This document contains a collection of analytic geometry problems involving finding points, lines, and calculating distances, midpoints, areas of triangles, determining whether a triangle is isosceles, and finding equations of lines parallel or perpendicular to given lines. The problems cover core concepts in analytic geometry including working with coordinate planes, lines, distances, angles and triangles.
The document discusses calculating distances between points and other geometric concepts. It contains 10 problems involving finding distances between points, determining if points are collinear, finding a point a given distance from another, and calculating circumference and area of circles and quadrilaterals using given points. The final problem directs the reader to exercise 4 for additional practice with these geometric concepts.
This document provides instructions and examples for converting between units of length including millimeters, centimeters, inches, and feet. It also explains how to determine actual dimensions from scale drawings using ratios, proportions, and unit conversion ratios. Students are assigned problems #1-5 and #7-8 which involve converting between units of length and determining actual sizes from scale drawings.
1) Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.
2) The document provides examples of finding slopes of parallel and perpendicular lines, including writing equations of lines given certain points and conditions.
3) One example shows how to find the slope of a line given two points on it, as well as the slope of the perpendicular line.
The document discusses key concepts about parallel and perpendicular lines including:
1) Parallel lines have the same slope
2) Perpendicular lines have negative reciprocal slopes
3) It provides examples of finding the slope of parallel and perpendicular lines given their equations or a point on each line.
The document discusses methods for graphing linear equations. It explains that linear equations have two intercepts: the x-intercept where the line crosses the x-axis and the y-intercept where it crosses the y-axis. It also introduces slope-intercept form as y=mx+b and states that equations must be converted to this form to graph using the slope-intercept method. Examples are given of graphing lines using intercepts and converting equations to slope-intercept form.
This document contains a collection of analytic geometry problems involving finding points, lines, and calculating distances, midpoints, areas of triangles, determining whether a triangle is isosceles, and finding equations of lines parallel or perpendicular to given lines. The problems cover core concepts in analytic geometry including working with coordinate planes, lines, distances, angles and triangles.
The document discusses calculating distances between points and other geometric concepts. It contains 10 problems involving finding distances between points, determining if points are collinear, finding a point a given distance from another, and calculating circumference and area of circles and quadrilaterals using given points. The final problem directs the reader to exercise 4 for additional practice with these geometric concepts.
This document provides instructions and examples for converting between units of length including millimeters, centimeters, inches, and feet. It also explains how to determine actual dimensions from scale drawings using ratios, proportions, and unit conversion ratios. Students are assigned problems #1-5 and #7-8 which involve converting between units of length and determining actual sizes from scale drawings.
1) Parallel lines have the same slope, while perpendicular lines have slopes that are negative reciprocals of each other.
2) The document provides examples of finding slopes of parallel and perpendicular lines, including writing equations of lines given certain points and conditions.
3) One example shows how to find the slope of a line given two points on it, as well as the slope of the perpendicular line.
The document discusses key concepts about parallel and perpendicular lines including:
1) Parallel lines have the same slope
2) Perpendicular lines have negative reciprocal slopes
3) It provides examples of finding the slope of parallel and perpendicular lines given their equations or a point on each line.
The document discusses methods for graphing linear equations. It explains that linear equations have two intercepts: the x-intercept where the line crosses the x-axis and the y-intercept where it crosses the y-axis. It also introduces slope-intercept form as y=mx+b and states that equations must be converted to this form to graph using the slope-intercept method. Examples are given of graphing lines using intercepts and converting equations to slope-intercept form.
This document provides instructions for simplifying compound algebraic fractions that have separate operations in the numerator and denominator. It gives examples of compound fractions with addition, subtraction, and multiplication in both the numerator and denominator, and explains how to simplify each type by distributing the operations.
This document provides examples of solving rational equations and examples of word problems involving rates. The first example shows how to solve the rational equation (3 - 2) / (x - 1) = (1) / (x + 1). The second example asks what time Luigi and Monica will meet if they jog toward each other from 27 km apart at rates of 4 km/h and 5 km/h, respectively. The third example asks how fast Mark was travelling if he travelled 27 km and Tamara travelled 21 km travelling in opposite directions at rates where Mark's is 2 km/h faster than Tamara's.
The document provides instructions for several analytic geometry problems involving finding points and lines based on given coordinates, distances, and equations. Problem #3 asks to find the coordinates of point R that divides the line segment between points A(8,0) and B(4,-8) in a ratio of 2 to 1.
Este documento presenta el plan de clases para una unidad sobre redes informáticas para estudiantes de grado 10. La clase se centrará en explicar conceptos básicos de redes, sus componentes y clasificaciones. Los estudiantes trabajarán en equipos para investigar sobre redes y crear una red Ad Hoc para compartir archivos. Al final, completarán una evaluación en línea sobre los temas cubiertos.
The document summarizes information from various sources about green living and energy efficiency. It provides an overview of the ENERGY STAR program and top states for ENERGY STAR homes in 2007. It also lists several inexpensive green projects under $500, factors that influence awareness of green homes, features of green homes, and returns on investments for various energy efficiency upgrades for homes.
This document discusses how to determine the equation of a line given either its slope and y-intercept or a point and slope. It provides examples of finding the equation in slope-intercept form when given the slope and y-intercept or when given a point on the line and its slope. The document also includes an exercise problem asking whether a point lies on a line with a given equation.
The Online Teaching Persona: Who are you online? Develop and Deliver Your On...Bill Phillips
1. The document discusses the importance of developing an online teaching persona, which is how instructors present themselves professionally to students online. It defines the online persona as the "mask" instructors speak through.
2. An effective online persona matches the instructor's teaching style and beliefs, and motivates students to learn. It involves taking on cognitive, affective, and managerial roles.
3. The document provides examples of tools instructors can use to communicate their persona, such as welcome emails, biographies, videos, and chats during office hours. These tools help establish credibility and build relationships with students.
Standard deviation is a measure of variability that measures how far each data point is from the mean. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. The document provides examples of calculating the standard deviation of test scores from two different high schools and comparing their means, ranges, and standard deviations.
Precal 20 S Adding And Subtracting Rational ExpressionsDMCI
The document provides examples for how to add and subtract rational expressions by finding a common denominator and then combining like terms. It lists the steps as: 1) factor and find the least common denominator, 2) change fractions to have common denominators, 3) add or subtract, 4) simplify or reduce, and 5) note any restrictions on variables. Several worked examples are shown applying these steps.
This document defines an obtuse angle and its standard position. It then uses the coordinate definition of trigonometric ratios to find the sine, cosine, and tangent of various obtuse angles given points on their terminal arms. Examples are provided to find the size of angles given their trigonometric ratios, identifying acute and obtuse angles where possible. The document provides context, definitions, examples, and an assignment to practice finding angle measures using trigonometric ratios.
This document discusses how to determine the equation of a line given different parameters such as the slope and y-intercept, a point and the slope, or the standard form equation. It provides examples of finding the equation when given the slope and y-intercept, and when given a point and the slope. The document also includes an exercise problem asking whether a point lies on a line with a given standard form equation.
The document discusses methods for graphing linear equations. It explains that linear equations have two intercepts: the x-intercept where the line crosses the x-axis and the y-intercept where it crosses the y-axis. It also introduces slope-intercept form as y=mx+b and states that equations must be converted to this form to graph using the slope-intercept method. Examples are given of graphing lines using intercepts and converting equations to slope-intercept form.
The document defines slope as the steepness and direction of a line, calculated as the rise over the run or change in y over the change in x between two points on the line. It provides examples of calculating the slope between two points and finding the y-value of a third point given the slope. It also describes how the sign of the slope indicates whether a line is diagonal up/right, horizontal, or diagonal down/right and when the slope is undefined when the line is vertical.
The document defines slope as the steepness and direction of a line, calculated as the rise over the run or change in y over the change in x between two points on the line. It provides examples of calculating the slope between two points and finding the y-value of a third point given the slope. It also describes how the sign of the slope indicates whether a line is diagonal left, horizontal, or diagonal right and whether the slope is undefined if the line is vertical.
This document discusses how to graph lines from a table of values using different forms of linear equations. It provides examples of graphing lines in slope-intercept form (y=mx+b), point-slope form (y-y1=m(x-x1)), and standard form (Ax + By = C). The key steps are to identify the slope (m) and y-intercept (b) from the equation and plot points that satisfy the relationship between x and y.
The document discusses various geometry concepts including the distance formula, finding the midpoint of a line segment between two points, finding the coordinates of the center of a circle given the endpoints of its diameter, and solving problems involving finding unknown values from the relationship between midpoints and points on the x- or y-axis. It also mentions there will be a quiz on these concepts and the remaining problems from Exercise 4 on Monday.
The document discusses a 5-step process but provides no details on the actual steps or content of the process. It refers to numbered sections but leaves them undefined. In short, the document introduces the idea of a 5-step process but does not explain or elaborate on it.
This document provides examples of solving rational equations and examples of word problems involving rates. The first example shows how to solve the rational equation (3-2)/(x-1) = (1)/(x+1). The second example asks what time Luigi and Monica will meet if they jog towards each other from 27 km apart at rates of 4 km/h and 5 km/h, respectively. The third example asks how fast Mark was travelling if he travelled 27 km and Tamara travelled 21 km in the same time, with Mark riding 2 km/h faster than Tamara.
This document provides instructions for simplifying compound algebraic fractions that have separate operations in the numerator and denominator. It gives examples of compound fractions with addition, subtraction, and multiplication in both the numerator and denominator, and explains how to simplify each type by distributing the operations.
This document provides instructions for simplifying compound algebraic fractions that have separate operations in the numerator and denominator. It gives examples of compound fractions with addition, subtraction, and multiplication in both the numerator and denominator, and explains how to simplify these types of algebraic fractions by distributing the operations. The document concludes by assigning the student problems 1 through 10 from Exercise 51 to practice multiplying and dividing rational expressions.
Precal 20S Multiplying and Dividing Rational ExpressionsDMCI
To multiply rational expressions, multiply the numerators and multiply the denominators. To divide rational expressions, keep the first expression as the dividend and the second as the divisor, then multiply the dividend's numerator and denominator by the divisor's denominator. The document then provides examples of multiplying and dividing rational expressions.
This document provides instructions for simplifying compound algebraic fractions that have separate operations in the numerator and denominator. It gives examples of compound fractions with addition, subtraction, and multiplication in both the numerator and denominator, and explains how to simplify each type by distributing the operations.
This document provides examples of solving rational equations and examples of word problems involving rates. The first example shows how to solve the rational equation (3 - 2) / (x - 1) = (1) / (x + 1). The second example asks what time Luigi and Monica will meet if they jog toward each other from 27 km apart at rates of 4 km/h and 5 km/h, respectively. The third example asks how fast Mark was travelling if he travelled 27 km and Tamara travelled 21 km travelling in opposite directions at rates where Mark's is 2 km/h faster than Tamara's.
The document provides instructions for several analytic geometry problems involving finding points and lines based on given coordinates, distances, and equations. Problem #3 asks to find the coordinates of point R that divides the line segment between points A(8,0) and B(4,-8) in a ratio of 2 to 1.
Este documento presenta el plan de clases para una unidad sobre redes informáticas para estudiantes de grado 10. La clase se centrará en explicar conceptos básicos de redes, sus componentes y clasificaciones. Los estudiantes trabajarán en equipos para investigar sobre redes y crear una red Ad Hoc para compartir archivos. Al final, completarán una evaluación en línea sobre los temas cubiertos.
The document summarizes information from various sources about green living and energy efficiency. It provides an overview of the ENERGY STAR program and top states for ENERGY STAR homes in 2007. It also lists several inexpensive green projects under $500, factors that influence awareness of green homes, features of green homes, and returns on investments for various energy efficiency upgrades for homes.
This document discusses how to determine the equation of a line given either its slope and y-intercept or a point and slope. It provides examples of finding the equation in slope-intercept form when given the slope and y-intercept or when given a point on the line and its slope. The document also includes an exercise problem asking whether a point lies on a line with a given equation.
The Online Teaching Persona: Who are you online? Develop and Deliver Your On...Bill Phillips
1. The document discusses the importance of developing an online teaching persona, which is how instructors present themselves professionally to students online. It defines the online persona as the "mask" instructors speak through.
2. An effective online persona matches the instructor's teaching style and beliefs, and motivates students to learn. It involves taking on cognitive, affective, and managerial roles.
3. The document provides examples of tools instructors can use to communicate their persona, such as welcome emails, biographies, videos, and chats during office hours. These tools help establish credibility and build relationships with students.
Standard deviation is a measure of variability that measures how far each data point is from the mean. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean. The document provides examples of calculating the standard deviation of test scores from two different high schools and comparing their means, ranges, and standard deviations.
Precal 20 S Adding And Subtracting Rational ExpressionsDMCI
The document provides examples for how to add and subtract rational expressions by finding a common denominator and then combining like terms. It lists the steps as: 1) factor and find the least common denominator, 2) change fractions to have common denominators, 3) add or subtract, 4) simplify or reduce, and 5) note any restrictions on variables. Several worked examples are shown applying these steps.
This document defines an obtuse angle and its standard position. It then uses the coordinate definition of trigonometric ratios to find the sine, cosine, and tangent of various obtuse angles given points on their terminal arms. Examples are provided to find the size of angles given their trigonometric ratios, identifying acute and obtuse angles where possible. The document provides context, definitions, examples, and an assignment to practice finding angle measures using trigonometric ratios.
This document discusses how to determine the equation of a line given different parameters such as the slope and y-intercept, a point and the slope, or the standard form equation. It provides examples of finding the equation when given the slope and y-intercept, and when given a point and the slope. The document also includes an exercise problem asking whether a point lies on a line with a given standard form equation.
The document discusses methods for graphing linear equations. It explains that linear equations have two intercepts: the x-intercept where the line crosses the x-axis and the y-intercept where it crosses the y-axis. It also introduces slope-intercept form as y=mx+b and states that equations must be converted to this form to graph using the slope-intercept method. Examples are given of graphing lines using intercepts and converting equations to slope-intercept form.
The document defines slope as the steepness and direction of a line, calculated as the rise over the run or change in y over the change in x between two points on the line. It provides examples of calculating the slope between two points and finding the y-value of a third point given the slope. It also describes how the sign of the slope indicates whether a line is diagonal up/right, horizontal, or diagonal down/right and when the slope is undefined when the line is vertical.
The document defines slope as the steepness and direction of a line, calculated as the rise over the run or change in y over the change in x between two points on the line. It provides examples of calculating the slope between two points and finding the y-value of a third point given the slope. It also describes how the sign of the slope indicates whether a line is diagonal left, horizontal, or diagonal right and whether the slope is undefined if the line is vertical.
This document discusses how to graph lines from a table of values using different forms of linear equations. It provides examples of graphing lines in slope-intercept form (y=mx+b), point-slope form (y-y1=m(x-x1)), and standard form (Ax + By = C). The key steps are to identify the slope (m) and y-intercept (b) from the equation and plot points that satisfy the relationship between x and y.
The document discusses various geometry concepts including the distance formula, finding the midpoint of a line segment between two points, finding the coordinates of the center of a circle given the endpoints of its diameter, and solving problems involving finding unknown values from the relationship between midpoints and points on the x- or y-axis. It also mentions there will be a quiz on these concepts and the remaining problems from Exercise 4 on Monday.
The document discusses a 5-step process but provides no details on the actual steps or content of the process. It refers to numbered sections but leaves them undefined. In short, the document introduces the idea of a 5-step process but does not explain or elaborate on it.
This document provides examples of solving rational equations and examples of word problems involving rates. The first example shows how to solve the rational equation (3-2)/(x-1) = (1)/(x+1). The second example asks what time Luigi and Monica will meet if they jog towards each other from 27 km apart at rates of 4 km/h and 5 km/h, respectively. The third example asks how fast Mark was travelling if he travelled 27 km and Tamara travelled 21 km in the same time, with Mark riding 2 km/h faster than Tamara.
This document provides instructions for simplifying compound algebraic fractions that have separate operations in the numerator and denominator. It gives examples of compound fractions with addition, subtraction, and multiplication in both the numerator and denominator, and explains how to simplify each type by distributing the operations.
This document provides instructions for simplifying compound algebraic fractions that have separate operations in the numerator and denominator. It gives examples of compound fractions with addition, subtraction, and multiplication in both the numerator and denominator, and explains how to simplify these types of algebraic fractions by distributing the operations. The document concludes by assigning the student problems 1 through 10 from Exercise 51 to practice multiplying and dividing rational expressions.
Precal 20S Multiplying and Dividing Rational ExpressionsDMCI
To multiply rational expressions, multiply the numerators and multiply the denominators. To divide rational expressions, keep the first expression as the dividend and the second as the divisor, then multiply the dividend's numerator and denominator by the divisor's denominator. The document then provides examples of multiplying and dividing rational expressions.
Net pay is the amount remaining after deductions are taken from gross pay. Canadian law requires deductions for Canada Pension Plan contributions, Employment Insurance premiums, and income tax. Employers may also deduct amounts for group insurance, union dues, and private health insurance. Additional voluntary deductions include charitable donations and retirement savings plan contributions. Employers must deduct Canada Pension Plan contributions from employees aged 18 to 69 and pay the same amount. Employment Insurance premiums are deducted from all employees and employers pay 1.4 times the employee amount. Income tax is deducted from all employees and self-employed individuals must report income and pay tax.
This document provides examples of rational expressions and instructions for simplifying them. It discusses that a rational expression can be written as A/B, where A and B are polynomials and B ≠ 0. Restrictions may exist when the denominator is equal to 0. Five examples of rational expressions are given and the task is to simplify each one and state any restrictions.
This document contains notes on rational expressions and reducing rational expressions. It provides definitions of rational numbers and rational expressions. Examples are given on reducing or simplifying rational expressions and stating any restrictions. An assignment is listed for Exercises 42 and 43 in the textbook due on Monday.