definition of geometric progression, general form of geometric progression, general term of geometric progression,
The document contains a series of multiple choice questions about geometric sequences, exponential functions, solving quadratic equations, and graphing quadratic functions. The questions cover topics like finding the equation that corresponds to a graph, finding the coordinates of the vertex of a quadratic equation, solving quadratic equations by taking the square root of each side, comparing the slopes of linear functions, finding the y-intercept of a function, evaluating a function given an x-value, identifying the next term in a geometric sequence, finding the geometric mean of a sequence, and finding the axis of symmetry and solutions of a quadratic equation.
This document contains 5 math problems involving multiplication and distribution. The first 3 problems ask the student to calculate expressions like 23 × 102, 15 × 98, and 12 × 99. The next problem asks the student to calculate 23 × 8.5 + 23 × 1.5. The final problem is 4.25 × 12 - 4.25 × 2. The second half of the document shows the step-by-step workings and solutions to each of the 5 problems.
This PowerPoint presentation discusses mathematical operations and properties involving addition, multiplication, and exponents. It provides examples of solving equations like 3×12+7×12 using the distributive property. It also reviews solving equations with negative numbers and provides an example reviewing exponent rules for negative one. It concludes with a follow up activity involving another equation to solve.
The document summarizes how to graph linear equations. It discusses:
1) The standard form of a linear equation is Ax + By = C, where A and B are integers with greatest common factor of 1.
2) Linear equations can also be written in y-intercept form as y = mx + b, where y has a coefficient of +1.
3) Examples are given of converting between standard and y-intercept form.
4) The document shows how to graph linear equations by plotting points in a table using the equation to relate x and y values.
The document contains solutions to 5 problems related to computer and network security concepts:
1. It finds the greatest common divisor (GCD) of several pairs of numbers using Euclid's algorithm.
2. It calculates several numbers modulo other numbers.
3. It uses Fermat's theorem to calculate 3201 modulo 11.
4. It performs encryption and decryption of messages using the RSA algorithm with sample public and private keys.
5. Given a cipher text and public key, it decrypts the plain text message using the RSA algorithm.
Pembahasan soal un matematika smp tahun 2014 paket 1-www.olimattohir.blogspot...Mathematics Sport
- The document contains step-by-step solutions to various mathematics problems involving algebra, geometry, trigonometry, and statistics.
- Examples of problems solved include simplifying algebraic expressions, finding missing values in equations, calculating lengths and angles in geometric shapes, determining median and mean of data sets, and calculating probabilities.
- The solutions are presented clearly and systematically with the work shown at each step.
This document provides solutions to 20 problems involving finding patterns in number sequences and calculating sums of sequences. Each problem is presented along with the solution steps. The solutions involve recognizing patterns in the terms and using formulas such as the sum of consecutive integers or the formulas for arithmetic and geometric sequences.
pedagogy of mathematics part ii (numbers and sequence - ex 2.7), numbers and sequences, Std X samacheer Kalvi, Geometric progression, definition of geometric progression, general form of geometric progression, general term of geometric progression,
The document contains a series of multiple choice questions about geometric sequences, exponential functions, solving quadratic equations, and graphing quadratic functions. The questions cover topics like finding the equation that corresponds to a graph, finding the coordinates of the vertex of a quadratic equation, solving quadratic equations by taking the square root of each side, comparing the slopes of linear functions, finding the y-intercept of a function, evaluating a function given an x-value, identifying the next term in a geometric sequence, finding the geometric mean of a sequence, and finding the axis of symmetry and solutions of a quadratic equation.
This document provides examples and rules for working with exponents and polynomials. It begins by showing the step-by-step working of three multiplication problems involving exponents. It then states the product rule for exponents and the rule for raising a power to another power. The document encourages positive thinking and hard work. It ends by having the reader say a phrase aloud together to reinforce a growth mindset towards math.
This document contains a 25 question math practice test for the Indonesian national exam (UN SMA/MA). It includes multiple choice questions on topics like algebra, geometry, trigonometry, and statistics. The questions have detailed explanations for each answer choice. This practice test provides sample problems and explanations to help students prepare for the types of questions on the UN math exam.
This document contains 22 math problems involving simplifying expressions, expanding polynomials, factorizing expressions, solving equations, inequalities, and systems of equations. The problems cover topics like algebra, functions, quadratic equations, simultaneous equations, and formula manipulation. The goal is to practice various revision test questions in Engineering Mathematics 1.
This document contains solutions to 6 math problems:
1) Finding the value of x2 - x + 1 when x = 2
2) Evaluating (a + b - c)(a - b + c) when a = 1, b = 2, c = 3
3) Simplifying (17 - 15)3 using the identity a3 - b3 = (a - b)(a2 + ab + b2)
4) Simplifying a3 - b2/(a-b) when a = 2 and b = -2
5) Simplifying a - b + b2/(1-a+b) when a = -1/2 and b = 3
The Bresenham's line drawing algorithm is an incremental scan conversion algorithm that uses only integer calculations. It works by calculating the difference between the ideal y value and the actual plotted pixel y value at each x value, and determining whether to plot the pixel above or below the line based on whether this difference is positive or negative. The algorithm takes the line endpoints as input, calculates the change in x and y per step, sets an initial decision parameter, and then iteratively plots pixels, updating the decision parameter to determine whether to plot above or below the line at each step.
1. The document contains solutions to problems from chapter 4 of Engineering Electromagnetics by Hayt, Buck. It involves calculating work done, electric fields, electric potentials, and energies for various charge distributions and field configurations.
2. Key steps include using the relations dW=-QE·dL, V=Q/4πε0r, and E=-∇V to solve for requested quantities like work done, potentials, and fields.
3. Calculations are shown for problems involving point charges, line charges, and volume charge distributions using the appropriate expressions for electric field, potential, and integrals over paths or volumes.
The document defines a real-valued function f(x,y) = x + y + x^2y^2 - sqrt(x^2y^2). It asks for the value of f(45,28), which is calculated by substituting x=45 and y=28 into the function. This gives a value of 53+452-sqrt(2025+784), which simplifies to sqrt(2809), or 53.
This document provides equations and calculations for determining the distance between two points. It defines a position vector QP pointing from point P to point Q, and a velocity vector V. It then shows the calculations for the magnitude of QP, the dot product of QP and V, and the distance between points P and V using these vectors. The distance is determined to be 28 based on the given vector components and equations.
The document contains a series of math word problems involving calculations with addition, subtraction, multiplication, division, and order of operations. There are over 100 separate calculations across 11 sections, asking the reader to solve expressions like (3+2)x(5-1)+4, 40-[3+(10-2):2], and (12+2.5)-8. The document provides the calculations and asks the reader to find the answer.
This document provides statistical information and calculations for 5 questions regarding different data sets. For each question, it lists the data, calculates order statistics like median and quartiles, and provides measures of center, spread, and variation for both the population and a sample, including range, variance, standard deviation, and coefficient of variation. It also calculates the mean absolute deviation for each data set.
Factoring 15.3 and 15.4 Grouping and Trial and Errorswartzje
This document discusses various methods for factoring trinomials of the form Ax^2 + Bx + C. It begins by outlining three main methods: trial and error, factoring by grouping, and the box method. It then provides examples of using the factoring by grouping method, demonstrating how to find two numbers whose product is AC and sum is B. The document also covers special cases like factoring the difference of squares using the form A^2 - B^2 = (A-B)(A+B), and factoring perfect square trinomials using the form A^2 + 2AB + B^2 = (A+B)^2. In all, it thoroughly explains the step-by
The document presents examples of cubic numbers from 1 to 10, where each number is the result of multiplying that integer by itself three times. It shows the calculations of 1 x 1 x 1 = 1, 2 x 2 x 2 = 8, and so on up to 10 x 10 x 10 = 1000. It then explains that these numbers resulting from cubing integers from 1 to 10 are called cubic numbers. The document also includes sample code for a basic For loop program to print out the cubic numbers from 1 to 10.
This document discusses factoring perfect-square trinomials, which are expressions of the form a^2x^2 ± 2abx + b^2. It provides examples of factoring different trinomials like x^2 - 49, 9a^2 - 25b^2, and 16x^4 - 64y^2. Readers are instructed to practice factoring additional examples like x^2 - 49, c^2 - 81, 4x^2 - 25, a^2b^2 - 64c^2, and 25x^2 - 121y^2.
The document contains examples of solving problems involving addition, subtraction, multiplication and division of integers. Some key examples include:
- Finding the balance in an account after a deposit and withdrawal.
- Calculating distance traveled east and west and the final position from a starting point.
- Verifying properties like commutativity, associativity and distributivity for operations on integers.
- Solving word problems involving gains, losses, temperature changes represented as positive and negative integers.
This document discusses the advantages and barriers of online marketing as well as opportunities and challenges. It provides an overview of key advantages such as low cost reach of large audiences, donor retention and cultivation opportunities. Barriers include costs, staff resistance, and technological issues. Opportunities discussed include mobile, social network and tablet advertising. Challenges include short attention spans, global competition and low conversion rates. Critical success factors and reasons for the slower evolution of online marketing in India are also examined, including infrastructure, cultural, and regulatory issues.
Recent Trends in Advertising 2012 provides a history of advertising and discusses current trends:
1. Advertising has evolved from early newspaper ads to include TV, radio, online/digital, and new strategies like product placement.
2. In the late 19th century, advertising agencies emerged to help companies develop complete advertising campaigns.
3. New technologies like cable TV, the internet, and social media have created new platforms and opportunities for interactive and embedded advertising.
Present status of advertising industry in indiaMeenal Kapoor
The document provides an overview of the present status and history of the advertising industry in India. It notes that the Indian advertising industry has grown to an estimated value of Rs 300 billion and has recorded 8% growth in 2011. It highlights that the industry has evolved from small-scale to a full-fledged sector that has placed itself on the global map. The top advertising companies in India are discussed and it is mentioned that over 80% of the business comes from Mumbai and Delhi.
The Indian market is changing fast. Internet growth is mainstreaming among the young population of India and the mobile access is growing in leaps and bounds. The pace of change continues to be rapid with digital channels constantly growing in volume and strength. More and More people are going online in India, with more than 200 Million people connected as on December 2013, digital content that they use is playing an ever-growing role in their lives. The focus of this presentation is to give a statistical overview of this market and is a compilation of proprietary data and a lot of research reports on the market. It gives a sense of scale India has seen so far and gives a sense of direction of the scale of what is coming.
India on Internet 2014 is a collectives of all thats happening in the digitally crazy market of India. With 200 Mn+ people on board and over 250 Mn smart phones sold, India is buzzing with the digital invasion like never before. Marketing is changing, Marketers are changing their opinions, brands are rewording their messages to 140 characters, 75% of the time mobile phones are used actions which are not the reasons for its invention. World is colliding, India is truly emerging as one of the top digital super power in the world.
This presentation is a small collective ode to all thats gone by and all that face us.
Digital marketing is marketing that makes use of electronic devices such as computers, tablets, smartphones, cellphones, digital billboards, and game consoles to engage with consumers and other business partners. Internet Marketing is a major component of digital marketing.
This document provides examples and rules for working with exponents and polynomials. It begins by showing the step-by-step working of three multiplication problems involving exponents. It then states the product rule for exponents and the rule for raising a power to another power. The document encourages positive thinking and hard work. It ends by having the reader say a phrase aloud together to reinforce a growth mindset towards math.
This document contains a 25 question math practice test for the Indonesian national exam (UN SMA/MA). It includes multiple choice questions on topics like algebra, geometry, trigonometry, and statistics. The questions have detailed explanations for each answer choice. This practice test provides sample problems and explanations to help students prepare for the types of questions on the UN math exam.
This document contains 22 math problems involving simplifying expressions, expanding polynomials, factorizing expressions, solving equations, inequalities, and systems of equations. The problems cover topics like algebra, functions, quadratic equations, simultaneous equations, and formula manipulation. The goal is to practice various revision test questions in Engineering Mathematics 1.
This document contains solutions to 6 math problems:
1) Finding the value of x2 - x + 1 when x = 2
2) Evaluating (a + b - c)(a - b + c) when a = 1, b = 2, c = 3
3) Simplifying (17 - 15)3 using the identity a3 - b3 = (a - b)(a2 + ab + b2)
4) Simplifying a3 - b2/(a-b) when a = 2 and b = -2
5) Simplifying a - b + b2/(1-a+b) when a = -1/2 and b = 3
The Bresenham's line drawing algorithm is an incremental scan conversion algorithm that uses only integer calculations. It works by calculating the difference between the ideal y value and the actual plotted pixel y value at each x value, and determining whether to plot the pixel above or below the line based on whether this difference is positive or negative. The algorithm takes the line endpoints as input, calculates the change in x and y per step, sets an initial decision parameter, and then iteratively plots pixels, updating the decision parameter to determine whether to plot above or below the line at each step.
1. The document contains solutions to problems from chapter 4 of Engineering Electromagnetics by Hayt, Buck. It involves calculating work done, electric fields, electric potentials, and energies for various charge distributions and field configurations.
2. Key steps include using the relations dW=-QE·dL, V=Q/4πε0r, and E=-∇V to solve for requested quantities like work done, potentials, and fields.
3. Calculations are shown for problems involving point charges, line charges, and volume charge distributions using the appropriate expressions for electric field, potential, and integrals over paths or volumes.
The document defines a real-valued function f(x,y) = x + y + x^2y^2 - sqrt(x^2y^2). It asks for the value of f(45,28), which is calculated by substituting x=45 and y=28 into the function. This gives a value of 53+452-sqrt(2025+784), which simplifies to sqrt(2809), or 53.
This document provides equations and calculations for determining the distance between two points. It defines a position vector QP pointing from point P to point Q, and a velocity vector V. It then shows the calculations for the magnitude of QP, the dot product of QP and V, and the distance between points P and V using these vectors. The distance is determined to be 28 based on the given vector components and equations.
The document contains a series of math word problems involving calculations with addition, subtraction, multiplication, division, and order of operations. There are over 100 separate calculations across 11 sections, asking the reader to solve expressions like (3+2)x(5-1)+4, 40-[3+(10-2):2], and (12+2.5)-8. The document provides the calculations and asks the reader to find the answer.
This document provides statistical information and calculations for 5 questions regarding different data sets. For each question, it lists the data, calculates order statistics like median and quartiles, and provides measures of center, spread, and variation for both the population and a sample, including range, variance, standard deviation, and coefficient of variation. It also calculates the mean absolute deviation for each data set.
Factoring 15.3 and 15.4 Grouping and Trial and Errorswartzje
This document discusses various methods for factoring trinomials of the form Ax^2 + Bx + C. It begins by outlining three main methods: trial and error, factoring by grouping, and the box method. It then provides examples of using the factoring by grouping method, demonstrating how to find two numbers whose product is AC and sum is B. The document also covers special cases like factoring the difference of squares using the form A^2 - B^2 = (A-B)(A+B), and factoring perfect square trinomials using the form A^2 + 2AB + B^2 = (A+B)^2. In all, it thoroughly explains the step-by
The document presents examples of cubic numbers from 1 to 10, where each number is the result of multiplying that integer by itself three times. It shows the calculations of 1 x 1 x 1 = 1, 2 x 2 x 2 = 8, and so on up to 10 x 10 x 10 = 1000. It then explains that these numbers resulting from cubing integers from 1 to 10 are called cubic numbers. The document also includes sample code for a basic For loop program to print out the cubic numbers from 1 to 10.
This document discusses factoring perfect-square trinomials, which are expressions of the form a^2x^2 ± 2abx + b^2. It provides examples of factoring different trinomials like x^2 - 49, 9a^2 - 25b^2, and 16x^4 - 64y^2. Readers are instructed to practice factoring additional examples like x^2 - 49, c^2 - 81, 4x^2 - 25, a^2b^2 - 64c^2, and 25x^2 - 121y^2.
The document contains examples of solving problems involving addition, subtraction, multiplication and division of integers. Some key examples include:
- Finding the balance in an account after a deposit and withdrawal.
- Calculating distance traveled east and west and the final position from a starting point.
- Verifying properties like commutativity, associativity and distributivity for operations on integers.
- Solving word problems involving gains, losses, temperature changes represented as positive and negative integers.
This document discusses the advantages and barriers of online marketing as well as opportunities and challenges. It provides an overview of key advantages such as low cost reach of large audiences, donor retention and cultivation opportunities. Barriers include costs, staff resistance, and technological issues. Opportunities discussed include mobile, social network and tablet advertising. Challenges include short attention spans, global competition and low conversion rates. Critical success factors and reasons for the slower evolution of online marketing in India are also examined, including infrastructure, cultural, and regulatory issues.
Recent Trends in Advertising 2012 provides a history of advertising and discusses current trends:
1. Advertising has evolved from early newspaper ads to include TV, radio, online/digital, and new strategies like product placement.
2. In the late 19th century, advertising agencies emerged to help companies develop complete advertising campaigns.
3. New technologies like cable TV, the internet, and social media have created new platforms and opportunities for interactive and embedded advertising.
Present status of advertising industry in indiaMeenal Kapoor
The document provides an overview of the present status and history of the advertising industry in India. It notes that the Indian advertising industry has grown to an estimated value of Rs 300 billion and has recorded 8% growth in 2011. It highlights that the industry has evolved from small-scale to a full-fledged sector that has placed itself on the global map. The top advertising companies in India are discussed and it is mentioned that over 80% of the business comes from Mumbai and Delhi.
The Indian market is changing fast. Internet growth is mainstreaming among the young population of India and the mobile access is growing in leaps and bounds. The pace of change continues to be rapid with digital channels constantly growing in volume and strength. More and More people are going online in India, with more than 200 Million people connected as on December 2013, digital content that they use is playing an ever-growing role in their lives. The focus of this presentation is to give a statistical overview of this market and is a compilation of proprietary data and a lot of research reports on the market. It gives a sense of scale India has seen so far and gives a sense of direction of the scale of what is coming.
India on Internet 2014 is a collectives of all thats happening in the digitally crazy market of India. With 200 Mn+ people on board and over 250 Mn smart phones sold, India is buzzing with the digital invasion like never before. Marketing is changing, Marketers are changing their opinions, brands are rewording their messages to 140 characters, 75% of the time mobile phones are used actions which are not the reasons for its invention. World is colliding, India is truly emerging as one of the top digital super power in the world.
This presentation is a small collective ode to all thats gone by and all that face us.
Digital marketing is marketing that makes use of electronic devices such as computers, tablets, smartphones, cellphones, digital billboards, and game consoles to engage with consumers and other business partners. Internet Marketing is a major component of digital marketing.
Online marketing involves promoting products and services over the Internet. It includes various digital marketing channels like email, search engine marketing, display ads, social media, and more. Effective online marketing requires building an email list, writing great content, using social media to drive people to the website, and optimizing paid search ads. Measurement of online marketing efforts is also important.
The document defines a real-valued function f(x,y) = x + y + x^2y^2 - sqrt(x^2y^2). It asks for the value of f(45,28), which is calculated by substituting x=45 and y=28 into the function. The value is found to be 53 + 452 - sqrt(2025 + 784) = sqrt(2809). A common mistake is to incorrectly simplify the square root term.
College algebra in context 5th edition harshbarger solutions manualAnnuzzi19
The document discusses solutions to exercises from a College Algebra textbook. It provides the steps to solve 16 different math equations involving variables like x and t. The equations use concepts like linear models, properties of equality, and combining like terms. Solutions are found by applying division, multiplication, addition or subtraction properties, or graphing the equations to find the intersection point of the lines.
College algebra real mathematics real people 7th edition larson solutions manualJohnstonTBL
This document contains information about the College Algebra Real Mathematics Real People 7th Edition Larson textbook including:
- A link to download the solutions manual and test bank for the textbook
- An overview of the content covered in Chapter 2 on solving equations and inequalities, including linear equations, identities, conditionals, and more.
- 51 example problems from Chapter 2 with step-by-step solutions.
1) The document provides examples of solving linear equations with one variable. It includes solving equations by isolating the variable, combining like terms, and distributing.
2) Examples are given for solving multi-step equations, equations with variables on both sides, equations with fractions, and equations with decimals.
3) The document also discusses cases where an equation has no solution or infinitely many solutions.
This document introduces integration with limits. It shows how to integrate simple functions without limits and with limits. When integrating with limits, the function is integrated as normal and then the upper and lower limits are substituted and subtracted, with no need for the +c term. Several examples integrate functions from limits of 1 to various numbers to demonstrate this process. The key question asks to find the value of a if the integral of (2x + 6) from 0 to a equals 27.
15.2 solving systems of equations by substitutionGlenSchlee
This document provides examples for solving systems of linear equations by substitution. It begins with an example showing the step-by-step process for solving a system using substitution. Subsequent examples demonstrate how to solve special systems that have no solution, infinitely many solutions, and systems with fractions or decimals. The final example walks through solving a system with fractions using clear fractions before substitution.
Rational expressions are fractions where the numerator and denominator are polynomials. To simplify rational expressions, we first factor the polynomials and then cancel any common factors. Adding and subtracting rational expressions follows the same process as fractions - find the least common denominator, multiply the numerators and denominators to get the same denominator, then add or subtract the numerators. Multiplying rational expressions involves factoring and cancelling common factors between the numerator and denominator. To divide rational expressions, we multiply the first expression by the reciprocal of the second expression and then factor and cancel. Word problems involving rational expressions can be solved by identifying what is known and unknown, setting up equations relating the known and unknown values, and then solving the equations.
09.30.2019 to 10.03.2019 Polynomials Algebra111 I.pptxMariaDorisBorja
This document contains an agenda and lesson plan for teaching polynomials. The agenda includes a number sense routine, introduction video, Cornell notes on arithmetic operations of polynomials, elbow partner activity, and ticket out the door. The lesson plan discusses polynomial vocabulary, modeling polynomials with algebra tiles, simplifying polynomials by combining like terms, and performing addition, subtraction, multiplication, and division on polynomials. It provides examples and guided practice problems for students to work through each type of polynomial operation.
factoring and the other ones polynomials2.pptScience18
The document discusses various methods for factoring polynomials:
1) Factoring out the greatest common factor (GCF) of each term.
2) Using the difference of squares formula a2 - b2 = (a + b)(a - b).
3) Grouping terms to produce common binomial factors.
4) Reversing the FOIL process to factor trinomials of the form x2 + bx + c.
5) Factoring polynomials completely by factoring out the GCF and then factoring the remaining terms.
This document provides information and examples on multiplying polynomials, including:
1) Multiplying a monomial and polynomial using the distributive property.
2) Multiplying two polynomials using both the horizontal and vertical methods.
3) Factoring trinomials and identifying similar and conjugate binomials. Methods like FOIL and grouping are discussed.
This is a lesson on the introduction about polynomials. This can help students to understand the basic terms needed to understand polynomials and all operations applied to polynomials
This document reviews concepts from Chapter 1 including:
- Calculating the distance between two points using the distance formula.
- Finding the midpoint and slope of a line between two points.
- Writing equations of lines in different forms such as slope-intercept, point-slope, and intercept forms.
- Solving quadratic equations by factoring, using the quadratic formula, and by completing the square.
- Identifying the vertex and line of symmetry of quadratic functions.
The document discusses methods for solving simultaneous linear equations, including elimination and substitution.
It provides examples of using elimination by adding or subtracting equations to remove a variable, and substitution by making one variable the subject of an equation and substituting it into the other equation. Fractions are converted to simple linear equations by finding a common denominator. The document also covers solving simultaneous equations when one equation is quadratic using substitution after making one variable the subject of the linear equation.
This document discusses solving polynomials using various numerical approximation methods and finding real roots. It provides examples of:
1) Finding the real roots of a cubic polynomial using numerical methods and comparing to the exact solution;
2) Approximating roots of a polynomial using the bisection method and comparing approximations to exact solutions;
3) Finding possible real roots of a quartic polynomial and approximating them using the bisection method.
This document provides examples and explanations of operations involving polynomials and rational expressions. It covers factoring polynomials, evaluating polynomial expressions, adding, subtracting, multiplying and dividing rational expressions, and simplifying complex fractions and expressions with radicals. Step-by-step solutions are shown for problems such as factoring expressions, evaluating polynomials for given values, combining like rational expressions, rationalizing denominators, and more. The document demonstrates various techniques for working with polynomials and rational expressions.
This document provides instructions on how to solve systems of linear equations using the linear combination method, also known as the elimination method or add/subtract method. It gives examples of using this method to solve systems by eliminating a variable through adding or subtracting the equations. Practice problems are provided for the reader to solve systems of equations using the linear combination method.
Addition and subtraction of polynomialsjesus abalos
The document provides information about adding and subtracting algebraic expressions:
- Like terms are algebraic expressions with the same variables and exponents.
- Unlike terms cannot be combined.
- To add algebraic expressions, combine like terms by adding the coefficients.
- To subtract expressions, change the sign of the second expression and then add as if adding.
(1) To square a binomial like (a + b)2, use the formula a2 + 2ab + b2. To square a difference like (a - b)2, use the formula a2 - 2ab + b2.
(2) The product of two binomials of the form (a + b)(a - b) is a2 - b2.
(3) Worked examples are provided to square binomials and multiply the sum and difference of the same two terms, along with practice problems for students to try.
Here are the steps to solve this equation by factorising:
1) Factorise the left hand side: 3(x - 1)(x + 2)
2) Set each factor equal to 0:
x - 1 = 0
x + 2 = 0
3) Solve for x:
x = 1
x = -2
Therefore, the solutions are x = 1 or x = -2.
O documento descreve a história da informática e sua evolução desde o ábaco chinês até os computadores modernos, destacando marcos como a máquina de somar de Pascal, as máquinas de Babbage, o ENIAC, o transistor e o microprocessador.
O documento resume a história da informática desde as máquinas mecânicas até a quinta geração de computadores. Começa com a máquina de somar de Pascal no século 17 e descreve as primeiras quatro gerações de computadores, desde os eletromecânicos até os baseados em circuitos integrados. Conclui perguntando sobre os próximos passos e mencionando a computação óptica, biológica e quântica como possibilidades para a quinta geração.
1. Os estudantes são bem-vindos à primeira semana do curso Ambientação em Educação a Distância, que discutirá os conceitos básicos de EaD.
2. Serão apresentados os objetivos do curso, como identificar os conceitos de EaD e conhecer a dinâmica do ambiente virtual de aprendizagem.
3. As primeiras atividades incluem a apresentação dos estudantes no perfil virtual e troca de mensagens, visando a integração do grupo.
O documento discute a evolução do conceito e da natureza do trabalho ao longo da história. Começa analisando as origens latinas da palavra trabalho e sua associação com sofrimento. Explora como o trabalho foi se transformando com a agricultura, industrialização e capitalismo, passando a ser visto como uma atividade central e produtiva para a sociedade. Finalmente, discute as mais recentes transformações flexíveis no mundo do trabalho.
O documento descreve a forma e os movimentos da Terra. A Terra é redonda mas levemente achatada nos pólos, e realiza um movimento de rotação em torno do seu eixo e um movimento de translação em torno do Sol, completando um ano. A inclinação do eixo da Terra causa as estações do ano.
O documento discute os conceitos fundamentais da administração da produção, incluindo: (1) a definição de produção e seu papel central nas organizações, (2) casos de sucesso como a IKEA, (3) os tipos de processos, entradas e saídas na produção, e (4) as responsabilidades da função de produção.
O documento discute conceitos, funções e objetivos dos sistemas de produção. Apresenta os conceitos de sistemas de produção, suas funções centrais e de apoio, e classificações dos sistemas de acordo com a atividade econômica e função. Também aborda os subsistemas dentro da categorização funcional e características de diferentes tipos de operações produtivas.
O documento discute os conceitos e evolução histórica da administração da produção/operações. Apresenta os principais conceitos como gerentes de produção, tipos de produção, sistemas de produção e pessoas-chave na história da gestão de operações. Também discute novos conceitos como just-in-time, engenharia simultânea e objetivos da administração da produção/operações como organização eficiente da produção.
Entenda como a cultura digital está presente na BNCC _ Planneta Educação.pdfJunior Oliveira
A BNCC inclui a cultura digital como uma competência essencial. Isso significa que as escolas devem ensinar estudantes a usar tecnologia de forma crítica, significativa e ética. Algumas sugestões incluem aulas de programação, design gráfico e edição de vídeos para ajudar os alunos a dominar o universo digital e produzir conteúdo útil.
O documento discute a história da computação, abordando: 1) A máquina de Turing como o computador mais simples, necessitando de apenas um tipo de instrução; 2) A evolução dos computadores, desde máquinas de contar primitivas até máquinas mecânicas de calcular nos séculos XVII-XVIII; 3) O computador a papel como recurso didático para ensinar conceitos básicos de computação.
O documento discute a evolução das tecnologias da informação e comunicação (TIC) e seu papel no mundo moderno. Aborda conceitos como computador, informática, informação digital e tecnologias de informação e comunicação. Também discute ergonomia no ambiente de trabalho e a importância de se ajustar postura e equipamentos para evitar fadiga.
O documento discute como a educação está se adaptando à era digital. Alguns pontos principais são: (1) A tecnologia está cada vez mais acessível ao público, mas nem todas as escolas possuem recursos tecnológicos; (2) Projetos como o da escola Rocinha no Rio de Janeiro mostram como a tecnologia pode melhorar o ensino quando cada aluno tem acesso a um computador; (3) É importante garantir que professores estejam preparados para usar tecnologia de forma a beneficiar a aprendizagem.
O documento discute como desenvolver a competência digital de professores e alunos através da integração de tecnologias digitais no ensino. Ele propõe 1) conectividade e aprendizagem com o uso de ferramentas digitais, 2) formação de professores focada em desenvolver competência digital, implementar a Base Curricular Comum e melhorar o IDEB, 3) uso de aplicativos e plataformas digitais para apoiar diferentes métodos de ensino como sala invertida.
1) O documento descreve as principais funções da Química Inorgânica: ácidos, bases, sais e óxidos.
2) Sais são compostos iônicos formados por um cátion e um ânion, exceto H+ e OH-. Sua nomenclatura é dada pelo nome do ânion e cátion.
3) Ácidos são substâncias que liberam íons hidrogênio na água, tendo sabor azedo. Sua nomenclatura leva em conta o ânion.
Substância, matéria, corpo e objeto o que sãoJunior Oliveira
O documento explica conceitos básicos de matéria, corpo, objeto e substância. Matéria é tudo que ocupa espaço, podendo ser visível como plantas ou invisível como o ar. Corpo é uma porção limitada de matéria, como água ou pedra. Objeto é um corpo transformado pelo ser humano, como uma cadeira de madeira. Substâncias são formadas por moléculas iguais, como a água ou o ouro.
1) O documento apresenta um caderno de apoio à aprendizagem de Química para a 1a série do Ensino Médio.
2) Aborda reações químicas, leis ponderais, balanceamento de equações e teoria ácido-base.
3) Foi elaborado por uma equipe de professores da rede estadual de educação da Bahia para auxiliar estudantes e professores no período de suspensão de aulas devido à pandemia.
O documento apresenta informações sobre os Cadernos de Apoio à Aprendizagem de Química para a 1a série do Ensino Médio da rede estadual de ensino da Bahia. O sumário descreve que o material foi elaborado por uma equipe de professores durante a pandemia para apoiar docentes e estudantes no processo de retomada das aulas presenciais. Além disso, o documento traz informações sobre as unidades, temas e atividades propostas nos cadernos, com foco em ligação iônica, ligação covalente e forças
1. O documento apresenta os Cadernos de Apoio à Aprendizagem de Química para a 1a série do Ensino Médio, elaborados por professores da rede estadual da Bahia durante a suspensão das aulas presenciais devido à pandemia.
2. Os Cadernos visam apoiar docentes e estudantes na retomada das atividades letivas, facilitando a conciliação dos tempos e espaços de aprendizagem de forma articulada com outras ações pedagógicas.
3. O governador da Bahia
How to Add Chatter in the odoo 17 ERP ModuleCeline George
In Odoo, the chatter is like a chat tool that helps you work together on records. You can leave notes and track things, making it easier to talk with your team and partners. Inside chatter, all communication history, activity, and changes will be displayed.
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.
Assessment and Planning in Educational technology.pptxKavitha Krishnan
In an education system, it is understood that assessment is only for the students, but on the other hand, the Assessment of teachers is also an important aspect of the education system that ensures teachers are providing high-quality instruction to students. The assessment process can be used to provide feedback and support for professional development, to inform decisions about teacher retention or promotion, or to evaluate teacher effectiveness for accountability purposes.
This presentation was provided by Steph Pollock of The American Psychological Association’s Journals Program, and Damita Snow, of The American Society of Civil Engineers (ASCE), for the initial session of NISO's 2024 Training Series "DEIA in the Scholarly Landscape." Session One: 'Setting Expectations: a DEIA Primer,' was held June 6, 2024.
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 slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
How to Build a Module in Odoo 17 Using the Scaffold MethodCeline George
Odoo provides an option for creating a module by using a single line command. By using this command the user can make a whole structure of a module. It is very easy for a beginner to make a module. There is no need to make each file manually. This slide will show how to create a module using the scaffold method.
Thinking of getting a dog? Be aware that breeds like Pit Bulls, Rottweilers, and German Shepherds can be loyal and dangerous. Proper training and socialization are crucial to preventing aggressive behaviors. Ensure safety by understanding their needs and always supervising interactions. Stay safe, and enjoy your furry friends!
This presentation includes basic of PCOS their pathology and treatment and also Ayurveda correlation of PCOS and Ayurvedic line of treatment mentioned in classics.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
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.