4.7solvinggraphing
•
0 likes•73 views
This document provides steps for solving linear equations graphically. The steps are to write the equation in y=ax+b form, isolate the variable y by moving it to one side of the equation, and graph the resulting linear equation. The point where the graph crosses the x-axis is the solution to the original equation. Examples are provided to demonstrate solving equations algebraically and graphically.
Report
Share
Report
Share
Download to read offline
Recommended
Factoring the sum and difference of two cubes
This document provides instructions for factoring the sum and difference of two cubes. It explains that to factor a3 + b3, one should use the formula (a + b)(a2 - ab + b2). To factor a3 - b3, the formula is (a - b)(a2 + ab + b2). Several examples are worked out applying these formulas to factor polynomials like x3 - 8, y3 + 1, and 8z3 - 27. Students are then asked to complete practice problems factoring polynomials that are the sum or difference of two cubes.
Factoring the difference of two squares
This document discusses factoring the difference of two squares. It explains that the difference of two squares, a2 - b2, can be factored into (a + b)(a - b). It provides an example of factoring y2 - 36 into (y + 6)(y - 6). The document then gives additional examples of factoring polynomials that are the difference of two squares. It provides a performance task for students to practice factoring the difference of two squares on their own. Finally, it gives an assessment task where students must factor five polynomials and show their work.
A19 1 square roots notes
The document discusses quadratic equations and square roots. It defines a square root as the number that, when multiplied by itself, equals the original number. Only positive integers have exact square roots, while other numbers result in non-terminating decimals. A quadratic equation is one that has the form ax^2 + bx + c = 0, where a is called the leading coefficient. Examples are provided of evaluating square roots, solving quadratic equations by finding the square roots of both sides, and evaluating expressions involving radicals.
Day 16 angle pairs day 2
This document contains notes from a geometry class on angle pairs. It includes examples of identifying vertical angles, adjacent angles, complementary angles, and supplementary angles. Students are asked to solve equations involving angles and find missing angle measures using properties of angles. The homework is to complete an angle pairs worksheet.
Power point aku
This document contains a 15 question math quiz for 2nd grade students in Malaysia. The questions cover topics like: [1] Writing numbers in words; [2] Identifying place values; [3] Solving addition, subtraction, multiplication and division word problems; [4] Comparing and ordering numbers; [5] Calculating sums and differences. The quiz tests students' understanding of basic math concepts taught in 2nd grade.
A25 5 completingsquare
This document provides instructions and examples for graphing complex numbers and using the completing the square method to solve quadratic equations. It explains that to graph a complex number, you plot the real part on the x-axis and the imaginary part on the y-axis. It also outlines the six step process for completing the square, which involves factorizing the quadratic term, finding the constant c, adding it to both sides, taking the square root of both sides, and then solving for x.
A19-5 solving quads by formula notes
The document discusses using the quadratic formula to solve quadratic equations. It states that in order to use the quadratic formula, the equation must equal 0 and be written in the form ax^2 + bx + c = 0. It then lists the steps as identifying the values of a, b, and c and then plugging those values into the quadratic formula to solve for x. The document provides an example of using the quadratic formula to solve the equation -x^2 + 8x = 1 and assigns homework problems from pages 536 problems 32-36 and 44-47.
EE201_Assignment3
This document contains instructions for MATLAB assignments involving:
1) Creating vectors and finding elements within them
2) Creating matrices, extracting elements, transposing, replacing elements, and finding maximum/minimum values
3) Performing element-wise operations on vectors and calculating expressions involving sin, square root and summation
Recommended
Factoring the sum and difference of two cubes
This document provides instructions for factoring the sum and difference of two cubes. It explains that to factor a3 + b3, one should use the formula (a + b)(a2 - ab + b2). To factor a3 - b3, the formula is (a - b)(a2 + ab + b2). Several examples are worked out applying these formulas to factor polynomials like x3 - 8, y3 + 1, and 8z3 - 27. Students are then asked to complete practice problems factoring polynomials that are the sum or difference of two cubes.
Factoring the difference of two squares
This document discusses factoring the difference of two squares. It explains that the difference of two squares, a2 - b2, can be factored into (a + b)(a - b). It provides an example of factoring y2 - 36 into (y + 6)(y - 6). The document then gives additional examples of factoring polynomials that are the difference of two squares. It provides a performance task for students to practice factoring the difference of two squares on their own. Finally, it gives an assessment task where students must factor five polynomials and show their work.
A19 1 square roots notes
The document discusses quadratic equations and square roots. It defines a square root as the number that, when multiplied by itself, equals the original number. Only positive integers have exact square roots, while other numbers result in non-terminating decimals. A quadratic equation is one that has the form ax^2 + bx + c = 0, where a is called the leading coefficient. Examples are provided of evaluating square roots, solving quadratic equations by finding the square roots of both sides, and evaluating expressions involving radicals.
Day 16 angle pairs day 2
This document contains notes from a geometry class on angle pairs. It includes examples of identifying vertical angles, adjacent angles, complementary angles, and supplementary angles. Students are asked to solve equations involving angles and find missing angle measures using properties of angles. The homework is to complete an angle pairs worksheet.
Power point aku
This document contains a 15 question math quiz for 2nd grade students in Malaysia. The questions cover topics like: [1] Writing numbers in words; [2] Identifying place values; [3] Solving addition, subtraction, multiplication and division word problems; [4] Comparing and ordering numbers; [5] Calculating sums and differences. The quiz tests students' understanding of basic math concepts taught in 2nd grade.
A25 5 completingsquare
This document provides instructions and examples for graphing complex numbers and using the completing the square method to solve quadratic equations. It explains that to graph a complex number, you plot the real part on the x-axis and the imaginary part on the y-axis. It also outlines the six step process for completing the square, which involves factorizing the quadratic term, finding the constant c, adding it to both sides, taking the square root of both sides, and then solving for x.
A19-5 solving quads by formula notes
The document discusses using the quadratic formula to solve quadratic equations. It states that in order to use the quadratic formula, the equation must equal 0 and be written in the form ax^2 + bx + c = 0. It then lists the steps as identifying the values of a, b, and c and then plugging those values into the quadratic formula to solve for x. The document provides an example of using the quadratic formula to solve the equation -x^2 + 8x = 1 and assigns homework problems from pages 536 problems 32-36 and 44-47.
EE201_Assignment3
This document contains instructions for MATLAB assignments involving:
1) Creating vectors and finding elements within them
2) Creating matrices, extracting elements, transposing, replacing elements, and finding maximum/minimum values
3) Performing element-wise operations on vectors and calculating expressions involving sin, square root and summation
A1 1 linear fxns notes
A linear function creates a straight line graph. A solution to a linear equation is a point on the line. The graph of a linear function is the set of all points (x, y) that satisfy the linear equation, with all these points forming a straight line. One way to graph a linear function is to choose sample x-values, calculate the corresponding y-values using the linear equation, plot these points, and connect them with a straight line.
Participación semana 9
This document contains instructions for calculating areas and volumes for calculus problems. Specifically:
1) Find the area between the curves y=x^2 and y=x+2, which is 4.5 units.
2) Find the area between the curves y=x^2 and y=x, which is 0.17 units.
3) Find the volume of the solid generated when the area between y=x+2, the x-axis, and the lines x=0 and x=2 revolves around y=-1, which is 120.63 cubic units.
Day 17 angle pairs day 3 (variables on both sides)
This document contains notes from a math class on solving equations with variables on both sides and finding complementary, vertical, and supplementary angles based on a diagram. The notes include examples of solving various equations by isolating the variable and finding corresponding angle measures. Homework assigned is to complete the class notes.
A2. u1. calculo diferencial. unadm
The document discusses solving inequalities using the axioms of real numbers. It contains two examples:
1) Solving the inequalities 3x-4>6 and 5x-4<2x+5 by manipulating and isolating the variable.
2) Solving inequalities with absolute values, such as |4(x+2)|<20 and |x+3/3|≤9, by considering both possible values inside the absolute value signs.
Bvco u1 a2_jogf
This document contains an activity on complex numbers and functions of a complex variable. The activity includes two problems. The first problem involves calculating the modulus of complex expressions. Various steps are shown to solve the expressions, including using binomial theorem to expand powers of complex numbers. The second problem expresses vectors representing complex numbers in the form a + ib. Steps are outlined to calculate the components from the vector properties like length and angle. Graphical representations of the complex numbers are also provided.
Activity 4 (answer key)
This document provides the answers to geometry questions about classifying and finding angle measures of different quadrilaterals. It identifies 10 shapes as trapezoids, parallelograms, squares, rectangles, or kites. It then finds that if one angle of a parallelogram is 82 degrees, the other angles are 98 degrees. Finally, it determines that if two consecutive angles of a parallelogram are (x + 30) and (2x - 60), x is 100 and 80, and if one base angle of an isosceles trapezoid is 85 degrees, the other angles are 95 degrees.
7th math(c2) -l4
This document contains notes from a math lesson on integers and number lines. It includes an assignment that is due the next day, examples showing the use of number lines for addition and subtraction of integers, and sequences to continue. The lesson covered integers on the number line, properties of addition and subtraction, comparing expressions, and simplifying subtraction.
Examen du seconde semestre g8
This document is the exam for the Class of G8 in CCS Mathematics from March 2014. It consists of 7 questions testing various math skills. Question I involves simplifying fractions and expressions. Question II requires writing fractions in irreducible form and determining properties. Question III has students developing, factorizing, and solving polynomials. Question IV asks about the locus of a midpoint on a circle. Question V proves properties of midpoints and determines a quadrilateral. Question VI expresses areas in terms of x and solves for x given an area condition. Question VII draws and analyzes a trapezoid, proving properties about its midpoints and segments.
1-1 Guide Notes Teacher Edition - Nets and Drawings for Visualizing Geometry
This is the Teacher Edition of the Guided Notes to go along with the PowerPoint on Nets and Drawings for Visualizing Geometry.
The Student Editions can be found at:
https://geometrycoach.com/nets-and-drawings-for-visualizing-geometry/
IME 2018 - fechada
The document contains 15 multiple choice questions from an IME 2018 exam. The questions cover topics such as determinants, functions, systems of equations, geometry, complex numbers, polynomials, trigonometry, and number representations in different bases. A key is provided with the correct answer for each question labeled A through E.
3.1 graphing systems
This document provides an agenda and notes for using graphing to solve systems of linear equations in two variables. It outlines the steps to graph each equation by writing it in slope-intercept form, graphing the y-intercept, using the slope to find another point, drawing a line through the points, and finding the point of intersection. It emphasizes the importance of drawing straight lines and presents three example problems to demonstrate the process.
Lesson5.1 complexnumbers demo
This document provides an introduction to complex numbers. It discusses:
1) The definition of the imaginary number i and its powers.
2) How complex numbers combine real and imaginary numbers in the form of a + bi.
3) The four basic operations that can be performed on complex numbers: addition, subtraction, multiplication, and division.
Complex nos demo 2
(1) This document provides an introduction to complex numbers, including: defining complex numbers using i as the square root of -1, addition and multiplication of complex numbers, expressing complex numbers in polar form, and De Moivre's theorem.
(2) De Moivre's theorem states that for a complex number r(cosθ + i sinθ) and integer n, (r(cosθ + i sinθ))n = rn(cos(nθ) + i sin(nθ)). It allows taking complex numbers to any power and finding roots of complex numbers.
(3) The document provides examples of using De Moivre's theorem to find powers and roots of complex numbers in both
2f predict the shape of a graph
This document discusses identifying linear and nonlinear graphs from tables of values. It defines linear graphs as having a constant ratio between the difference in y-values and difference in x-values. Students are instructed to plot points from tables on handouts to draw both a linear and nonlinear graph, labeling points and connecting points for the nonlinear graph. The purpose is to practice predicting graph shapes from tables of values and identifying linear vs nonlinear relationships.
5.4 Complex Numbers
This document introduces complex numbers. It defines the imaginary unit i as the square root of -1, which allows quadratic equations with no real solutions, like x^2=-1, to be solved. Complex numbers have both a real part and an imaginary part in the form a + bi. They can be added, subtracted, multiplied, and divided by distributing terms and using properties of i such as i^2 = -1. Complex numbers are plotted on a plane with real numbers on the x-axis and imaginary numbers on the y-axis.
Review Unit 12 Test Form B
This document is an algebra worksheet reviewing concepts for a test, including:
1) Raising monomials to a power by multiplying the base by itself the number of times of the exponent.
2) Multiplying monomials and polynomials using the distributive property.
3) Adding and subtracting polynomials by combining like terms.
4) Multiplying binomials using the FOIL (First, Outer, Inner, Last) method.
Core 3 Modulus 1
This document discusses sketching the graphs of the functions y = x^2 - 2 and y = |x^2 - 2|. It notes that the graph of y = |x^2 - 2| will have a V-shape, as modulus functions involving linear equations always do. It provides an example of sketching the graph of y = |x + 2|, explaining that it crosses the y-axis at y = 2 and the x-axis at x = -2.
Vector multiplication dot product
The document discusses vector multiplication using the dot product. It provides two formulas for calculating the dot product:
1) a.b = |a| |b| cosθ, where |a| and |b| are the magnitudes of the vectors, θ is the angle between them, and cosθ gives the effectiveness of their interaction. The dot product is largest when the vectors are parallel (θ = 0).
2) For vectors in 3D space, a.b = x1x2 + y1y2 + z1z2, where the x, y, z components of each vector are multiplied and summed.
It provides examples of calculating the dot product using both formulas in different vector
A1 12 scatter plots
Scatter plots use a series of points to represent a relationship between two variables, with the x-axis representing one variable and the y-axis representing the other. A scatter plot should include a title, labeled x-axis, and labeled y-axis. Correlation can be positive if points increase from left to right, negative if points decrease from left to right, or no correlation if points have no trend. A line of best fit shows the overall trend of the data by having the same number of points above and below the line.
A1 11 functions
The document discusses functions, their domains and ranges, function notation, evaluating functions, and sequences. It provides examples of arithmetic and geometric sequences and how they can be defined using equations. It also discusses determining whether numbers are in the domain of a function and finding the domain and range of functions given their equations or graphs.
A1 11 functions
This document covers functions, including evaluating functions at given inputs, domains and ranges of functions, and sequences. It defines arithmetic and geometric sequences, providing examples of writing equations for each type of sequence and generating additional terms. Students are asked to evaluate functions, write equations for sequences, and find subsequent terms of given arithmetic and geometric sequences.
A2 Test 3 with answers 2011
This study guide covers polynomials, including classifying polynomials by degree and terms, adding and subtracting polynomials, multiplying polynomials, dividing polynomials using long division and synthetic division, factoring quadratics, solving quadratics, and graphing quadratics by finding the vertex, axis of symmetry, and x-intercepts. Key concepts are polynomials having only positive integer exponents, the degree being the highest exponent, and the leading coefficient being the coefficient of the term with the highest exponent.
More Related Content
What's hot
A1 1 linear fxns notes
A linear function creates a straight line graph. A solution to a linear equation is a point on the line. The graph of a linear function is the set of all points (x, y) that satisfy the linear equation, with all these points forming a straight line. One way to graph a linear function is to choose sample x-values, calculate the corresponding y-values using the linear equation, plot these points, and connect them with a straight line.
Participación semana 9
This document contains instructions for calculating areas and volumes for calculus problems. Specifically:
1) Find the area between the curves y=x^2 and y=x+2, which is 4.5 units.
2) Find the area between the curves y=x^2 and y=x, which is 0.17 units.
3) Find the volume of the solid generated when the area between y=x+2, the x-axis, and the lines x=0 and x=2 revolves around y=-1, which is 120.63 cubic units.
Day 17 angle pairs day 3 (variables on both sides)
This document contains notes from a math class on solving equations with variables on both sides and finding complementary, vertical, and supplementary angles based on a diagram. The notes include examples of solving various equations by isolating the variable and finding corresponding angle measures. Homework assigned is to complete the class notes.
A2. u1. calculo diferencial. unadm
The document discusses solving inequalities using the axioms of real numbers. It contains two examples:
1) Solving the inequalities 3x-4>6 and 5x-4<2x+5 by manipulating and isolating the variable.
2) Solving inequalities with absolute values, such as |4(x+2)|<20 and |x+3/3|≤9, by considering both possible values inside the absolute value signs.
Bvco u1 a2_jogf
This document contains an activity on complex numbers and functions of a complex variable. The activity includes two problems. The first problem involves calculating the modulus of complex expressions. Various steps are shown to solve the expressions, including using binomial theorem to expand powers of complex numbers. The second problem expresses vectors representing complex numbers in the form a + ib. Steps are outlined to calculate the components from the vector properties like length and angle. Graphical representations of the complex numbers are also provided.
Activity 4 (answer key)
This document provides the answers to geometry questions about classifying and finding angle measures of different quadrilaterals. It identifies 10 shapes as trapezoids, parallelograms, squares, rectangles, or kites. It then finds that if one angle of a parallelogram is 82 degrees, the other angles are 98 degrees. Finally, it determines that if two consecutive angles of a parallelogram are (x + 30) and (2x - 60), x is 100 and 80, and if one base angle of an isosceles trapezoid is 85 degrees, the other angles are 95 degrees.
7th math(c2) -l4
This document contains notes from a math lesson on integers and number lines. It includes an assignment that is due the next day, examples showing the use of number lines for addition and subtraction of integers, and sequences to continue. The lesson covered integers on the number line, properties of addition and subtraction, comparing expressions, and simplifying subtraction.
Examen du seconde semestre g8
This document is the exam for the Class of G8 in CCS Mathematics from March 2014. It consists of 7 questions testing various math skills. Question I involves simplifying fractions and expressions. Question II requires writing fractions in irreducible form and determining properties. Question III has students developing, factorizing, and solving polynomials. Question IV asks about the locus of a midpoint on a circle. Question V proves properties of midpoints and determines a quadrilateral. Question VI expresses areas in terms of x and solves for x given an area condition. Question VII draws and analyzes a trapezoid, proving properties about its midpoints and segments.
1-1 Guide Notes Teacher Edition - Nets and Drawings for Visualizing Geometry
This is the Teacher Edition of the Guided Notes to go along with the PowerPoint on Nets and Drawings for Visualizing Geometry.
The Student Editions can be found at:
https://geometrycoach.com/nets-and-drawings-for-visualizing-geometry/
IME 2018 - fechada
The document contains 15 multiple choice questions from an IME 2018 exam. The questions cover topics such as determinants, functions, systems of equations, geometry, complex numbers, polynomials, trigonometry, and number representations in different bases. A key is provided with the correct answer for each question labeled A through E.
3.1 graphing systems
This document provides an agenda and notes for using graphing to solve systems of linear equations in two variables. It outlines the steps to graph each equation by writing it in slope-intercept form, graphing the y-intercept, using the slope to find another point, drawing a line through the points, and finding the point of intersection. It emphasizes the importance of drawing straight lines and presents three example problems to demonstrate the process.
Lesson5.1 complexnumbers demo
This document provides an introduction to complex numbers. It discusses:
1) The definition of the imaginary number i and its powers.
2) How complex numbers combine real and imaginary numbers in the form of a + bi.
3) The four basic operations that can be performed on complex numbers: addition, subtraction, multiplication, and division.
Complex nos demo 2
(1) This document provides an introduction to complex numbers, including: defining complex numbers using i as the square root of -1, addition and multiplication of complex numbers, expressing complex numbers in polar form, and De Moivre's theorem.
(2) De Moivre's theorem states that for a complex number r(cosθ + i sinθ) and integer n, (r(cosθ + i sinθ))n = rn(cos(nθ) + i sin(nθ)). It allows taking complex numbers to any power and finding roots of complex numbers.
(3) The document provides examples of using De Moivre's theorem to find powers and roots of complex numbers in both
2f predict the shape of a graph
This document discusses identifying linear and nonlinear graphs from tables of values. It defines linear graphs as having a constant ratio between the difference in y-values and difference in x-values. Students are instructed to plot points from tables on handouts to draw both a linear and nonlinear graph, labeling points and connecting points for the nonlinear graph. The purpose is to practice predicting graph shapes from tables of values and identifying linear vs nonlinear relationships.
5.4 Complex Numbers
This document introduces complex numbers. It defines the imaginary unit i as the square root of -1, which allows quadratic equations with no real solutions, like x^2=-1, to be solved. Complex numbers have both a real part and an imaginary part in the form a + bi. They can be added, subtracted, multiplied, and divided by distributing terms and using properties of i such as i^2 = -1. Complex numbers are plotted on a plane with real numbers on the x-axis and imaginary numbers on the y-axis.
Review Unit 12 Test Form B
This document is an algebra worksheet reviewing concepts for a test, including:
1) Raising monomials to a power by multiplying the base by itself the number of times of the exponent.
2) Multiplying monomials and polynomials using the distributive property.
3) Adding and subtracting polynomials by combining like terms.
4) Multiplying binomials using the FOIL (First, Outer, Inner, Last) method.
Core 3 Modulus 1
This document discusses sketching the graphs of the functions y = x^2 - 2 and y = |x^2 - 2|. It notes that the graph of y = |x^2 - 2| will have a V-shape, as modulus functions involving linear equations always do. It provides an example of sketching the graph of y = |x + 2|, explaining that it crosses the y-axis at y = 2 and the x-axis at x = -2.
Vector multiplication dot product
The document discusses vector multiplication using the dot product. It provides two formulas for calculating the dot product:
1) a.b = |a| |b| cosθ, where |a| and |b| are the magnitudes of the vectors, θ is the angle between them, and cosθ gives the effectiveness of their interaction. The dot product is largest when the vectors are parallel (θ = 0).
2) For vectors in 3D space, a.b = x1x2 + y1y2 + z1z2, where the x, y, z components of each vector are multiplied and summed.
It provides examples of calculating the dot product using both formulas in different vector
What's hot (18)
Day 17 angle pairs day 3 (variables on both sides)
Day 17 angle pairs day 3 (variables on both sides)
1-1 Guide Notes Teacher Edition - Nets and Drawings for Visualizing Geometry
1-1 Guide Notes Teacher Edition - Nets and Drawings for Visualizing Geometry
More from vhiggins1
A1 12 scatter plots
Scatter plots use a series of points to represent a relationship between two variables, with the x-axis representing one variable and the y-axis representing the other. A scatter plot should include a title, labeled x-axis, and labeled y-axis. Correlation can be positive if points increase from left to right, negative if points decrease from left to right, or no correlation if points have no trend. A line of best fit shows the overall trend of the data by having the same number of points above and below the line.
A1 11 functions
The document discusses functions, their domains and ranges, function notation, evaluating functions, and sequences. It provides examples of arithmetic and geometric sequences and how they can be defined using equations. It also discusses determining whether numbers are in the domain of a function and finding the domain and range of functions given their equations or graphs.
A1 11 functions
This document covers functions, including evaluating functions at given inputs, domains and ranges of functions, and sequences. It defines arithmetic and geometric sequences, providing examples of writing equations for each type of sequence and generating additional terms. Students are asked to evaluate functions, write equations for sequences, and find subsequent terms of given arithmetic and geometric sequences.
A2 Test 3 with answers 2011
This study guide covers polynomials, including classifying polynomials by degree and terms, adding and subtracting polynomials, multiplying polynomials, dividing polynomials using long division and synthetic division, factoring quadratics, solving quadratics, and graphing quadratics by finding the vertex, axis of symmetry, and x-intercepts. Key concepts are polynomials having only positive integer exponents, the degree being the highest exponent, and the leading coefficient being the coefficient of the term with the highest exponent.
A1 Test 3 study guide with answers
1. The solution to a system of equations is a point, while the solution to a system of inequalities is a shaded region on a graph.
2. Parallel lines have the same slope and never intersect, so they have no solution. Coinciding lines are the same single line, so they have infinitely many solutions.
3. The document provides examples of solving systems of equations and inequalities through graphing, substitution, and elimination. The solutions are given as points or descriptions of regions.
PC Test 2 study guide 2011
1. The document is a study guide for a precalculus test that covers topics involving vectors, complex numbers, and their representations and operations.
2. It lists 15 problems involving finding magnitudes and direction of vectors, vector components, dot and cross products, complex numbers in rectangular and polar form, and converting between polar and rectangular coordinates.
3. The problems cover basic vector and complex number calculations, representations, properties and conversions.
A2 Test 2 study guide with answers (revised)
The document is an algebra 2 study guide that provides practice problems for graphing and solving various types of inequalities and systems of equations, including:
1) Graphing linear and compound inequalities on number lines and coordinate planes
2) Solving absolute value equations and inequalities
3) Solving systems of linear equations through graphing, substitution, and elimination
The study guide contains over 50 problems to help students prepare for an algebra 2 test.
A2 Test 2 study guide with answers
This document provides a study guide with answers for an Algebra 2 Test 2. It includes instructions to graph and solve various types of inequalities, systems of equations and absolute value equations, including linear and compound inequalities, systems of linear equations solved by graphing, substitution and elimination, and absolute value equations and inequalities.
A1 Test 2 study guide with answers 2011
The document is an algebra 1 test study guide containing 30 problems involving graphing and solving various types of inequalities, including linear, compound, absolute value, and graphing solutions on number lines. Key topics covered include writing inequalities from graphs, solving single-variable and compound inequalities, graphing linear inequalities on a coordinate plane, and solving absolute value equations and inequalities.
A1 Test 2 study guide
1. The document provides a study guide for an Algebra 1 Test 2 with questions about: graphing and writing inequalities on number lines, solving linear inequalities and compound inequalities, graphing linear inequalities on the xy-plane, and solving absolute value equations and inequalities.
2. Questions involve skills like graphing inequalities, writing inequalities from graphs, solving one-step and two-step inequalities, and solving absolute value equations and inequalities.
3. The study guide covers key Algebra 1 concepts to help prepare for Test 2.
PCExam 1 practice with answers
1. This practice exam covers topics like complex numbers, functions, limits, and graphing.
2. It asks students to choose problems involving adding, multiplying, composing, and finding inverses of various functions like f(x)=9x^2+1 and g(x)=x-1.
3. Students also must graph and classify functions, evaluate limits, and perform operations on complex numbers, plotting them on a plane. The exam covers concepts in precalculus.
PCExam 1 study guide answers
1. The document provides examples and definitions for various mathematical concepts including natural numbers, integers, rational numbers, real numbers, imaginary numbers, and complex numbers.
2. It also includes problems involving composition of functions, finding inverses of functions, operations on complex numbers, graphing and classifying functions, and evaluating limits.
3. Examples cover topics like composition and inverses of functions, operations on complex numbers, classifying functions as linear, quadratic, constant, etc. and their domains and ranges, and evaluating limits including ones that are undefined.
PC Exam 1 study guide
This study guide covers topics in precalculus including:
1) Examples of natural numbers, integers, rational numbers, and real numbers.
2) Composition of functions including finding f(g(x)) and g(f(x)) for given functions f(x) and g(x).
3) Finding inverses of functions and verifying inverses by composition.
4) Operations on complex numbers including plotting, finding modulus, distance, midpoint, addition, subtraction, multiplication, and division.
5) Graphing functions, classifying function types, and stating domains and ranges.
6) Finding limits of functions as x approaches values.
PC 1 continuity notes
A continuous function is defined as one that is defined at a point c, where the limit exists and the function approaches the same y-value from both sides of point c. A function may be discontinuous due to an infinite jump, a jump, or a point discontinuity. Rational functions are defined as the quotient of two polynomial functions. They have asymptotes which occur where the denominator is zero, creating either a vertical or horizontal asymptote in the graph. The end behavior of functions can be determined by considering whether they are increasing or decreasing over different intervals.
PC 1 continuity
This document discusses continuity and discontinuities in functions, defining continuous functions as smooth curves where the domain includes all real numbers. It presents tests for continuity, requiring a function to be defined at a point, have an existing function value, and approach the same y-value from both sides. Critical points and extrema are defined as maximums where a function changes from increasing to decreasing, and minimums where it changes from decreasing to increasing. Rational functions are described as the quotient of two polynomial functions, with limited domains and possible vertical asymptotes.
A1 3 linear fxns
The document discusses the slope-intercept form of a linear equation, y=mx+b. It explains that x represents the input, y represents the output, m is the slope of the line, and b is the y-intercept. It provides instructions for graphing a linear equation in slope-intercept form, which is to first plot the y-intercept and then use the slope to rise and run to the next point, connecting the points with a line.
A1 3 linear fxns notes
The document discusses slope and linear equations. It defines slope as rise over run and provides examples of calculating slope from graphs and ordered pairs. It also defines the standard form of a linear equation as y=mx+b, where m is the slope and b is the y-intercept. The document explains how to graph lines from their equations in standard form by plotting the y-intercept and using the slope to rise and run to the next point.
A1 2 linear fxns
This document discusses the slope-intercept form of a linear equation, y=mx+b. It explains that x represents the input, y represents the output, m is the slope of the line, and b is the y-intercept. It provides instructions for graphing a linear equation in slope-intercept form, which is to first plot the y-intercept, then use the slope to rise and run to the next point and connect them with a line.
A1 2 linear fxns notes
This document discusses intercepts and slope of lines in algebra 1. It defines x-intercepts as where the line crosses the x-axis and y-intercepts as where it crosses the y-axis. It provides the equations for finding each, and includes two examples of finding intercepts and graphing lines. It also defines slope as rise over run and asks what the slope is of a given graph, with homework assigned on slope of lines and graphing lines intuitively.
A2 2 linear fxns notes
This document provides instructions and examples for finding the slope and y-intercept of a line from its equation, ordered pairs, or graph and using them to graph the line. It explains that slope is defined as rise over run and is used along with the y-intercept to graph lines by standard form, plotting the y-intercept and using slope to find successive points. Exercises are provided to have students practice finding slope, y-intercept, and graphing lines from different representations.
More from vhiggins1 (20)
Recently uploaded
Columbus Data & Analytics Wednesdays - June 2024
Columbus Data & Analytics Wednesdays, June 2024 with Maria Copot 20
Video Streaming: Then, Now, and in the Future
In his public lecture, Christian Timmerer provides insights into the fascinating history of video streaming, starting from its humble beginnings before YouTube to the groundbreaking technologies that now dominate platforms like Netflix and ORF ON. Timmerer also presents provocative contributions of his own that have significantly influenced the industry. He concludes by looking at future challenges and invites the audience to join in a discussion.
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.
20240605 QFM017 Machine Intelligence Reading List May 2024
Everything I found interesting about machines behaving intelligently during May 2024
GraphRAG for Life Science to increase LLM accuracy
GraphRAG for life science domain, where you retriever information from biomedical knowledge graphs using LLMs to increase the accuracy and performance of generated answers
Best 20 SEO Techniques To Improve Website Visibility In SERP
Boost your website's visibility with proven SEO techniques! Our latest blog dives into essential strategies to enhance your online presence, increase traffic, and rank higher on search engines. From keyword optimization to quality content creation, learn how to make your site stand out in the crowded digital landscape. Discover actionable tips and expert insights to elevate your SEO game.
OpenID AuthZEN Interop Read Out - Authorization
During Identiverse 2024 and EIC 2024, members of the OpenID AuthZEN WG got together and demoed their authorization endpoints conforming to the AuthZEN API
Essentials of Automations: The Art of Triggers and Actions in FME
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
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.
CAKE: Sharing Slices of Confidential Data on Blockchain
Presented at the CAiSE 2024 Forum, Intelligent Information Systems, June 6th, Limassol, Cyprus.
Synopsis: Cooperative information systems typically involve various entities in a collaborative process within a distributed environment. Blockchain technology offers a mechanism for automating such processes, even when only partial trust exists among participants. The data stored on the blockchain is replicated across all nodes in the network, ensuring accessibility to all participants. While this aspect facilitates traceability, integrity, and persistence, it poses challenges for adopting public blockchains in enterprise settings due to confidentiality issues. In this paper, we present a software tool named Control Access via Key Encryption (CAKE), designed to ensure data confidentiality in scenarios involving public blockchains. After outlining its core components and functionalities, we showcase the application of CAKE in the context of a real-world cyber-security project within the logistics domain.
Paper: https://doi.org/10.1007/978-3-031-61000-4_16
“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.
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.
Mind map of terminologies used in context of Generative AI
Mind map of common terms used in context of Generative AI.
HCL Notes and Domino License Cost Reduction in the World of DLAU
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
Join HCL Ambassador Marc Thomas in this webinar with a special guest appearance from Franz Walder. It will give you the tools and know-how to stay on top of what is going on with Domino licensing. You will be able lower your cost through an optimized configuration and keep it low going forward.
These topics will be covered
- Reducing license cost by finding and fixing misconfigurations and superfluous accounts
- How do CCB and CCX licenses really work?
- Understanding the DLAU tool and how to best utilize it
- Tips for common problem areas, like team mailboxes, functional/test users, etc
- Practical examples and best practices to implement right away
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
* What is Vector Search?
* Importance and benefits of vector search
* Practical use cases across various industries
* Step-by-step implementation guide
* Live demos with code snippets
* Enhancing LLM capabilities with vector search
* Best practices and optimization strategies
Perfect for developers, AI enthusiasts, and tech leaders. Learn how to leverage MongoDB Atlas to deliver highly relevant, context-aware search results, transforming your data retrieval process. Stay ahead in tech innovation and maximize the potential of your applications.
#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
June Patch Tuesday
Ivanti’s Patch Tuesday breakdown goes beyond patching your applications and brings you the intelligence and guidance needed to prioritize where to focus your attention first. Catch early analysis on our Ivanti blog, then join industry expert Chris Goettl for the Patch Tuesday Webinar Event. There we’ll do a deep dive into each of the bulletins and give guidance on the risks associated with the newly-identified vulnerabilities.
Fueling AI with Great Data with Airbyte Webinar
This talk will focus on how to collect data from a variety of sources, leveraging this data for RAG and other GenAI use cases, and finally charting your course to productionalization.
Recently uploaded (20)
20240605 QFM017 Machine Intelligence Reading List May 2024
20240605 QFM017 Machine Intelligence Reading List May 2024
GraphRAG for Life Science to increase LLM accuracy
GraphRAG for Life Science to increase LLM accuracy
Best 20 SEO Techniques To Improve Website Visibility In SERP
Best 20 SEO Techniques To Improve Website Visibility In SERP
Essentials of Automations: The Art of Triggers and Actions in FME
Essentials of Automations: The Art of Triggers and Actions in FME
Climate Impact of Software Testing at Nordic Testing Days
Climate Impact of Software Testing at Nordic Testing Days
CAKE: Sharing Slices of Confidential Data on Blockchain
CAKE: Sharing Slices of Confidential Data on Blockchain
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
Mind map of terminologies used in context of Generative AI
Mind map of terminologies used in context of Generative AI
HCL Notes and Domino License Cost Reduction in the World of DLAU
HCL Notes and Domino License Cost Reduction in the World of DLAU
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdf
4.7solvinggraphing
- 1. Algebra 1 4.7 Solving Linear Equation Using Graphs (p. 250) Steps for solving: 1. Write the equation in the form __________________________. 2. ___________________ ‘0’ with ‘y’: y = ax + b. 3. _________________ the equation. The ___________________ to ax + b = 0 is the _____________________ of the graph y = ax + b. EX1: Solve the equation 2x – 5 = 1 algebraically and then graphically. EX2: Solve 5x – 1 = 9x 2 2 HW p. 253 (12, 20 – 28)