Unit 5.6
•Download as PPT, PDF•
0 likes•202 views
The document discusses identifying the slope and y-intercept of a line from its equation. It provides examples of finding the slope and y-intercept for different line equations by rewriting the equations in slope-intercept form as needed. Specifically, it shows identifying the slope as 3 and the y-intercept as 4 for the equation y = 3x + 4, and identifying the slope as -3 and y-intercept as 2 for the equation 3x + y = 2 after rewriting it as y = -3x + 2.
Report
Share
Report
Share
Recommended
Math 17 midterm exam review jamie
1. The document provides a review for a midterm exam in Mathematics 17 covering topics like simplifying expressions, properties of sets, graphing functions, solving equations and word problems.
2. The review contains 6 sections with multiple parts testing skills in algebra, functions, coordinate geometry, and problem solving.
3. Questions range from simplifying expressions and determining true/false statements to graphing functions, finding intersections of graphs, and solving rate and time word problems.
7 4 multiply to eliminate - day 1
1. To solve linear systems by multiplying, arrange the equations so that like terms are in columns. Multiply one or both equations by a number to obtain opposite coefficients for one variable.
2. Add or subtract the equations to eliminate one variable. Solve for the remaining variable and substitute back into the original equations.
3. Check the solution by substituting the values back into the original equations.
Grumpy Cat Foo
The document discusses solving a quadratic equation for a parabola with a vertex of (4,3) and a point of (2,2). It shows the steps taken to solve for the equation, arriving at y=-1/4(x-4)^2 +3. This is simplified to a final equation of y=-.28x^2+2.1x-1.2, which matches the original parabola.
Number Sequences
Here are the nth terms for the given sequences:
(a) The nth term is: 3n + 1
(b) The nth term is: n + 2
(c) The nth term is: n + 1
(d) The nth term is: 10n
(e) The nth term is: 5n - 1
Sequences finding a rule
The document discusses sequences, which are sets of terms in a definite order obtained by some rule. It provides examples of finite and infinite sequences and discusses notation for representing sequences. It also covers finding the formula for the terms of a sequence using recurrence relations, which define the initial terms and the relationship between successive terms. The document gives examples of identifying patterns in sequences and finding subsequent terms.
Binomial theorem
The document discusses expanding binomial expressions like (x + y)n using Pascal's triangle and the binomial theorem. It explains that each term in the expansion has exponents of x and y that add up to n, with the x exponent decreasing by 1 and the y exponent increasing by 1 in subsequent terms. The coefficients of the terms form Pascal's triangle. It also presents the binomial theorem formula for finding the coefficients and discusses using factorials. It provides an example of finding a specific term in a binomial expansion by identifying which value of k corresponds to that term number.
Number sequence
This slide created by Abdullah Al Mehedi.
A sequence, in mathematics, is a string of objects, like numbers, that follow a particular pattern..
Factoring Reviewed
Factoring for non-math lovers. This slide presentation is designed to help remove some of the stress out of factoring at t he Algebra 2 level.
Recommended
Math 17 midterm exam review jamie
1. The document provides a review for a midterm exam in Mathematics 17 covering topics like simplifying expressions, properties of sets, graphing functions, solving equations and word problems.
2. The review contains 6 sections with multiple parts testing skills in algebra, functions, coordinate geometry, and problem solving.
3. Questions range from simplifying expressions and determining true/false statements to graphing functions, finding intersections of graphs, and solving rate and time word problems.
7 4 multiply to eliminate - day 1
1. To solve linear systems by multiplying, arrange the equations so that like terms are in columns. Multiply one or both equations by a number to obtain opposite coefficients for one variable.
2. Add or subtract the equations to eliminate one variable. Solve for the remaining variable and substitute back into the original equations.
3. Check the solution by substituting the values back into the original equations.
Grumpy Cat Foo
The document discusses solving a quadratic equation for a parabola with a vertex of (4,3) and a point of (2,2). It shows the steps taken to solve for the equation, arriving at y=-1/4(x-4)^2 +3. This is simplified to a final equation of y=-.28x^2+2.1x-1.2, which matches the original parabola.
Number Sequences
Here are the nth terms for the given sequences:
(a) The nth term is: 3n + 1
(b) The nth term is: n + 2
(c) The nth term is: n + 1
(d) The nth term is: 10n
(e) The nth term is: 5n - 1
Sequences finding a rule
The document discusses sequences, which are sets of terms in a definite order obtained by some rule. It provides examples of finite and infinite sequences and discusses notation for representing sequences. It also covers finding the formula for the terms of a sequence using recurrence relations, which define the initial terms and the relationship between successive terms. The document gives examples of identifying patterns in sequences and finding subsequent terms.
Binomial theorem
The document discusses expanding binomial expressions like (x + y)n using Pascal's triangle and the binomial theorem. It explains that each term in the expansion has exponents of x and y that add up to n, with the x exponent decreasing by 1 and the y exponent increasing by 1 in subsequent terms. The coefficients of the terms form Pascal's triangle. It also presents the binomial theorem formula for finding the coefficients and discusses using factorials. It provides an example of finding a specific term in a binomial expansion by identifying which value of k corresponds to that term number.
Number sequence
This slide created by Abdullah Al Mehedi.
A sequence, in mathematics, is a string of objects, like numbers, that follow a particular pattern..
Factoring Reviewed
Factoring for non-math lovers. This slide presentation is designed to help remove some of the stress out of factoring at t he Algebra 2 level.
Identify Polynomials ch14
The document discusses polynomials. It defines a monomial as a number or product of numbers and variables with whole number exponents, and a polynomial as a sum or difference of monomials. It explains that the degree of a monomial or polynomial is determined by summing the exponents of its variables. The document provides examples of identifying the degree of monomials, classifying polynomials by their leading coefficient, degree, and number of terms, and adding or subtracting polynomials.
Calc 5.1a
The document discusses properties and definitions related to natural logarithmic functions:
1) It defines the natural logarithmic function as the antiderivative of 1/x, which is neither algebraic nor trigonometric.
2) It shows that the slope of the natural logarithmic function graph at different x-values corresponds to the reciprocal of those x-values.
3) It reminds that logarithmic expressions can be expanded using properties that apply to all logarithms, but sums and differences cannot be further expanded.
4) It emphasizes that when expanding logarithmic functions, the domain must be checked to ensure it is the same as the original function.
11.2
The document defines rational expressions as expressions that can be written as a ratio of two polynomials where the denominator is not 0. It provides examples of finding excluded values, which make the expression undefined, by setting the denominator equal to 0. It also discusses simplifying rational expressions by dividing out common factors in the numerator and denominator and putting them in simplest form. Examples are provided of factoring, dividing out monomials, recognizing opposites, and simplifying a rational model.
Pythagorean theorem and distance formula power point
The document discusses the Pythagorean theorem and distance formula. The Pythagorean theorem states that for any right triangle, a2 + b2 = c2, where c is the hypotenuse and a and b are the legs. The distance formula calculates the distance between two points in a plane by taking the difference of their x- and y-coordinates and plugging them into the formula (x2 - x1)2 + (y2 - y1)2. An example of using each formula to solve for the length of a side of a triangle and the distance between two points is provided.
Binomial Theorem, Recursion ,Tower of Honai, relations
These slides contain proof of Binomial theorem , Tower of Honai , recursion a d properties of relation...
Aljabar
1. The document defines algebraic expressions and terms. It explains that algebraic expressions show combinations of coefficients and variables in algebraic equations.
2. It defines like terms as terms that have exactly the same variables and unlike terms as terms that have different variables. Examples are given of simplifying expressions by combining like terms.
3. Rules and examples are provided for adding and subtracting algebraic expressions, including combining like terms and distributing coefficients. Exercises are included for students to practice simplifying, adding, and subtracting algebraic expressions.
Division Of Polynomials
Division of polynomials follows the same rules as division of real numbers. To divide a polynomial by a monomial, each term of the dividend is divided by the monomial divisor. To divide a polynomial by a polynomial, long division is used by repeatedly determining the quotient and remainder until the division is complete. The steps of long division are shown through an example of dividing a third degree polynomial by a linear polynomial divisor. The quotient and remainder are checked by multiplying the divisor and quotient together.
Trig identities
This document discusses trigonometric identities. It includes:
- Pythagorean identities relating sine, cosine, and their reciprocals
- Tangent/cotangent identities relating tangent and cotangent to sine and cosine
- Fundamental trig identities for sine, tangent, cotangent, and secant
- Examples of simplifying trig expressions using identities and of proving trig identities by manipulating expressions until they are equal.
Infinite series & sequence lecture 2
The document discusses sequences and their properties. A sequence is a function whose domain is the positive integers. Sequences are commonly represented using subscript notation rather than standard function notation. The nth term of a sequence is denoted an. [/SUMMARY]
Brians Trinomials
This document provides directions on how to factor the trinomial 3x^2 + 5x + 2 into two binomials. It shows setting up the trinomial with the x terms grouped on the left and the numeric terms on the right, then finding two numbers that multiply to the last term and add to the middle term, resulting in the factored form of (x+1)(3x+2).
9.4 part 1 and 2 combined worked
This document provides information about number patterns, sequences, and series. It defines recursive and explicit formulas for sequences and discusses arithmetic and geometric sequences. For arithmetic sequences, the common difference is constant between terms. For geometric sequences, the common ratio between consecutive terms is constant. Formulas are provided to find later terms in sequences, whether defined recursively or explicitly. Examples are given to practice identifying sequence types and using the formulas to find missing or future terms.
9.4 part 2.ppt worked
This document provides information about geometric sequences including their key properties and formulas. It defines a geometric sequence as one where the ratio between consecutive terms is constant, known as the common ratio. Formulas given include the recursive formula an = an-1r and explicit formula an = a1rn-1. Examples are provided for identifying geometric sequences and using the formulas to find missing terms. Additional notes state that arithmetic sequences have linear graphs while geometric sequences have exponential graphs.
Evaluate the given expression
The document contains examples of evaluating mathematical expressions for given values of variables.
1) It evaluates the expressions x + y, 2xy, and 5x/3y for x = 3 and y = 5, obtaining answers of 8, 30, and 1.
2) It evaluates the expression 3x + 2y for x = 3 and y = 5, obtaining the answer 19.
3) It evaluates the expression m + 2n for m = 5 and n = 2, obtaining the answer 9.
4) It evaluates the expression 18m + 7 for m = 1/3, obtaining the answer 13.
Pre-Cal 40S June 3, 2009
The document defines sequences and their patterns, including arithmetic and geometric sequences. It provides the recursive and implicit definitions of each, explaining how to find the common difference or ratio, and the nth term in the sequences. Examples are given for finding the common difference and the nth term in an arithmetic sequence, and the implicit definition and nth term for a geometric sequence.
Exponents, Fractions And Factors
This document contains math problems and questions covering several topics: factors and divisibility, simplifying fractions, rational numbers, exponents, scientific notation, and operations with exponents and scientific notation. Sample problems include finding the prime factorization of numbers, determining if fractions are equivalent, simplifying expressions with exponents, and performing operations in scientific notation.
Math unit8 number sequences
This document outlines an instructional unit on number sequences. The unit contains 5 presentations that cover: 1) simple number patterns, 2) recognizing patterns, 3) geometric patterns, 4) linear sequences, and 5) general laws. Each presentation provides examples and problems for students to work through related to the particular type of number sequence. The goal is for students to learn how to identify patterns in sequences and determine rules or formulas to describe the relationships.
4th quarter long test review
This document contains a 10 question review for a 4th quarter long test covering circle equations, polynomial division, factoring, and finding zeros of polynomials. The questions cover finding equations of circles given properties like center and radius, performing polynomial division and finding quotients and remainders, factoring polynomials, and solving polynomials for real zeros.
Exponents
The document reviews exponents and exponential notation. It defines the base as the starting number being used to an exponent, and the exponent as the number of times the base is used as a factor. It then provides rules for multiplying, dividing, and raising exponential expressions to a power:
- When multiplying expressions with the same base, add the exponents
- When dividing expressions with the same base, subtract the exponents
- When raising an expression to a power, multiply the exponents
It also notes that any number to the zero power equals one, and negative exponents represent the reciprocal of the base number rather than making the expression negative.
Edu 290 powerpoint1
The document discusses linear equations and their two main forms - slope-intercept form (y=mx+b) and point-slope form (y-y1=m(x-x1)). It explains how to use each form to find the equation of a line given values for the slope and/or a point on the line. Examples are provided for finding linear equations using both forms.
16Nov16 - The Dr Jack Watters Debate - Tackling antimicrobial resistance in...
The Jack Watters debate - tackling antimicrobial resistance in an ageing society, took place on the 16th November 2016 at the Old Operating Theatre Museum in London.
This event was dedicated to a long term supporter of the ILC and a pioneer in championing the health and well-being of ageing people, Dr. Jack Watters.
The debate was chaired by Baroness Sally Greengross (Chief Executive, ILC-UK) and saw the participation of the following speakers:
- Professor David Salisbury CB, Associate Fellow, Centre on Global Health Security Chatham House
- Matthew Edwards, Head of Mortality and Longevity, Towers Watson
- Michelle Bresnahan, Founder, A Life for a Cure
- Dr Gina Radford, Deputy Chief Medical Officer
http://www.ilcuk.org.uk/index.php/events/tackling_antimicrobial_resistance_in_an_ageing_society
Why Were We Created? - Dr. Bilal Philips
Not just Muslims, but every single human being has to answer the most fundamental question at some point in his or her lifetime:
"Why was I created? Why am I here? What am I doing in this world? Why did God create me?"
These questions are questions which each and everyone of us reflects on at some point during their life. We have some answers, which are given generally but usually these answers don't satisfy us - seeming somewhat simplistic. So, we still wonder: "Why me? Why here?". I know all of you (Muslims), are saying, "To worship Allah, khallas (finish). What more is there to say? Why do we need to have a big long talk on why we were created when we all know it is to worship Allah?!"
But wait. If this is presented to a non-Muslim, the next logical question would be, "Why does Allah want us to worship Him?" Then your stuck, which can only mean that in our own minds it is not really clear. Why did Allah create us to worship Him?
More Related Content
What's hot
Identify Polynomials ch14
The document discusses polynomials. It defines a monomial as a number or product of numbers and variables with whole number exponents, and a polynomial as a sum or difference of monomials. It explains that the degree of a monomial or polynomial is determined by summing the exponents of its variables. The document provides examples of identifying the degree of monomials, classifying polynomials by their leading coefficient, degree, and number of terms, and adding or subtracting polynomials.
Calc 5.1a
The document discusses properties and definitions related to natural logarithmic functions:
1) It defines the natural logarithmic function as the antiderivative of 1/x, which is neither algebraic nor trigonometric.
2) It shows that the slope of the natural logarithmic function graph at different x-values corresponds to the reciprocal of those x-values.
3) It reminds that logarithmic expressions can be expanded using properties that apply to all logarithms, but sums and differences cannot be further expanded.
4) It emphasizes that when expanding logarithmic functions, the domain must be checked to ensure it is the same as the original function.
11.2
The document defines rational expressions as expressions that can be written as a ratio of two polynomials where the denominator is not 0. It provides examples of finding excluded values, which make the expression undefined, by setting the denominator equal to 0. It also discusses simplifying rational expressions by dividing out common factors in the numerator and denominator and putting them in simplest form. Examples are provided of factoring, dividing out monomials, recognizing opposites, and simplifying a rational model.
Pythagorean theorem and distance formula power point
The document discusses the Pythagorean theorem and distance formula. The Pythagorean theorem states that for any right triangle, a2 + b2 = c2, where c is the hypotenuse and a and b are the legs. The distance formula calculates the distance between two points in a plane by taking the difference of their x- and y-coordinates and plugging them into the formula (x2 - x1)2 + (y2 - y1)2. An example of using each formula to solve for the length of a side of a triangle and the distance between two points is provided.
Binomial Theorem, Recursion ,Tower of Honai, relations
These slides contain proof of Binomial theorem , Tower of Honai , recursion a d properties of relation...
Aljabar
1. The document defines algebraic expressions and terms. It explains that algebraic expressions show combinations of coefficients and variables in algebraic equations.
2. It defines like terms as terms that have exactly the same variables and unlike terms as terms that have different variables. Examples are given of simplifying expressions by combining like terms.
3. Rules and examples are provided for adding and subtracting algebraic expressions, including combining like terms and distributing coefficients. Exercises are included for students to practice simplifying, adding, and subtracting algebraic expressions.
Division Of Polynomials
Division of polynomials follows the same rules as division of real numbers. To divide a polynomial by a monomial, each term of the dividend is divided by the monomial divisor. To divide a polynomial by a polynomial, long division is used by repeatedly determining the quotient and remainder until the division is complete. The steps of long division are shown through an example of dividing a third degree polynomial by a linear polynomial divisor. The quotient and remainder are checked by multiplying the divisor and quotient together.
Trig identities
This document discusses trigonometric identities. It includes:
- Pythagorean identities relating sine, cosine, and their reciprocals
- Tangent/cotangent identities relating tangent and cotangent to sine and cosine
- Fundamental trig identities for sine, tangent, cotangent, and secant
- Examples of simplifying trig expressions using identities and of proving trig identities by manipulating expressions until they are equal.
Infinite series & sequence lecture 2
The document discusses sequences and their properties. A sequence is a function whose domain is the positive integers. Sequences are commonly represented using subscript notation rather than standard function notation. The nth term of a sequence is denoted an. [/SUMMARY]
Brians Trinomials
This document provides directions on how to factor the trinomial 3x^2 + 5x + 2 into two binomials. It shows setting up the trinomial with the x terms grouped on the left and the numeric terms on the right, then finding two numbers that multiply to the last term and add to the middle term, resulting in the factored form of (x+1)(3x+2).
9.4 part 1 and 2 combined worked
This document provides information about number patterns, sequences, and series. It defines recursive and explicit formulas for sequences and discusses arithmetic and geometric sequences. For arithmetic sequences, the common difference is constant between terms. For geometric sequences, the common ratio between consecutive terms is constant. Formulas are provided to find later terms in sequences, whether defined recursively or explicitly. Examples are given to practice identifying sequence types and using the formulas to find missing or future terms.
9.4 part 2.ppt worked
This document provides information about geometric sequences including their key properties and formulas. It defines a geometric sequence as one where the ratio between consecutive terms is constant, known as the common ratio. Formulas given include the recursive formula an = an-1r and explicit formula an = a1rn-1. Examples are provided for identifying geometric sequences and using the formulas to find missing terms. Additional notes state that arithmetic sequences have linear graphs while geometric sequences have exponential graphs.
Evaluate the given expression
The document contains examples of evaluating mathematical expressions for given values of variables.
1) It evaluates the expressions x + y, 2xy, and 5x/3y for x = 3 and y = 5, obtaining answers of 8, 30, and 1.
2) It evaluates the expression 3x + 2y for x = 3 and y = 5, obtaining the answer 19.
3) It evaluates the expression m + 2n for m = 5 and n = 2, obtaining the answer 9.
4) It evaluates the expression 18m + 7 for m = 1/3, obtaining the answer 13.
Pre-Cal 40S June 3, 2009
The document defines sequences and their patterns, including arithmetic and geometric sequences. It provides the recursive and implicit definitions of each, explaining how to find the common difference or ratio, and the nth term in the sequences. Examples are given for finding the common difference and the nth term in an arithmetic sequence, and the implicit definition and nth term for a geometric sequence.
Exponents, Fractions And Factors
This document contains math problems and questions covering several topics: factors and divisibility, simplifying fractions, rational numbers, exponents, scientific notation, and operations with exponents and scientific notation. Sample problems include finding the prime factorization of numbers, determining if fractions are equivalent, simplifying expressions with exponents, and performing operations in scientific notation.
Math unit8 number sequences
This document outlines an instructional unit on number sequences. The unit contains 5 presentations that cover: 1) simple number patterns, 2) recognizing patterns, 3) geometric patterns, 4) linear sequences, and 5) general laws. Each presentation provides examples and problems for students to work through related to the particular type of number sequence. The goal is for students to learn how to identify patterns in sequences and determine rules or formulas to describe the relationships.
4th quarter long test review
This document contains a 10 question review for a 4th quarter long test covering circle equations, polynomial division, factoring, and finding zeros of polynomials. The questions cover finding equations of circles given properties like center and radius, performing polynomial division and finding quotients and remainders, factoring polynomials, and solving polynomials for real zeros.
Exponents
The document reviews exponents and exponential notation. It defines the base as the starting number being used to an exponent, and the exponent as the number of times the base is used as a factor. It then provides rules for multiplying, dividing, and raising exponential expressions to a power:
- When multiplying expressions with the same base, add the exponents
- When dividing expressions with the same base, subtract the exponents
- When raising an expression to a power, multiply the exponents
It also notes that any number to the zero power equals one, and negative exponents represent the reciprocal of the base number rather than making the expression negative.
Edu 290 powerpoint1
The document discusses linear equations and their two main forms - slope-intercept form (y=mx+b) and point-slope form (y-y1=m(x-x1)). It explains how to use each form to find the equation of a line given values for the slope and/or a point on the line. Examples are provided for finding linear equations using both forms.
What's hot (19)
Pythagorean theorem and distance formula power point
Pythagorean theorem and distance formula power point
Binomial Theorem, Recursion ,Tower of Honai, relations
Binomial Theorem, Recursion ,Tower of Honai, relations
Viewers also liked
16Nov16 - The Dr Jack Watters Debate - Tackling antimicrobial resistance in...
The Jack Watters debate - tackling antimicrobial resistance in an ageing society, took place on the 16th November 2016 at the Old Operating Theatre Museum in London.
This event was dedicated to a long term supporter of the ILC and a pioneer in championing the health and well-being of ageing people, Dr. Jack Watters.
The debate was chaired by Baroness Sally Greengross (Chief Executive, ILC-UK) and saw the participation of the following speakers:
- Professor David Salisbury CB, Associate Fellow, Centre on Global Health Security Chatham House
- Matthew Edwards, Head of Mortality and Longevity, Towers Watson
- Michelle Bresnahan, Founder, A Life for a Cure
- Dr Gina Radford, Deputy Chief Medical Officer
http://www.ilcuk.org.uk/index.php/events/tackling_antimicrobial_resistance_in_an_ageing_society
Why Were We Created? - Dr. Bilal Philips
Not just Muslims, but every single human being has to answer the most fundamental question at some point in his or her lifetime:
"Why was I created? Why am I here? What am I doing in this world? Why did God create me?"
These questions are questions which each and everyone of us reflects on at some point during their life. We have some answers, which are given generally but usually these answers don't satisfy us - seeming somewhat simplistic. So, we still wonder: "Why me? Why here?". I know all of you (Muslims), are saying, "To worship Allah, khallas (finish). What more is there to say? Why do we need to have a big long talk on why we were created when we all know it is to worship Allah?!"
But wait. If this is presented to a non-Muslim, the next logical question would be, "Why does Allah want us to worship Him?" Then your stuck, which can only mean that in our own minds it is not really clear. Why did Allah create us to worship Him?
1.8 notes
This document provides examples of solving equations by using properties of equality. It gives the identity property and shows that multiplying or dividing both sides of an equation by the same nonzero number preserves equality. It then has two examples of using these properties to solve equations: one set involves solving for x and y, and another set involves solving equations with fractions for t and l.
Report
This document provides an executive summary and analysis of operations for a company. It includes financial information such as revenue, expenses, profit, cash flow, and utilization rates. It also analyzes technical and non-technical staffing levels and overtime. The company had over $1.9 million in revenue year-to-date and $795,000 in gross profit. Staffing levels were stable at around 45 full-time equivalents total.
9.3
This document provides information about finding the area of squares, using the square of a binomial pattern, using the sum and difference pattern, and examples of applying these patterns to find products of binomial expressions. It introduces shorthand methods for finding products like (a + b)2, (a - b)2, and (a + b)(a - b) more quickly than using the traditional FOIL (First, Outer, Inner, Last) method. Examples are provided to demonstrate finding products like (3x + 4)2, (5x - 2y)2, (t + 5)(t - 5), and using mental math to find 26 • 34. Warm-up problems at the end ask the reader to
Lead Generation Content For Advisors: 13 Tax Tips For Doctors For 2013
You can purchase this special report targeted to doctors branded with your logo. Post it for all to see on your website, or require visitors submit their contact information to view the report in order to generate leads.
Search Marketers are the new Data Driven Storytellers
Keynote presentation given at the SEMPDX Searchfest conference in Portland discussing topics such as data storytelling, ad storytelling, cross channel measurement, cross channel advertising and attribution.
Ns dsc1110 a-10-0197_v2_web_english_final_lr
This user guide provides instructions for setting up and using a 10 megapixel digital camera. It describes the camera features such as the LCD screen and menus for changing settings. The guide also explains how to take photos and videos, view media, and adjust settings using the camera menus. Troubleshooting tips and product specifications are included at the end.
Js 单元测试框架介绍
The document discusses several JavaScript unit testing frameworks: QUnit, Jasmine, and YUITest. It provides overviews of each framework including features and how to set them up. For YUITest specifically, it describes how to create test cases and test suites, use assertions, mocks, asynchronous tests, and more. The document serves as a guide to using the YUITest framework for JavaScript unit testing.
Chapter3.3
The document provides examples of solving multi-step equations, equations containing fractions, and word problems involving rates and averages. It includes 4 practice problems and asks the reader to solve them. It also provides a word problem about a person's hourly rate and earnings that requires setting up and solving an equation.
Ejemplo cambio climático
El documento trata sobre el cambio climático pero no proporciona información relevante debido a que consiste en texto sin sentido.
Youtubers in Czech Republic
Tom leads the digital research department at Gizmax. A survey found that 90% of 15-24 year olds in the Czech Republic know what a youtuber is. Youtubers have evolved from people who just watch videos to celebrities with large followings and their own original content. It is logical for brands to partner with popular youtubers in the Czech Republic like PewDiePie, ViralBrothers, GoGoMan, Teri Blitzen, and Jirka Král due to their ability to influence consumers.
Chapter5.6
The document provides examples of using proportions to solve problems involving similar triangles formed by objects and their shadows. It includes two examples: 1) Finding the length of one side of a similar triangle where the other sides are given. The length is found to be 12 feet. 2) Finding the height of a tree using the height and shadow length of a building and the shadow length of the tree. The height of the tree is found to be 14 feet. It also includes a practice problem to check understanding.
Chapter2.2
This document provides examples for comparing fractions, decimals, and numbers on a number line. It shows how to write fractions with a common denominator and compare them, write fractions as decimals to compare them, and place numbers on a number line to order them from least to greatest. Examples are provided to demonstrate comparing fractions with common denominators, fractions written as decimals, and using a number line to order percentages representing population changes from different states.
Unit 5.5
This document discusses how to calculate the slope of a line from two points on the line. It provides the formula for slope as the rise over the run, or (y2 - y1) / (x2 - x1). Several examples are worked through, finding the slopes of lines passing through different pairs of points. The key points are:
- Slope is the ratio of the vertical change (rise) to the horizontal change (run) between two points
- The formula to calculate slope from two points (x1, y1) and (x2, y2) is: (y2 - y1) / (x2 - x1)
- Slope can be positive, negative, zero
Viewers also liked (20)
16Nov16 - The Dr Jack Watters Debate - Tackling antimicrobial resistance in...
16Nov16 - The Dr Jack Watters Debate - Tackling antimicrobial resistance in...
Lead Generation Content For Advisors: 13 Tax Tips For Doctors For 2013
Lead Generation Content For Advisors: 13 Tax Tips For Doctors For 2013
Search Marketers are the new Data Driven Storytellers
Search Marketers are the new Data Driven Storytellers
Similar to Unit 5.6
Unit 6.1
The document provides examples for writing linear equations in slope-intercept form (y=mx+b) given different representations of a line:
1) Given the slope (m) and y-intercept (b), write the equation.
2) Given a graph of the line, calculate the slope and y-intercept to write the equation.
3) Given the coordinates of two points on the line, calculate the slope and use it to write the equation.
4) Given an equation and a point that the line passes through, solve for the missing slope (m) or y-intercept (b) value.
Ultimate guide to coordinate plane
The document provides examples and explanations for writing and working with equations of lines using slope-intercept form. It includes examples of writing equations given the slope and y-intercept, given two points, using point-slope form, and determining whether lines are parallel or perpendicular. It also provides a multi-step example involving writing an equation to model combinations of small and large vans used to transport a class on a field trip. The examples progress from simple to more complex and include step-by-step solutions and guided practice problems.
LECTURE-EQUATION OF A LINE
The document provides examples and exercises on writing linear equations in standard form, slope-intercept form, and two-point form. It discusses transforming equations between these forms and finding the slope and y-intercept. Examples are provided for writing equations of lines given the slope and a point, or two points. Exercises have students write equations of lines through points or with given slope, identifying slopes and y-intercepts of lines, and sketching line graphs.
5.5 parallel and perpendicular lines (equations) day 1
The document discusses writing equations of parallel and perpendicular lines, including identifying whether lines are parallel or perpendicular based on their slopes. It provides examples of writing equations of parallel and perpendicular lines given a point and the slope or line of another line. Guidance problems are also included to practice these skills.
Integrated 2 Section 3-4
This document provides examples for solving two-step equations and formulas. It begins by defining a two-step equation as an equation that requires two steps to solve. It then shows worked examples of solving two-step equations by adding or subtracting the same quantity to both sides. The document also demonstrates solving formulas for a given variable and checking solutions. Key steps include isolating the variable of interest and performing inverse operations.
Equation Of A Line
This document discusses different methods for finding the equation of a line, including:
1) Given the slope and y-intercept
2) Using a graph
3) Given a point and the slope
4) Given two points
It provides examples of how to write the line equation using each method.
January 23
Steps are shown for solving systems of equations by the elimination method, including multiplying one equation by a constant to eliminate a variable before adding the equations. Examples are provided of solving systems by substitution, where one variable is solved for in one equation and substituted into the other equation. Practice problems are given for students to apply
7.1 7.3 reteach (review)
The document provides examples and exercises for solving systems of linear equations by graphing, substitution, and elimination. It explains that when graphing two linear equations, the point of intersection is the solution to the system. For substitution, one equation is solved for one variable in terms of the other and substituted into the other equation. For elimination, like terms are eliminated by adding or subtracting the equations to solve for one variable in terms of the other.
7.4
This document provides examples of solving systems of nonlinear equations in two variables. It begins with definitions, including that a nonlinear system contains at least one equation that is not of the form Ax + By = C. Methods for solving nonlinear systems include substitution and addition. Examples walk through both methods step-by-step for various systems. Key steps are rewriting equations in terms of variables, substituting values, solving resulting equations, back-substituting, and checking solutions satisfy both original equations.
2.4 writing equations of lines
1) This document discusses writing linear equations in slope-intercept form (y=mx+b) given different information: the slope (m) and y-intercept (b), a graph, the slope and a point, or two points.
2) It provides examples of writing equations of lines given: the slope and y-intercept, a graph, the slope and a point, two points, or the x- and y-intercepts.
3) The key steps are to identify the slope (m) and y-intercept (b) from the information provided, then substitute those values into the slope-intercept form equation to write the linear equation.
Dec.18
The document provides instructions for a double agent located at coordinates (-2,-3) who needs to escape to one of two safe houses. The safe houses are located in the direction of a -2/3 slope from the agent's current location. The document requests the coordinates of the two safe houses to help the agent narrowly escape death.
Ultimate guide to coordinate plane
1) The document provides examples and explanations for writing equations of lines given slope and y-intercept, two points, or one point and being parallel/perpendicular to another line. It also covers graphing lines and solving word problems involving linear equations.
2) Worked examples are presented for writing linear equations to represent real-world contexts like transportation options for a class field trip.
3) Guided practice problems reinforce the concepts with additional examples for students to work through, including determining if lines are parallel/perpendicular and solving multi-step word problems.
Lesson 3 (write the equation of a line)
The document provides steps to determine the equation of a line given certain information:
1) If the slope is -5 and y-intercept is 8, the equation is y = -5x + 8.
2) If the slope is 4 and the line passes through point (-2, -3), the equation is y = 4x + 5.
3) If a line passes through (3, -5) and is parallel to y = -2x + 9, the equation is y = -2x + 1.
Topic 8 (Writing Equations Of A Straight Lines)
The document provides information on properties of straight lines and methods to write equations of straight lines given different conditions. It also discusses solving systems of linear equations using different methods like graphing, substitution, elimination and Cramer's rule. Key points covered include writing equations in slope-intercept and standard form, finding slopes of parallel and perpendicular lines, and properties of consistent, inconsistent and dependent systems of linear equations.
Module 3 exponential and logarithmic functions
This module discusses inverse relations and functions. It defines inverse relations and explains how to find the inverse of a function using arrow diagrams, ordered pairs, and equations. It also discusses how to graph the inverse of a function. The document provides examples of finding the inverse of various functions by interchanging variables in equations and tables of values. It explains that the inverse of a function is obtained by reflecting the original function's graph over the line y=x. The inverse of a function may not always be a function itself.
Module 5 Inequalities
1. The document provides examples of graphing systems of inequalities on a coordinate plane. It contains 7 problems where students are asked to shade the region satisfying 3 given inequalities on a graph.
2. The problems involve skills like drawing lines representing linear equations, identifying the region between lines, and determining which inequalities define the shaded region.
3. Feedback is provided on the answers, noting correct graphing of lines and shading of regions, as well as common errors like drawing lines as solid instead of dashed.
MODULE 5- Inequalities
1. The document provides examples of graphing systems of inequalities on a coordinate plane. It contains 7 problems where students are asked to shade the region satisfying 3 given inequalities on a graph.
2. The problems involve skills like drawing lines representing linear equations, identifying the region between lines, and determining the intersecting area that satisfies all inequalities simultaneously.
3. Feedback is provided on the answers with notes on common mistakes like drawing lines as solid instead of dashed.
Topic 15 algebra 2
The document summarizes key concepts about sequences and simultaneous equations in algebra 2. It provides examples and explanations of linear sequences, writing the nth term formula, and solving simultaneous equations using substitution and elimination methods. Sample examination questions are also included to assess understanding of finding missing terms in a sequence, writing the nth term formula, and solving simultaneous equations word problems involving two unknown variables.
5.1 writing linear equations day 1
This chapter discusses writing linear equations in slope-intercept form (y=mx+b) by either knowing the slope and y-intercept or by being given two points on the line. It provides examples of writing equations of lines from graphical representations or when given the slope and y-intercept numerically. Students are guided in writing linear equations from different scenarios like being given two points or the cost equation of a recording studio based on hours of studio time.
Equation of the line
1. The document discusses various forms of linear equations including general, two-point, intercept, point-slope, and slope-intercept forms.
2. It provides examples of writing equations in each form given specific information like two points, an x-intercept and y-intercept, a point and slope, or just a slope and y-intercept.
3. Guided practice problems are included for writing equations parallel or perpendicular to a given line.
Similar to Unit 5.6 (20)
5.5 parallel and perpendicular lines (equations) day 1
5.5 parallel and perpendicular lines (equations) day 1
More from nglaze10
add and subtract decimals
This document provides instructions and examples for adding and subtracting decimals. It explains the basic steps of lining up the decimal point and filling in missing places with zeros before adding or subtracting. Several examples are worked through, including subtracting across zeros by borrowing from the first non-zero digit. The document concludes with a quiz to assess understanding of adding and subtracting decimals.
3 3 i can add and subtract decimals
This document provides instructions and examples for adding and subtracting decimals. It explains the basic steps of lining up the decimal point and filling in missing places with zeros before adding or subtracting. When subtracting across zeros, it notes to borrow from the first non-zero digit if needed. Several examples show evaluating decimal expressions by substituting values for variables and performing the indicated operations. The document concludes with a quiz to assess understanding of adding and subtracting decimals.
Integers day 2 hour 1
This document provides examples of multiplying and dividing integers. For multiplying integers, the examples show multiplying a negative number times a positive number results in a negative product, and multiplying two negative numbers results in a positive product. For dividing integers, the examples demonstrate that when dividing a negative number by a positive number the result is negative, and when dividing a positive number by a negative number the result is negative.
New week 6
This document outlines the daily schedule and assignments for a pre-algebra class over the course of a week. It includes instructions to have homework on desks, complete warm-ups, discuss previous homework, do assignments from textbooks and workbooks, take a quiz, play an integer product game, and complete a mathematical reflection. The schedule is detailed for Monday through Friday with different assignments and activities each day.
New week 5
This document provides an overview of the daily lessons and assignments for a Pre-Algebra class over the course of a week. It includes warm-up problems, homework assignments from the textbook, discussions of previous lessons, and introductions to new topics like multiplication patterns with integers and division of rational numbers. The class will cover investigations and vocabulary related to rational numbers and operations involving integers.
New week 4
The document contains summaries of pre-algebra warm ups and lessons for four days of the week. It includes tasks to complete tables, find differences, identify numbers between given values, calculate new scores, and make charts. It also lists homework assignments and materials needed for the lessons.
New week 3
This document contains summaries of daily lessons and activities for a Pre-Algebra class over the course of a week. It includes warm-up problems, learning objectives, homework assignments, quizzes, and vocabulary terms. The class focuses on topics like using chip models to represent addition and subtraction, ordering numbers, properties of rational numbers, and extending addition to rational numbers.
Newweek2
The document provides information about a pre-algebra class that covers topics like the number line and rational numbers. It includes warm-up problems, homework assignments, and discussions of investigations into extending the number line and using it to represent number sentences for changes in temperature. The class materials are aimed at helping students understand rational numbers and how to use the number line to compare numbers and represent number sentences.
10.3
This document provides examples of using quadratic functions in intercept form. It demonstrates how to identify the x-intercepts from the function, graph the function by plotting intercepts and the vertex, write a function given intercepts and a point, and model a real-world scenario like a dolphin's leap using a quadratic function. Key aspects covered include the intercept form equation, finding the vertex and axis of symmetry, and completing the steps to graph or write a quadratic function based on given information.
New week 1
The document provides information about a pre-algebra class, including:
1) Instructions for students to write down their homework, review class expectations, and get out notebooks.
2) Details about classroom rules and expectations for students.
3) An overview of the upcoming unit on operations with integers which will cover comparing and ordering numbers on a number line.
New week 10
This document contains a multi-part math problem about using similar triangles to estimate heights and distances. Part A asks students to use similar triangles to find the height of a building from given measurements. Part B asks students to use the mirror method with their group to estimate the height of an object and provide their measurements and explanation. Part C compares the estimates from Parts A and B and asks if they seem reasonable. Follow-up questions involve pooling the class data and comparing estimates from the two methods.
New week 9
The document contains instructions and information about using similar triangles to estimate heights and distances that are difficult to measure directly. It discusses using shadows and mirrors to form similar triangles and estimate heights of objects. Measurements are taken of shadows, mirrors, and distances that allow heights to be calculated through properties of similar triangles. Students work through examples estimating heights of buildings using these methods.
11.6
This document provides an example of how to use the work formula to solve problems involving work done at a steady rate. It gives the formula for work rate as the amount of a job completed in a given time. It then works through two examples - one calculating the time for two people to complete a job together, and another multiple choice problem calculating the time for one person to complete a job alone based on work rates.
11.5
This document discusses solving rational equations by using the cross product property. It provides three examples of solving rational equations:
1) Solving a simple rational equation with a single rational expression on each side. The solutions are -6 and 2.
2) Solving a rational equation with rational expressions on both sides. The solution appears to be 2, but it is an extraneous solution.
3) Solving a rational equation by factoring the denominators to find the least common denominator (LCD).
11.4
1) To add or subtract rational expressions with the same or different denominators, we first find the least common denominator (LCD), which is the least common multiple of the denominators.
2) We then rewrite the rational expressions with the LCD as the common denominator before adding or subtracting the numerators.
3) Once the rational expressions have been rewritten with the same denominator, we can perform the addition or subtraction operation as we would with numerical fractions.
New week 8
Raphael wants to make enlarged posters of his advertisement to display at a sale. He has an 8.5" by 11" ad and wants to enlarge it as much as possible using the copy machines at his local copy shop, which can enlarge documents between 50-200% and have paper sizes of 8.5" by 11", 11" by 14", and 11" by 17". The best option would be to use the 11" by 17" paper and enlarge the ad 150% to make it a similar, larger poster without trimming off the edges of the paper.
11.1
This document provides examples of direct and inverse variation, including how to identify, graph, and write equations for direct and inverse variation relationships. It also contains examples of solving work problems using inverse variation.
Key points covered include:
- Direct variation is when y=kx and inverse variation is when y=k/x, where k is the constant of variation.
- Example 1 shows how to identify if an equation represents direct, inverse, or neither type of variation.
- Examples 2 and 3 demonstrate how to graph inverse variation equations.
- Examples 4, 5, and 6 show how to write inverse variation equations from tables of data or real-world context and solve problems using inverse variation equations.
New week 6
This document provides instructions and materials for a math lesson on similarity and scale factors. It includes examples of similar figures with questions about their side lengths, scale factors, and areas. It also discusses how police use measurements and similar figures to determine characteristics like a criminal's height from surveillance photos. Students are asked to use a photo of a teacher holding an object of known size to calculate the teacher's height, and to explain how police may have used a similar technique to determine a robber's height from a store surveillance photo.
9.9
The document provides examples of factoring polynomials completely. It begins by outlining guidelines for factoring polynomials completely, such as factoring out the greatest common monomial factor, looking for differences of squares or perfect square trinomials, and factoring trinomials and polynomials with four terms by grouping. It then works through examples of factoring various polynomials completely by applying these guidelines. These include factoring trinomials, solving a polynomial equation, and solving a multi-step problem involving factoring a polynomial to find dimensions.
9.8
The document discusses factoring polynomials using the difference of squares pattern and perfect square trinomial pattern. It provides examples of factoring expressions involving these patterns, including solving polynomial equations. The examples illustrate factoring expressions with variables and evaluating expressions to solve vertical motion problems.
More from nglaze10 (20)
Unit 5.6
- 1. Unit 5.6 Slope and y-intercept y = mx + b
- 3. Example 1 Identify slope and y-intercept Identify the slope and y-intercept of the line with the given equation. a. y = 3x + 4 b. 3x + y = 2 SOLUTION a. The equation is in the form y = mx + b. So, the slope of the line is 3, and the y-intercept is 4. b. Rewrite the equation in slope-intercept form by solving for y. 3x + y = 2 Write original equation. y = – 3x + 2 Subtract 3x from each side.
- 4. Example 1 Identify slope and y-intercept ANSWER The line has a slope of –3 and a y-intercept of 2.
- 5. W MUP AR Identify the slope and y-intercept of the line with the given equation. 1. y = 5x – 3 ANSWER 5; – 3 2. 3x – 3y = 12 ANSWER 1; – 4 1; 1 – 1 3. x + 4y = 6 ANSWER 4 2