3.2 Notes A
•
0 likes•258 views
The document provides 3 examples of systems of equations and assigns homework problems from the textbook. Specifically, it gives 3 systems of equations using the addition/elimination method, and assigns homework from page 158 problems 6-11, 20-23, 25, 31 as well as Proof Worksheet #1.
Report
Share
Report
Share
Download to read offline
Recommended
What is Order of Operations?
The document explains the order of operations (PEMDAS) for solving math problems with multiple operations. PEMDAS stands for "Please Excuse My Dear Aunt Sally" and dictates that operations in parentheses, exponents, multiplication/division (left to right), and addition/subtraction (left to right) take precedence from left to right when evaluating expressions. Several examples are provided to demonstrate applying the order of operations to solve multi-step math problems.
GRE QUANT ALGEBRA, PROBABILITY
1) The last digit of 5033,813,273,93,33,54,32,1 is 9 based on the pattern that the last digits of multiples of 4 are 6, 2, 8, and 4.
2) Quantity A is 72. The number of positive integers less than 81 that are not perfect squares is 72, since there are 8 perfect squares between 1 and 81.
3) The probability that managers A and B are both selected from a group of 5 managers where 2 people are randomly selected to attend a conference is 1/10.
Bidmas
The document discusses BIDMAS/BODMAS/PEDMAS, which are acronyms that represent the order of operations in mathematics. It explains that B/P stands for brackets/parentheses, I/O/E/P stands for indices/orders/exponents/powers, D/M stands for division and multiplication, and A/S stands for addition and subtraction. Several practice equations are included to demonstrate applying the proper order of operations. The document also notes that different regions may use varying acronyms but they all refer to the same concept of resolving equations in a set sequence.
Order of Operations (MDAS Rules) Math 4
This document provides an explanation of the order of operations when solving mathematical expressions. It states that multiplication and division should be performed before addition and subtraction, from left to right if these operations are at the same level of precedence. It provides examples of solving expressions step-by-step using the proper order of operations. Finally, it gives practice problems for the reader to solve.
PEMDAS - The Proper Order of Mathematical Operations
The document discusses the proper order of mathematical operations known as PEMDAS. It covers absolute values, addition and subtraction of signed numbers, multiplication and division of signed numbers, and the order of operations using PEMDAS. Examples are provided to illustrate how to use PEMDAS to simplify expressions involving multiple operations. Exercises with answers are included to help readers practice applying these concepts.
Skill31 c writing equation of a line
This document provides instruction on writing the equation of a line given two points. It explains that you need to find the slope (m) using the slope formula, and the y-intercept (b) by substituting a point into the line equation y=mx+b. Several examples are worked through step-by-step to demonstrate this process. First the slope and one point are given, then students are asked to find the full equation. Finally, students are instructed to practice writing the full equation on their own given just two points on a line.
Order Of Operations
The document discusses the order of operations for evaluating mathematical expressions. It provides examples of how to use the PEMDAS/GEMDAS method (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to properly evaluate expressions and get the correct answer. The homework assignment is to practice using the order of operations to evaluate basic algebra expressions.
004#pedagogy math test
The document discusses number patterns and sequences. It provides examples of finite and infinite sequences, with the first being a pattern of numbers increasing by 4 and the second having a missing number of 30. Number patterns establish relationships between numbers and can be used to determine the rules that generate the sequence. Infinite sequences continue indefinitely according to their rule, such as even numbers counting up by 2.
Recommended
What is Order of Operations?
The document explains the order of operations (PEMDAS) for solving math problems with multiple operations. PEMDAS stands for "Please Excuse My Dear Aunt Sally" and dictates that operations in parentheses, exponents, multiplication/division (left to right), and addition/subtraction (left to right) take precedence from left to right when evaluating expressions. Several examples are provided to demonstrate applying the order of operations to solve multi-step math problems.
GRE QUANT ALGEBRA, PROBABILITY
1) The last digit of 5033,813,273,93,33,54,32,1 is 9 based on the pattern that the last digits of multiples of 4 are 6, 2, 8, and 4.
2) Quantity A is 72. The number of positive integers less than 81 that are not perfect squares is 72, since there are 8 perfect squares between 1 and 81.
3) The probability that managers A and B are both selected from a group of 5 managers where 2 people are randomly selected to attend a conference is 1/10.
Bidmas
The document discusses BIDMAS/BODMAS/PEDMAS, which are acronyms that represent the order of operations in mathematics. It explains that B/P stands for brackets/parentheses, I/O/E/P stands for indices/orders/exponents/powers, D/M stands for division and multiplication, and A/S stands for addition and subtraction. Several practice equations are included to demonstrate applying the proper order of operations. The document also notes that different regions may use varying acronyms but they all refer to the same concept of resolving equations in a set sequence.
Order of Operations (MDAS Rules) Math 4
This document provides an explanation of the order of operations when solving mathematical expressions. It states that multiplication and division should be performed before addition and subtraction, from left to right if these operations are at the same level of precedence. It provides examples of solving expressions step-by-step using the proper order of operations. Finally, it gives practice problems for the reader to solve.
PEMDAS - The Proper Order of Mathematical Operations
The document discusses the proper order of mathematical operations known as PEMDAS. It covers absolute values, addition and subtraction of signed numbers, multiplication and division of signed numbers, and the order of operations using PEMDAS. Examples are provided to illustrate how to use PEMDAS to simplify expressions involving multiple operations. Exercises with answers are included to help readers practice applying these concepts.
Skill31 c writing equation of a line
This document provides instruction on writing the equation of a line given two points. It explains that you need to find the slope (m) using the slope formula, and the y-intercept (b) by substituting a point into the line equation y=mx+b. Several examples are worked through step-by-step to demonstrate this process. First the slope and one point are given, then students are asked to find the full equation. Finally, students are instructed to practice writing the full equation on their own given just two points on a line.
Order Of Operations
The document discusses the order of operations for evaluating mathematical expressions. It provides examples of how to use the PEMDAS/GEMDAS method (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to properly evaluate expressions and get the correct answer. The homework assignment is to practice using the order of operations to evaluate basic algebra expressions.
004#pedagogy math test
The document discusses number patterns and sequences. It provides examples of finite and infinite sequences, with the first being a pattern of numbers increasing by 4 and the second having a missing number of 30. Number patterns establish relationships between numbers and can be used to determine the rules that generate the sequence. Infinite sequences continue indefinitely according to their rule, such as even numbers counting up by 2.
Order Of Operations
The document discusses order of operations, which is the order in which mathematical operations should be performed in a problem containing multiple operations. The standard order is: 1) operations within parentheses, 2) exponents, 3) multiplication and division from left to right, 4) addition and subtraction from left to right. It provides examples of solving problems using the proper order of operations and asks readers to try solving sample problems on their own.
Order of Operations (Algebra1 1_2)
The document discusses the order of operations, which is a rule for evaluating mathematical expressions containing multiple operations. It explains that the order of operations is: 1) Evaluate expressions inside grouping symbols (parentheses, brackets, braces) from innermost to outermost. 2) Evaluate exponents. 3) Perform multiplication and division from left to right. 4) Perform addition and subtraction from left to right. Mnemonics like PEMDAS are provided to help remember the order. Examples of applying the order of operations to evaluate expressions are provided.
Dividing integers
The document discusses dividing integers and their rules:
- There are four rules for dividing integers based on the signs of the numbers: two positives or negatives give a positive, opposite signs give a negative.
- Examples are provided to demonstrate applying the rules.
- The mean, or average, of a data set is calculated by summing the values and dividing by the number of values.
- Order of operations must be followed when evaluating expressions.
When math meets microbit
This document discusses using micro:bit to solve math problems involving sequences. It provides an example problem of counting the number of black pieces in a triangular arrangement over 50 layers. This can be solved either through a formula approach as it is an arithmetic sequence, or through a programming approach by observing the pattern and coding the logic. The document demonstrates both approaches, with the formula solution being faster but programming able to solve it without a formula by iterating through loops. The key lessons are that programming helps train logical thinking and problem solving even without memorizing syntax, and both math formulas and coding can be used to arrive at the right solution.
Order of operations Unit3
The document discusses order of operations, which is the standard sequence for performing mathematical calculations involving multiple arithmetic operations. The order is: 1) Perform operations inside parentheses, 2) Evaluate exponents, 3) Perform multiplication and division from left to right, 4) Perform addition and subtraction from left to right. A mnemonic device - PEMDAS - is provided to help remember this sequence: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Examples are given to demonstrate applying order of operations to solve multi-step arithmetic problems step-by-step.
Chapter 1 Study Guide
The document discusses the order of operations (PEMDAS) and provides examples of how to evaluate expressions and solve equations. It explains that parentheses, exponents, multiplication/division from left to right, and addition/subtraction from left to right have precedence based on the PEMDAS acronym. Integers, absolute value, adding, subtracting, multiplying, and dividing integers are also covered along with writing algebraic expressions and solving different types of equations.
Order of operations
The document discusses the order of operations for evaluating numerical expressions. It provides examples of step-by-step evaluations using the PEMDAS mnemonic (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to determine the proper sequence. It also notes that when multiple grouping symbols are present, the expression should be evaluated starting with the innermost grouping symbol working outwards.
Order of operations
The document discusses order of operations, which is the standard sequence for performing mathematical calculations involving multiple arithmetic operations. The order is: 1) operations within parentheses, 2) exponents, 3) multiplication and division from left to right, 4) addition and subtraction from left to right. A mnemonic is provided to help remember the order: "Please Excuse My Dear Aunt Sally" which represents Parentheses, Exponents, Multiplication, Division, Addition, Subtraction from left to right. Examples are given to demonstrate applying the order of operations to solve multi-step math problems.
8 1 Exponents
The document discusses exponents and multiplying monomials. It provides examples of exponents like 32 meaning 3 x 3 and explains that 32 does not mean 3 x 2. It also shows how to evaluate exponents, like 63 = (6 x 6) x 6 = 216. The document then explains that when multiplying terms with the same base, you add the exponents, like 32 x 33 = 35. Finally, it defines monomials as expressions involving constants and variables and shows how to multiply them by separating coefficients and variables, like (5t)(20t3) = 100t4.
Adding and subtracting
The document describes several methods for adding and subtracting multi-digit numbers:
The partial-sums method involves adding numbers column-by-column from left to right, recording partial sums, and then adding the partial sums.
The column-addition method adds each column separately in any order, carrying numbers to the next column as needed.
The partial-difference method performs subtraction column-by-column from left to right, subtracting the smaller number from the larger number in each column and recording partial differences.
Math 7 lesson 8 multiplication of integers
The document discusses multiplication of integers. It explains that multiplying integers involves multiplying signed numbers, and that the product of the absolute values remains the same but the signs may differ. It provides two rules for the sign of the product: if two integers have the same sign, the product is positive, and if they have opposite signs, the product is negative. Examples are given to illustrate the rules.
Systems
The document provides instructions on solving systems of linear equations using different methods:
1) The substitution method involves solving one equation for one variable and substituting it into the other equation.
2) The addition/subtraction method involves adding or subtracting the equations to eliminate one variable.
3) The multiplication method involves multiplying one or both equations by constants to make the coefficients of one variable equal, then adding or subtracting the equations.
Examples are provided for each method along with step-by-step workings. Readers are instructed to practice these methods on an assessment with several systems of equations provided.
Factorials
Factorials are the product of all positive integers from a given number down to 1. This document provides examples of calculating factorials such as 4! = 24 and discusses the rules for operations involving factorials such as cancellation rules that apply when dividing factorials. Practice problems are included with explanations to reinforce understanding of how to calculate and operate with factorial expressions.
Repeat Terminate Number
The document is a summary of key concepts from a math textbook chapter on rational numbers and decimals including:
1) Evaluating expressions like 3x-1 and 4(x+3) for values of x.
2) Definitions of terminating and repeating decimals. 0.8 terminates while 0.625 repeats.
3) Using greater than (>), less than (<) and equal to (≤, ≥) symbols to order numbers like -7, -14.8, -14.6, 532,028 and 523,828.
4) The meaning of opposite numbers and using them in equations like -9 + 9 = 0.
5) Defining absolute value
Thursday, september 26, 2013
The document provides instructions and examples for solving integer equations and working with absolute values. It discusses key concepts like:
- The rules for adding, subtracting, multiplying and dividing integers
- Classifying numbers as natural, whole, integer, rational or real
- Understanding that the absolute value of a number represents its distance from zero
- Solving problems involving absolute values and performing operations inside and outside of absolute value signs
Algebra
The document provides 5 algebra word problems and their step-by-step solutions. It begins with a disclaimer that the document was prepared by trainees and is not an official document. It then presents 5 multi-step algebra word problems, showing the work and reasoning for arriving at each solution. The document concludes by providing contact information and a thank you.
Factorising algebraic expressions
This document provides examples of factorizing algebraic expressions by finding the highest common factor (HCF) of the terms. It shows expressions being factorized, such as 2a+6 being written as 2(a+3), and 8m+12 being written as 4(2m+3). The document explains that algebraic expressions can sometimes be written as the HCF multiplied by grouped terms in parentheses. It provides steps for finding the factors of each term and the HCF to factorize expressions like 9jk+4k as k(9j+4).
Q1 lesson 3 integers
The document discusses integers and operations on integers. Integers include all whole numbers and their opposites. It provides examples and rules for adding, subtracting, multiplying, and dividing integers. The key rules are: for addition and subtraction, integers with the same sign are added/subtracted and opposites are subtracted/added; for multiplication and division, integers with the same sign are multiplied/divided and opposites are multiplied/divided with a negative result. Multiple examples are worked through to demonstrate each rule.
Tips And Tricks To Do The Match Quickly
Most of the people don’t like to do the math, and when it comes to the use of large fractions, they are always the source of irritation to such people at the first moment. If you want to learn the techniques to do the match quickly and easily, then have a look at all the tips listed below to get the most benefit.
NSM Seminar
1. The document contains solutions to math problems from different schools.
2. One problem involves finding the maximum value of the function 20t - 5t^2, which is 20.
3. Another involves finding the average speed and time taken to travel 189x meters, where the average speed is 84 m/s and the time taken is 130 minutes.
3.5 Notes A
This document is a lesson on slopes of lines. It defines slope as rise over run and includes examples of finding the slope of different lines using the slope formula. It discusses how to identify if lines are parallel, perpendicular, or neither based on their slopes. Specifically, parallel lines have the same slope and perpendicular lines have slopes that multiply to -1. There are also examples of graphing lines and determining if they are parallel, perpendicular, or neither based on their slopes. The document concludes with assigning homework problems on finding slopes and classifying lines.
More Related Content
What's hot
Order Of Operations
The document discusses order of operations, which is the order in which mathematical operations should be performed in a problem containing multiple operations. The standard order is: 1) operations within parentheses, 2) exponents, 3) multiplication and division from left to right, 4) addition and subtraction from left to right. It provides examples of solving problems using the proper order of operations and asks readers to try solving sample problems on their own.
Order of Operations (Algebra1 1_2)
The document discusses the order of operations, which is a rule for evaluating mathematical expressions containing multiple operations. It explains that the order of operations is: 1) Evaluate expressions inside grouping symbols (parentheses, brackets, braces) from innermost to outermost. 2) Evaluate exponents. 3) Perform multiplication and division from left to right. 4) Perform addition and subtraction from left to right. Mnemonics like PEMDAS are provided to help remember the order. Examples of applying the order of operations to evaluate expressions are provided.
Dividing integers
The document discusses dividing integers and their rules:
- There are four rules for dividing integers based on the signs of the numbers: two positives or negatives give a positive, opposite signs give a negative.
- Examples are provided to demonstrate applying the rules.
- The mean, or average, of a data set is calculated by summing the values and dividing by the number of values.
- Order of operations must be followed when evaluating expressions.
When math meets microbit
This document discusses using micro:bit to solve math problems involving sequences. It provides an example problem of counting the number of black pieces in a triangular arrangement over 50 layers. This can be solved either through a formula approach as it is an arithmetic sequence, or through a programming approach by observing the pattern and coding the logic. The document demonstrates both approaches, with the formula solution being faster but programming able to solve it without a formula by iterating through loops. The key lessons are that programming helps train logical thinking and problem solving even without memorizing syntax, and both math formulas and coding can be used to arrive at the right solution.
Order of operations Unit3
The document discusses order of operations, which is the standard sequence for performing mathematical calculations involving multiple arithmetic operations. The order is: 1) Perform operations inside parentheses, 2) Evaluate exponents, 3) Perform multiplication and division from left to right, 4) Perform addition and subtraction from left to right. A mnemonic device - PEMDAS - is provided to help remember this sequence: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Examples are given to demonstrate applying order of operations to solve multi-step arithmetic problems step-by-step.
Chapter 1 Study Guide
The document discusses the order of operations (PEMDAS) and provides examples of how to evaluate expressions and solve equations. It explains that parentheses, exponents, multiplication/division from left to right, and addition/subtraction from left to right have precedence based on the PEMDAS acronym. Integers, absolute value, adding, subtracting, multiplying, and dividing integers are also covered along with writing algebraic expressions and solving different types of equations.
Order of operations
The document discusses the order of operations for evaluating numerical expressions. It provides examples of step-by-step evaluations using the PEMDAS mnemonic (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) to determine the proper sequence. It also notes that when multiple grouping symbols are present, the expression should be evaluated starting with the innermost grouping symbol working outwards.
Order of operations
The document discusses order of operations, which is the standard sequence for performing mathematical calculations involving multiple arithmetic operations. The order is: 1) operations within parentheses, 2) exponents, 3) multiplication and division from left to right, 4) addition and subtraction from left to right. A mnemonic is provided to help remember the order: "Please Excuse My Dear Aunt Sally" which represents Parentheses, Exponents, Multiplication, Division, Addition, Subtraction from left to right. Examples are given to demonstrate applying the order of operations to solve multi-step math problems.
8 1 Exponents
The document discusses exponents and multiplying monomials. It provides examples of exponents like 32 meaning 3 x 3 and explains that 32 does not mean 3 x 2. It also shows how to evaluate exponents, like 63 = (6 x 6) x 6 = 216. The document then explains that when multiplying terms with the same base, you add the exponents, like 32 x 33 = 35. Finally, it defines monomials as expressions involving constants and variables and shows how to multiply them by separating coefficients and variables, like (5t)(20t3) = 100t4.
Adding and subtracting
The document describes several methods for adding and subtracting multi-digit numbers:
The partial-sums method involves adding numbers column-by-column from left to right, recording partial sums, and then adding the partial sums.
The column-addition method adds each column separately in any order, carrying numbers to the next column as needed.
The partial-difference method performs subtraction column-by-column from left to right, subtracting the smaller number from the larger number in each column and recording partial differences.
Math 7 lesson 8 multiplication of integers
The document discusses multiplication of integers. It explains that multiplying integers involves multiplying signed numbers, and that the product of the absolute values remains the same but the signs may differ. It provides two rules for the sign of the product: if two integers have the same sign, the product is positive, and if they have opposite signs, the product is negative. Examples are given to illustrate the rules.
Systems
The document provides instructions on solving systems of linear equations using different methods:
1) The substitution method involves solving one equation for one variable and substituting it into the other equation.
2) The addition/subtraction method involves adding or subtracting the equations to eliminate one variable.
3) The multiplication method involves multiplying one or both equations by constants to make the coefficients of one variable equal, then adding or subtracting the equations.
Examples are provided for each method along with step-by-step workings. Readers are instructed to practice these methods on an assessment with several systems of equations provided.
Factorials
Factorials are the product of all positive integers from a given number down to 1. This document provides examples of calculating factorials such as 4! = 24 and discusses the rules for operations involving factorials such as cancellation rules that apply when dividing factorials. Practice problems are included with explanations to reinforce understanding of how to calculate and operate with factorial expressions.
Repeat Terminate Number
The document is a summary of key concepts from a math textbook chapter on rational numbers and decimals including:
1) Evaluating expressions like 3x-1 and 4(x+3) for values of x.
2) Definitions of terminating and repeating decimals. 0.8 terminates while 0.625 repeats.
3) Using greater than (>), less than (<) and equal to (≤, ≥) symbols to order numbers like -7, -14.8, -14.6, 532,028 and 523,828.
4) The meaning of opposite numbers and using them in equations like -9 + 9 = 0.
5) Defining absolute value
Thursday, september 26, 2013
The document provides instructions and examples for solving integer equations and working with absolute values. It discusses key concepts like:
- The rules for adding, subtracting, multiplying and dividing integers
- Classifying numbers as natural, whole, integer, rational or real
- Understanding that the absolute value of a number represents its distance from zero
- Solving problems involving absolute values and performing operations inside and outside of absolute value signs
Algebra
The document provides 5 algebra word problems and their step-by-step solutions. It begins with a disclaimer that the document was prepared by trainees and is not an official document. It then presents 5 multi-step algebra word problems, showing the work and reasoning for arriving at each solution. The document concludes by providing contact information and a thank you.
Factorising algebraic expressions
This document provides examples of factorizing algebraic expressions by finding the highest common factor (HCF) of the terms. It shows expressions being factorized, such as 2a+6 being written as 2(a+3), and 8m+12 being written as 4(2m+3). The document explains that algebraic expressions can sometimes be written as the HCF multiplied by grouped terms in parentheses. It provides steps for finding the factors of each term and the HCF to factorize expressions like 9jk+4k as k(9j+4).
Q1 lesson 3 integers
The document discusses integers and operations on integers. Integers include all whole numbers and their opposites. It provides examples and rules for adding, subtracting, multiplying, and dividing integers. The key rules are: for addition and subtraction, integers with the same sign are added/subtracted and opposites are subtracted/added; for multiplication and division, integers with the same sign are multiplied/divided and opposites are multiplied/divided with a negative result. Multiple examples are worked through to demonstrate each rule.
Tips And Tricks To Do The Match Quickly
Most of the people don’t like to do the math, and when it comes to the use of large fractions, they are always the source of irritation to such people at the first moment. If you want to learn the techniques to do the match quickly and easily, then have a look at all the tips listed below to get the most benefit.
NSM Seminar
1. The document contains solutions to math problems from different schools.
2. One problem involves finding the maximum value of the function 20t - 5t^2, which is 20.
3. Another involves finding the average speed and time taken to travel 189x meters, where the average speed is 84 m/s and the time taken is 130 minutes.
What's hot (20)
Viewers also liked
3.5 Notes A
This document is a lesson on slopes of lines. It defines slope as rise over run and includes examples of finding the slope of different lines using the slope formula. It discusses how to identify if lines are parallel, perpendicular, or neither based on their slopes. Specifically, parallel lines have the same slope and perpendicular lines have slopes that multiply to -1. There are also examples of graphing lines and determining if they are parallel, perpendicular, or neither based on their slopes. The document concludes with assigning homework problems on finding slopes and classifying lines.
1.5 1.6 notes a
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6. Students are asked to work on vocabulary and postulates after the quiz.
2. Examples are given for finding midpoints and distances between points on a coordinate plane using formulas like the midpoint formula, Pythagorean theorem, and distance formula.
3. Homework assignments include problems from the textbook on the topics of formulas in geometry, midpoints, and distance.
2.2 notes a
1. When entering class each day, students should say hi, have their homework out, write any questions on the board, and start the opener problem.
2. The document then provides examples of algebra problems involving variables to represent unknown quantities and expressions combining variables, operators, and constants.
3. Students are instructed to complete a set of practice problems from page 94 in their workbook and have their work checked by the teacher.
3.1 3.2 Notes
1. The document discusses coordinate planes and identifying points using ordered pairs. It provides examples of ordered pairs and asks the reader to identify other coordinates.
2. It then discusses a vertical line l that passes through the point (3,7) and asks the reader to find 6 points on the line and 6 points not on the line, as well as how to tell if a point is on the line based on its coordinates.
3. Finally, it introduces transformations on coordinate planes and asks the reader questions about finding points with specific x- and y-coordinates or where the y-coordinate is less than the x-coordinate. It provides homework problems for further practice.
2.5 notes b
This document contains notes and instructions for a math lesson that includes:
1) Solving expressions and evaluating them for given values.
2) Completing an in-class activity with partners to review basic arithmetic rules.
3) Practicing the basic rules of arithmetic through examples of simplifying expressions using properties like commutative, associative, and distributive properties.
Alg2.5 A Notes
1. The document provides examples to evaluate the expression 2(x+1) for different values of x, and asks students to explain why 2(x+1) is always even and 2(x)+1 is always odd when x is an integer.
2. Students are given a homework assignment involving basic algebraic rules and properties. They complete an activity with a partner involving these rules.
3. The document asks students to rephrase basic algebraic rules without using variables, evaluate expressions using properties like distributive property, and find products of fractions. Patterns in the products are explored.
4. Homework assigned includes a mini quiz, practice problems, and studying for an upcoming test.
Unit 1 test 2.9 notes a
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
Las Hayas Hotel en Fotos
Hotel Las Hayas. 5 Star resort in Ushuaia, Tierra de Fuego, Argentina. Please visit us in www.lashayashotel.com
4 7 Notes B
This document provides instruction on writing and graphing linear equations in different forms. It begins with a review of equivalent forms of linear equations, including point-slope, slope-intercept, and standard form. Students are then given examples of writing equations of lines given a point and slope, or two points. The document concludes with examples of graphing lines by using the point-slope and slope-intercept forms to easily find points and draw the line. Students are challenged to graph a line given in standard form and explain their process.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
11.6 notes b
The document provides instructions for students to complete homework questions, check their answers to a previous worksheet with a partner, and work with partners on new problems involving theorems about segment relationships in circles. Students are assigned one problem to present to the class, with the goal of serving as clear notes examples from the lesson. They are to fill out a graphic organizer in their notes summarizing the three theorems covered.
Unit 1 test 2.9 notes b
1) The document provides 4 math word problems and equations to solve using techniques like backtracking and defining variables.
2) It asks the reader to simplify the expression 2(x+6) - 4(3x - 1) and evaluate it for x = -2.
3) Another problem defines a variable to represent the number of giraffes at Brookfield Zoo and writes an expression relating it to the number of giraffes at Lincoln Park Zoo.
3.6 Boards Up
The document provides instructions for working problems on whiteboards and lists 10 multi-part math word problems involving writing equations of lines (WEL) given various conditions such as being parallel or perpendicular to other lines, passing through given points, or having a given slope or intercepts. Students are to write the equations of the lines on their whiteboards.
Walt Disney
Walt Disney was an American entrepreneur and film innovator who was born in 1901 in Chicago. He created many famous cartoon characters like Mickey Mouse and founded The Walt Disney Company. Disney opened the first Disneyland theme park in California in 1955 and later built Disney World in Florida. The Disney Company owns theme parks, cruise ships, film studios, television networks and merchandising rights that generate billions in revenue annually and support tens of thousands of jobs.
Andrew Carnegie
Andrew Carnegie was born in Scotland but immigrated to the United States as a young boy. He worked for the Pennsylvania Railroad and learned about the Bessemer Process for mass producing steel. With this knowledge, Carnegie started his own steel company and became the richest man in the world after selling it in 1901. He donated much of his wealth to charitable causes like building over 1,600 public libraries across America and establishing the Carnegie Endowment to promote world peace.
Viewers also liked (18)
More from mbetzel
2.2 2.3 notes a
The document describes a numeric pattern where each row contains consecutive odd integers centered around 1. It asks students to conjecture the pattern and sum of terms in each row. It also provides homework questions on conditional statements, deductive reasoning, and analyzing the truth value of related conditional statements.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
2.8 notes a
1. The document discusses solving equations by backtracking. It begins by defining an equation and identifying true and false equations. It then discusses the concept of solutions - the values that make the equation true.
2. Examples are provided to illustrate finding solutions to equations by reversing the steps of number tricks. Backtracking involves working backwards through the operations to determine the starting value.
3. Readers are instructed to solve sample equations by listing the number trick steps and then reversing the steps through backtracking to find the solution values.
Chapter 1 rev notes (a)
This document provides homework questions and a review packet for a chapter. It lists 7 numbered sections that appear to be questions or tasks related to reviewing material from the first chapter. The document aims to help students review and reinforce their understanding of the concepts covered in the initial chapter through completing the homework and review activities.
1.6 1.7 notes b
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of segments. It also defines different types of transformations, such as translations, reflections, and rotations. Students are given homework problems applying these concepts, and examples of identifying transformations and describing them with arrow notation.
1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations (translations, reflections, rotations, and dilations) and provides examples of identifying each type using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.6 1.7 notes a
This document provides examples and explanations of the midpoint and distance formulas, as well as transformations in the coordinate plane. It includes 4 examples of using the midpoint and distance formulas to find midpoints and lengths of line segments. It also discusses the different types of transformations - translations, reflections, rotations, and dilations - and provides examples of identifying each type of transformation using arrow notation. The homework assignments are to complete practice problems from sections 1.6 and 1.7 in the textbook, as listed.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. Students are asked to work on their vocabulary packet silently after finishing the quiz. Then the class will review geometry formulas.
3. The homework assignments are to complete problems on page 38 from section 1.5 and page 47 from section 1.6 in the textbook. These cover midpoints, distances, and the midpoint and distance formulas.
1.5 1.6 notes b
1. The document provides instructions for a quiz and homework assignments on geometry chapters 1.5 and 1.6.
2. It includes examples of using the midpoint formula to find the midpoint of a segment and using given midpoints and endpoints to find missing endpoints.
3. There are also examples of using the Pythagorean theorem and distance formula to find the length of a segment between two points.
2.6 2.7 notes a
1. The document provides instructions and tasks for students to complete mathematical expressions, homework questions, and a lesson on reversible and non-reversible operations.
2. Students are asked to simplify expressions, complete homework problems, and determine whether example operations are reversible by considering if the starting number can be determined.
3. The document demonstrates how to "backtrack" through a multi-step operation to find the original starting number using reversible operations.
2.4 notes b
1. Students were asked to put math problems on the board from previous homework. The document then provides examples of expressions and teaches how to simplify them using order of operations and properties like the distributive property. Students are asked to simplify sample expressions involving variables.
2. The document reviews that expressions need to have "like terms" to be simplified, such as terms with the same variables. Students practice simplifying expressions with multiple variables and terms by combining like terms.
3. To conclude, students are instructed to write their name and ID number on raffle tickets and provide just the simplified answer, practicing the skills of defining a variable, writing an expression, simplifying it, and evaluating it.
2.3 notes b
This document contains instructions for students to complete various math exercises on their TI-Nspire calculators. It asks students to match expressions to steps, write an expression for the area of a rectangle, simplify an algebraic expression, evaluate expressions for different variable values, and complete an activity on their calculators worth daily work points. Students are told to work with partners but can ask other group members for help if needed and to raise their hand once finished.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions on graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages. Finally, it addresses solving an equation like x^3 + 5x = 7x^2 - 5 by graphing and reflects on graphing techniques from prior lessons.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions about graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages.
8.7 notes
The document discusses a 4 step process but provides no details on the actual steps or content of the process. It references numbered sections but provides no information within those sections. Overall, the document does not contain any substantive information that could be summarized due to the lack of details provided within the numbered sections.
8.7 d2 a
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions on graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages.
8.7 notes b
This document contains notes from multiple sections on solving systems of equations by graphing. It includes questions about graphing systems like y = 3x - 4 and y = -2x + 5. It also asks how to solve an absolute value equation like |x+4| = x^2 - 3 and discusses the pros and cons of the graphing method, listing advantages and disadvantages.
More from mbetzel (20)
Recently uploaded
Artificial Intelligence for XMLDevelopment
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
GraphSummit Singapore | Enhancing Changi Airport Group's Passenger Experience...
Dr. Sean Tan, Head of Data Science, Changi Airport Group
Discover how Changi Airport Group (CAG) leverages graph technologies and generative AI to revolutionize their search capabilities. This session delves into the unique search needs of CAG’s diverse passengers and customers, showcasing how graph data structures enhance the accuracy and relevance of AI-generated search results, mitigating the risk of “hallucinations” and improving the overall customer journey.
Presentation of the OECD Artificial Intelligence Review of Germany
Consult the full report at https://www.oecd.org/digital/oecd-artificial-intelligence-review-of-germany-609808d6-en.htm
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Discover the seamless integration of RPA (Robotic Process Automation), COMPOSER, and APM with AWS IDP enhanced with Slack notifications. Explore how these technologies converge to streamline workflows, optimize performance, and ensure secure access, all while leveraging the power of AWS IDP and real-time communication via Slack notifications.
Climate Impact of Software Testing at Nordic Testing Days
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
“I’m still / I’m still / Chaining from the Block”
“An Outlook of the Ongoing and Future Relationship between Blockchain Technologies and Process-aware Information Systems.” Invited talk at the joint workshop on Blockchain for Information Systems (BC4IS) and Blockchain for Trusted Data Sharing (B4TDS), co-located with with the 36th International Conference on Advanced Information Systems Engineering (CAiSE), 3 June 2024, Limassol, Cyprus.
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...Edge AI and Vision Alliance
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/building-and-scaling-ai-applications-with-the-nx-ai-manager-a-presentation-from-network-optix/
Robin van Emden, Senior Director of Data Science at Network Optix, presents the “Building and Scaling AI Applications with the Nx AI Manager,” tutorial at the May 2024 Embedded Vision Summit.
In this presentation, van Emden covers the basics of scaling edge AI solutions using the Nx tool kit. He emphasizes the process of developing AI models and deploying them globally. He also showcases the conversion of AI models and the creation of effective edge AI pipelines, with a focus on pre-processing, model conversion, selecting the appropriate inference engine for the target hardware and post-processing.
van Emden shows how Nx can simplify the developer’s life and facilitate a rapid transition from concept to production-ready applications.He provides valuable insights into developing scalable and efficient edge AI solutions, with a strong focus on practical implementation.How to Get CNIC Information System with Paksim Ga.pptx
Pakdata Cf is a groundbreaking system designed to streamline and facilitate access to CNIC information. This innovative platform leverages advanced technology to provide users with efficient and secure access to their CNIC details.
Full-RAG: A modern architecture for hyper-personalization
Mike Del Balso, CEO & Co-Founder at Tecton, presents "Full RAG," a novel approach to AI recommendation systems, aiming to push beyond the limitations of traditional models through a deep integration of contextual insights and real-time data, leveraging the Retrieval-Augmented Generation architecture. This talk will outline Full RAG's potential to significantly enhance personalization, address engineering challenges such as data management and model training, and introduce data enrichment with reranking as a key solution. Attendees will gain crucial insights into the importance of hyperpersonalization in AI, the capabilities of Full RAG for advanced personalization, and strategies for managing complex data integrations for deploying cutting-edge AI solutions.
20240609 QFM020 Irresponsible AI Reading List May 2024
Everything I found interesting about the irresponsible use of machine intelligence in May 2024
TrustArc Webinar - 2024 Global Privacy Survey
How does your privacy program stack up against your peers? What challenges are privacy teams tackling and prioritizing in 2024?
In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
Building RAG with self-deployed Milvus vector database and Snowpark Container...
This talk will give hands-on advice on building RAG applications with an open-source Milvus database deployed as a docker container. We will also introduce the integration of Milvus with Snowpark Container Services.
Large Language Model (LLM) and it’s Geospatial Applications
Large Language Model (LLM) and it’s Geospatial Applications.
A tale of scale & speed: How the US Navy is enabling software delivery from l...
Rapid and secure feature delivery is a goal across every application team and every branch of the DoD. The Navy’s DevSecOps platform, Party Barge, has achieved:
- Reduction in onboarding time from 5 weeks to 1 day
- Improved developer experience and productivity through actionable findings and reduction of false positives
- Maintenance of superior security standards and inherent policy enforcement with Authorization to Operate (ATO)
Development teams can ship efficiently and ensure applications are cyber ready for Navy Authorizing Officials (AOs). In this webinar, Sigma Defense and Anchore will give attendees a look behind the scenes and demo secure pipeline automation and security artifacts that speed up application ATO and time to production.
We will cover:
- How to remove silos in DevSecOps
- How to build efficient development pipeline roles and component templates
- How to deliver security artifacts that matter for ATO’s (SBOMs, vulnerability reports, and policy evidence)
- How to streamline operations with automated policy checks on container images
Generative AI Deep Dive: Advancing from Proof of Concept to Production
Join Maher Hanafi, VP of Engineering at Betterworks, in this new session where he'll share a practical framework to transform Gen AI prototypes into impactful products! He'll delve into the complexities of data collection and management, model selection and optimization, and ensuring security, scalability, and responsible use.
Recently uploaded (20)
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...
GraphSummit Singapore | Enhancing Changi Airport Group's Passenger Experience...
GraphSummit Singapore | Enhancing Changi Airport Group's Passenger Experience...
Presentation of the OECD Artificial Intelligence Review of Germany
Presentation of the OECD Artificial Intelligence Review of Germany
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Let's Integrate MuleSoft RPA, COMPOSER, APM with AWS IDP along with Slack
Climate Impact of Software Testing at Nordic Testing Days
Climate Impact of Software Testing at Nordic Testing Days
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
“Building and Scaling AI Applications with the Nx AI Manager,” a Presentation...
How to Get CNIC Information System with Paksim Ga.pptx
How to Get CNIC Information System with Paksim Ga.pptx
Full-RAG: A modern architecture for hyper-personalization
Full-RAG: A modern architecture for hyper-personalization
20240609 QFM020 Irresponsible AI Reading List May 2024
20240609 QFM020 Irresponsible AI Reading List May 2024
Monitoring Java Application Security with JDK Tools and JFR Events
Monitoring Java Application Security with JDK Tools and JFR Events
Building RAG with self-deployed Milvus vector database and Snowpark Container...
Building RAG with self-deployed Milvus vector database and Snowpark Container...
Large Language Model (LLM) and it’s Geospatial Applications
Large Language Model (LLM) and it’s Geospatial Applications
A tale of scale & speed: How the US Navy is enabling software delivery from l...
A tale of scale & speed: How the US Navy is enabling software delivery from l...
Generative AI Deep Dive: Advancing from Proof of Concept to Production
Generative AI Deep Dive: Advancing from Proof of Concept to Production
3.2 Notes A
- 2. 2
- 3. Solving Systems of Equations Review: Addition/ Elimination Method 1.) • 3x + 3y = 9 ‚ 4x – 3y = 16 2.) • 4x – 3y = 9 ‚ 3x + 5y = 7 3.) • 3x + 4y = 1 ‚ 7x + 9y = 0 3
- 4. 4
- 5. 5
- 6. 6
- 7. 3.2 Homework: • Pg. 158 # 6-11, 20-23, 25, 31 • Proof Worksheet # 1 7