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7th pre alg -l60
This document contains notes from a math lesson on January 23, 2014. It includes an assignment that is due the next day, examples of simplifying expressions and solving equations, information about calculating sales tax and finding the area of parallelograms. It also has example problems for finding the areas and perimeters of squares, rhombi, and dilated parallelograms.
8th pre alg -l60
This document contains notes from a math lesson on January 23, 2014. It includes an assignment that is due the next day, examples of simplifying expressions and solving equations, notes on finding the area of parallelograms using base times height, worked examples of finding areas of different parallelograms, and an example of finding the area of a parallelogram and its dilated version with a given scale factor.
Properties real numbers basic
Real numbers follow basic properties including:
1) Commutative and associative properties for addition and multiplication, meaning order does not matter.
2) Distributive property relates multiplication of a number and the sum of two numbers.
3) Identity properties define the additive identity of 0 and multiplicative identity of 1.
4) Inverse properties define additive inverses and multiplicative inverses.
5) Equality properties define how equal numbers behave under operations.
Calc05a
This document provides the formulas and an example calculation for finding the area of a triangle and square. It gives the formula for calculating the area of a triangle as A=B×h/2, and uses the example of a triangle with a base of 8 cm and height of 5 cm, finding the area is 20 cm^2. It also gives the formula for calculating the area of a square as A=a^2, and uses the example of a square with sides of 5 cm, finding the area is 25 cm^2.
Finding.zeros.algebraically.vertex.form
The document discusses finding the real zeros of quadratic functions algebraically. It explains that to find the zeros, one must use the square root property, which states that if x^2 = a, then x = ±√a. This allows the equation to have two possible solutions. The document walks through an example problem of finding Cartman's starting number in a sequence that results in 0. Both 4 and -2 are found to be valid solutions, demonstrating that the square root property must include the ± symbol to account for both possible values.
Trig right angle_problems
The document contains two geometry word problems involving right triangles and trigonometry. The first problem asks the reader to find the height of a television antenna using the angle of elevation measurements from two points on the ground. The second problem asks the reader to find the height of a flagpole using the angle of elevation measurement from a student looking out a second story window. Both problems provide diagrams of the situations and show the calculations to solve for the unknown heights using trigonometric functions like tangent.
Solicitud inmofianza aprobada bucaramanga
The document summarizes the results of a rental guarantee study application for a property located at Calle 47 N° 28 - 32. It lists the renter's name, address of the property, monthly rent, identification information, and credit rating. There are four observations notes on the application dated at different times. The renter and co-signer signatures are included to finalize the rental contract pending the study results. The regulation of general conditions of the Guarantee service establishes the responsibility of both Inmofianza S.A.S. and the real estate agency requiring strict compliance.
รายงานเรื่องการใช้งานเครื่องมือ Edit
The document appears to be a list of keyboard shortcuts for an editing program. It includes shortcuts for common editing commands like undo, cut, copy, paste as well as shortcuts for code formatting and navigation commands. The shortcuts are numbered and associated with brief descriptions of their functions.
Recommended
7th pre alg -l60
This document contains notes from a math lesson on January 23, 2014. It includes an assignment that is due the next day, examples of simplifying expressions and solving equations, information about calculating sales tax and finding the area of parallelograms. It also has example problems for finding the areas and perimeters of squares, rhombi, and dilated parallelograms.
8th pre alg -l60
This document contains notes from a math lesson on January 23, 2014. It includes an assignment that is due the next day, examples of simplifying expressions and solving equations, notes on finding the area of parallelograms using base times height, worked examples of finding areas of different parallelograms, and an example of finding the area of a parallelogram and its dilated version with a given scale factor.
Properties real numbers basic
Real numbers follow basic properties including:
1) Commutative and associative properties for addition and multiplication, meaning order does not matter.
2) Distributive property relates multiplication of a number and the sum of two numbers.
3) Identity properties define the additive identity of 0 and multiplicative identity of 1.
4) Inverse properties define additive inverses and multiplicative inverses.
5) Equality properties define how equal numbers behave under operations.
Calc05a
This document provides the formulas and an example calculation for finding the area of a triangle and square. It gives the formula for calculating the area of a triangle as A=B×h/2, and uses the example of a triangle with a base of 8 cm and height of 5 cm, finding the area is 20 cm^2. It also gives the formula for calculating the area of a square as A=a^2, and uses the example of a square with sides of 5 cm, finding the area is 25 cm^2.
Finding.zeros.algebraically.vertex.form
The document discusses finding the real zeros of quadratic functions algebraically. It explains that to find the zeros, one must use the square root property, which states that if x^2 = a, then x = ±√a. This allows the equation to have two possible solutions. The document walks through an example problem of finding Cartman's starting number in a sequence that results in 0. Both 4 and -2 are found to be valid solutions, demonstrating that the square root property must include the ± symbol to account for both possible values.
Trig right angle_problems
The document contains two geometry word problems involving right triangles and trigonometry. The first problem asks the reader to find the height of a television antenna using the angle of elevation measurements from two points on the ground. The second problem asks the reader to find the height of a flagpole using the angle of elevation measurement from a student looking out a second story window. Both problems provide diagrams of the situations and show the calculations to solve for the unknown heights using trigonometric functions like tangent.
Solicitud inmofianza aprobada bucaramanga
The document summarizes the results of a rental guarantee study application for a property located at Calle 47 N° 28 - 32. It lists the renter's name, address of the property, monthly rent, identification information, and credit rating. There are four observations notes on the application dated at different times. The renter and co-signer signatures are included to finalize the rental contract pending the study results. The regulation of general conditions of the Guarantee service establishes the responsibility of both Inmofianza S.A.S. and the real estate agency requiring strict compliance.
รายงานเรื่องการใช้งานเครื่องมือ Edit
The document appears to be a list of keyboard shortcuts for an editing program. It includes shortcuts for common editing commands like undo, cut, copy, paste as well as shortcuts for code formatting and navigation commands. The shortcuts are numbered and associated with brief descriptions of their functions.
Numerical
The trapezoidal method splits the area under a curve into trapezoids, calculates the area of each trapezoid, and sums the individual areas to approximate the total area under the curve, which represents the definite integral. It uses the formula: Integral = (h/2) * (y0 + 2*y1 + 2*y2 + ... + 2*yn-1 + yn), where h is the width of each interval between the x-values x0, x1, etc., and y0, y1, etc. are the corresponding y-values of the function. Simpson's 1/3 Rule similarly divides the interval into sub-intervals, but approximates each using a quadratic curve
Operaciones con enteros
1. The document discusses applying knowledge of integers to various math problems including representing integers on number lines, identifying solution sets for linear inequalities, performing operations like addition, subtraction, multiplication and division on integers, and representing intervals on number lines.
2. Specific examples provided include representing the numbers 45, -90, 270, etc. on a number line; identifying solution sets for inequalities like x < 90, x > -15; performing operations like 12 - 18 - 10 - 15; and representing intervals like -5 ≤ m ≤ -15 on a number line.
3. The document evaluates the skills developed in representing and operating on integers through various math exercises.
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This document discusses two methods for solving linear programming problems: analytical and graphical.
The analytical method involves 1) representing the feasible region, 2) obtaining the vertices of this region, and 3) evaluating the objective function at each vertex to find the optimal solution. The graphical method involves 1) graphing the feasible region and 2) drawing lines parallel to the objective function to determine the maximum and minimum values.
An example problem is presented to illustrate both methods. The feasible region is defined, its vertices are identified, and the objective function is evaluated at each vertex to find the optimal solution analytically. Graphically, lines parallel to the objective function are drawn to identify the vertices with the maximum and minimum function values.
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The Pythagorean theorem states that the sum of the squares of the two sides of a right triangle equals the square of the hypotenuse. The document provides examples of using the Pythagorean theorem to calculate missing sides of right triangles and the diagonals of rectangles. It also gives an example of using the theorem to calculate the height of a cone given the radius.
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This document contains mathematical formulas including the Pythagorean theorem for the relationship between the sides of a right triangle, the circumference of a circle, the definition of an integral as the sum of infinitesimally small areas, and exponential and integral notation.
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This document provides instructions for homework assignment 12 due on December 21, 2015. It involves implementing high precision arithmetic functions for adding, subtracting, multiplying and scanning high precision numbers. As an example, it shows how to add and subtract the numbers 1.0947 and 0.00248 by aligning the decimal points and then performing the operations digit-by-digit, accounting for carries and borrows. Multiplication is shown by multiplying the digits of each number individually and adding them with carries into the answer array.
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The document establishes that the limit represents the derivative of some function f at a number x=a. It gives an example where f(x)=√x/4 and a=16. It then shows that the limit as h approaches 0 of (√16+h/4 - 2)/h is equal to the derivative of f at 16, f'(16). Therefore, the function f(x)=√x/4 with a=16 satisfies the original limit statement.
Moms Maths Manual PPT Grd 4 - sample
The document contains examples and explanations of various math concepts for students including:
- Diagrams showing representations of time on clocks
- Steps for completing addition problems by breaking numbers into place values
- Examples of using relation symbols like <, >, = in equations
- Instructions for long multiplication and long division problems
- Explanations of fractions, time, perimeter, geometry terms, and conversions between units.
Ch01 23
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Boundary Fill Algorithm in C
This document contains code for a boundary filling algorithm. It defines arrays for the x and y coordinates of a polygon with 4 points. It includes functions to draw the polygon, fill it using a 4-connected algorithm, and fill it using an 8-connected algorithm. The main function initializes graphics, draws the polygon in a boundary color, fills it using the 4-connected approach, and ends the program.
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This document contains a math problem solving 3x + x + 20 = 180, instructions to define complementary and supplementary angles, and a diagram showing a set of parallel lines cut by a transversal forming eight angles. Students are asked to identify how many angles were formed by the parallel lines and transversal, and to find the measures of angles 2 through 8.
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To factor an expression of the form ax^2 + bx + c:
1) Write the expression in the form ax^2 + bx + c and identify a, b, and c.
2) Multiply a and c to find ac and find the greatest common factor of a and c.
3) Find a pair of numbers that multiply to ac and add to b.
4) Write the factored expression by grouping the terms with the numbers found in step 3.
Slope intercept
Mr. Roberts had $20 initially and earns money at a rate of $4 per day. Using the equation y=mx+b and the information that Mr. Roberts had $20 initially (day 0) and $24 after 4 days, we can determine that the equation is y=$4x+20. Therefore, after 14 days Mr. Roberts will have $20 + 14 * $4 = $20 + $56 = $76.
Linear functions
This document provides steps for graphing a line from an equation. It explains that the equation must be solved for y and defines the slope as "rise over run" and the y-intercept as b. The specific equation given is y=2/3x-4. It provides instructions to plot the y-intercept at (0,-4), then rise 2 and go right 3 to plot additional points and connect them with a line and arrows.
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Class 10
The document outlines 4 classroom activities:
1) Recalling the previous lesson about recipes and ingredients.
2) A warm-up activity where students describe real or fictional situations for others to guess.
3) Listening to a conversation and answering questions about food orders using phrases like "I'd like a chicken sandwich."
4) Reviewing unit 8 on simple past tense by completing exercises in the workbook.
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Numerical
The trapezoidal method splits the area under a curve into trapezoids, calculates the area of each trapezoid, and sums the individual areas to approximate the total area under the curve, which represents the definite integral. It uses the formula: Integral = (h/2) * (y0 + 2*y1 + 2*y2 + ... + 2*yn-1 + yn), where h is the width of each interval between the x-values x0, x1, etc., and y0, y1, etc. are the corresponding y-values of the function. Simpson's 1/3 Rule similarly divides the interval into sub-intervals, but approximates each using a quadratic curve
Operaciones con enteros
1. The document discusses applying knowledge of integers to various math problems including representing integers on number lines, identifying solution sets for linear inequalities, performing operations like addition, subtraction, multiplication and division on integers, and representing intervals on number lines.
2. Specific examples provided include representing the numbers 45, -90, 270, etc. on a number line; identifying solution sets for inequalities like x < 90, x > -15; performing operations like 12 - 18 - 10 - 15; and representing intervals like -5 ≤ m ≤ -15 on a number line.
3. The document evaluates the skills developed in representing and operating on integers through various math exercises.
Act2_GalindoChavezJaqueline_GrupoA
This document discusses two methods for solving linear programming problems: analytical and graphical.
The analytical method involves 1) representing the feasible region, 2) obtaining the vertices of this region, and 3) evaluating the objective function at each vertex to find the optimal solution. The graphical method involves 1) graphing the feasible region and 2) drawing lines parallel to the objective function to determine the maximum and minimum values.
An example problem is presented to illustrate both methods. The feasible region is defined, its vertices are identified, and the objective function is evaluated at each vertex to find the optimal solution analytically. Graphically, lines parallel to the objective function are drawn to identify the vertices with the maximum and minimum function values.
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The Pythagorean theorem states that the sum of the squares of the two sides of a right triangle equals the square of the hypotenuse. The document provides examples of using the Pythagorean theorem to calculate missing sides of right triangles and the diagonals of rectangles. It also gives an example of using the theorem to calculate the height of a cone given the radius.
Formulas
This document contains mathematical formulas including the Pythagorean theorem for the relationship between the sides of a right triangle, the circumference of a circle, the definition of an integral as the sum of infinitesimally small areas, and exponential and integral notation.
Hw12#5
This document provides instructions for homework assignment 12 due on December 21, 2015. It involves implementing high precision arithmetic functions for adding, subtracting, multiplying and scanning high precision numbers. As an example, it shows how to add and subtract the numbers 1.0947 and 0.00248 by aligning the decimal points and then performing the operations digit-by-digit, accounting for carries and borrows. Multiplication is shown by multiplying the digits of each number individually and adding them with carries into the answer array.
Problema 34
The document establishes that the limit represents the derivative of some function f at a number x=a. It gives an example where f(x)=√x/4 and a=16. It then shows that the limit as h approaches 0 of (√16+h/4 - 2)/h is equal to the derivative of f at 16, f'(16). Therefore, the function f(x)=√x/4 with a=16 satisfies the original limit statement.
Moms Maths Manual PPT Grd 4 - sample
The document contains examples and explanations of various math concepts for students including:
- Diagrams showing representations of time on clocks
- Steps for completing addition problems by breaking numbers into place values
- Examples of using relation symbols like <, >, = in equations
- Instructions for long multiplication and long division problems
- Explanations of fractions, time, perimeter, geometry terms, and conversions between units.
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This document presents a table calculating the cost of production (PRA), fixed costs (FG), cost price (Prix de revient), additional costs (BN), selling price without tax (PVN), discount (Rabais), and selling price with tax (PVB) for an item. It shows the PRA is 200, FG is 40, cost price is 240, BN is 48, PVN is 288, discount is 12, and PVB is 300. It then shows calculations to determine the FG and BN amounts based on percentages of the PRA.
12 - Scala. Empty and unit types
The document discusses empty and unit types in dependent type theory. It defines the empty type, which has no values, and the unit type, which has a single value (). It provides the formation rules, constructors, eliminators, computation rules, and uniqueness principles for each type. It also compares how empty and unit types are represented in Haskell, Scala, Java, and a ProvingGround library for dependent types in Scala.
Boundary Fill Algorithm in C
This document contains code for a boundary filling algorithm. It defines arrays for the x and y coordinates of a polygon with 4 points. It includes functions to draw the polygon, fill it using a 4-connected algorithm, and fill it using an 8-connected algorithm. The main function initializes graphics, draws the polygon in a boundary color, fills it using the 4-connected approach, and ends the program.
Trigonometry 2
This document discusses trigonometry graphs and their uses. It provides instructions on using a calculator to find sine values and creating a table of x- and y-values for sine. Students are asked to work in groups to draw a graph of y=sinχ from 0 to 3600 degrees and individually draw a graph of y=cosχ over the same interval. The document emphasizes accurate graphing of trigonometric functions and their periodic patterns.
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The document contains 4 tables with statistical data that are partially filled in. It provides the calculations to determine the missing values in each table. The calculations use the formula that the frequency of each category divided by the total number of data points equals the relative frequency. It then fills in each table with the full statistical data.
Transversals edmodo 2013 14
This document contains a math problem solving 3x + x + 20 = 180, instructions to define complementary and supplementary angles, and a diagram showing a set of parallel lines cut by a transversal forming eight angles. Students are asked to identify how many angles were formed by the parallel lines and transversal, and to find the measures of angles 2 through 8.
Germany population keynote
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How to factor powerpoint
To factor an expression of the form ax^2 + bx + c:
1) Write the expression in the form ax^2 + bx + c and identify a, b, and c.
2) Multiply a and c to find ac and find the greatest common factor of a and c.
3) Find a pair of numbers that multiply to ac and add to b.
4) Write the factored expression by grouping the terms with the numbers found in step 3.
Slope intercept
Mr. Roberts had $20 initially and earns money at a rate of $4 per day. Using the equation y=mx+b and the information that Mr. Roberts had $20 initially (day 0) and $24 after 4 days, we can determine that the equation is y=$4x+20. Therefore, after 14 days Mr. Roberts will have $20 + 14 * $4 = $20 + $56 = $76.
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This document provides steps for graphing a line from an equation. It explains that the equation must be solved for y and defines the slope as "rise over run" and the y-intercept as b. The specific equation given is y=2/3x-4. It provides instructions to plot the y-intercept at (0,-4), then rise 2 and go right 3 to plot additional points and connect them with a line and arrows.
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