Geometry dots & lines
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This document provides an overview of basic geometry concepts including: - Points have no dimension and are named using capital letters - A line has no end points, is straight, and goes off to infinity in two directions - A line segment is part of a straight line with two distinct end points - A ray has one endpoint and extends off to infinity in one direction - Lines, line segments, and rays can intersect at a single point - A plane is a flat, two-dimensional surface that can be named using points or a cursive letter
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Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
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Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
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Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
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Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
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Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
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Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
Mathematics 7 of Basic of Geometry. Points, Lines, Planes in Geometry.
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1. Points, lines, and planes are basic geometric objects. A point has no size or dimensions. A line extends indefinitely in both directions and has one dimension. A plane extends indefinitely and has two dimensions.
2. Collinear points lie on the same line, while coplanar points lie in the same plane. Noncollinear points do not lie on the same line, and noncoplanar points do not lie in the same plane.
3. A line segment connects two points and contains all points between them. A ray starts at an endpoint and extends indefinitely in one direction. Planes and geometric objects are named using points, lines, and planes.More from ListeningDaisy (11)
Stem & leaf plots + histograms
Stem & leaf plots + histogramsListeningDaisy
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This document provides instructions and examples for creating different types of data displays, including stem-and-leaf plots, histograms, back-to-back stem-and-leaf plots, and box-and-whisker plots. It includes examples using temperature data and adoption prices for dogs. Key terms and how to interpret the visuals are explained through mini lessons within the document.Measures of central tendency
Measures of central tendencyListeningDaisy
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This document discusses measures of central tendency and uses the scores of 28, 18, 24, 22, 18 to demonstrate how to calculate the median, mean, mode, and range. It defines median as the middle number when values are ordered from lowest to highest. Mean is calculated by adding all values and dividing by the total count. Mode is the number with the most occurrences. Range is found by subtracting the minimum from the maximum value.Factor by grouping
Factor by groupingListeningDaisy
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The document provides steps for factoring polynomial expressions:
1) Separate the expression into terms with common factors and group those terms;
2) Find the greatest common factor (GCF) of the grouped terms;
3) Enclose the GCF and the grouped terms in parentheses to arrive at the factored expression.
Worked examples demonstrate factoring various polynomials, including using negative signs properly.Factoring polynomials completely
Factoring polynomials completelyListeningDaisy
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The document provides instructions on how to completely factor polynomials. It gives examples of factoring expressions like 4n^2 - 16, 5x^2 - 45, and 3x^2 - 18x - 21. The steps explained are to find the greatest common factor, factor any binomials or trinomials, and simplify the expression as much as possible. Additional practice problems and their factored solutions are provided.Factoring Special Products in Difference of Squares
Factoring Special Products in Difference of SquaresListeningDaisy
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The document provides examples of factoring quadratic expressions of the form a^2 +/- b^2 into the form (a +/- b)(a -/+ b). It demonstrates factoring several quadratic expressions using this method, including expressions with coefficients other than 1. It also introduces a formula for factoring expressions of the form a^2 + 2ab + b^2 and applies this formula to one example. Finally, it factors one expression where the middle term is negative by distributing the negative sign appropriately.Factoring Pt. 2/2 (x^2 + bx + c)
Factoring Pt. 2/2 (x^2 + bx + c)ListeningDaisy
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1. The document discusses factoring quadratic expressions using the greatest common factor (GCF) method.
2. It provides examples of factoring expressions such as 3x^2 + 8x + 4 by trying different pairs of binomials that multiply to the GCF and constant term.
3. The document also addresses factoring expressions with negative coefficients, explaining that you can factor the expression inside the parentheses and multiply the whole expression by -1.Factoring pt. 1/2
Factoring pt. 1/2ListeningDaisy
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1. The document provides step-by-step instructions for factoring quadratic expressions using reverse FOIL. It explains that the factors are determined by the constant term's factors and shows examples of factoring expressions with positive and negative coefficients.
2. Problems include factoring expressions into standard form, factoring expressions with variables, and solving a word problem involving the area of two shapes to determine the width of one. The document breaks problems down into clear steps and provides answers on subsequent slides.Solving polynomial equations in factored form
Solving polynomial equations in factored formListeningDaisy
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The document provides instructions for solving polynomial equations in factored form. It begins by explaining that to solve an equation like (x ¨C 5)(x + 4) = 0, one should not use the FOIL method but rather split the equation into two separate problems that each equal zero: x ¨C 5 = 0 and x + 4 = 0. It then works through several examples of solving factored polynomial equations by finding the values of x that make each factor equal to zero. The document also covers factoring out the greatest common factor from expressions.
Math vocab 1
Math vocab 1ListeningDaisy
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1. The document defines key math vocabulary terms including variable, constant, coefficient, leading coefficient, like terms, monomial, polynomial, binomial, and trinomial.
2. Examples are provided to demonstrate identifying variables, constants, coefficients, like terms, and determining if expressions are monomials, polynomials, binomials, or trinomials.
3. The degree of a polynomial is defined as the highest exponent present in the polynomial. Examples show determining the degree of various polynomials.Recently uploaded (20)
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https://ncracked.com/7961-2/
Note: >>?? Please copy the link and paste it into Google New Tab now Download link
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DAO UTokyo 2025
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https://utbciii.com/2024/12/12/announcing-dao-utokyo-2025-conference/
Session 1 :DLT mass adoption
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Trends in the marketplace
Take advantage of UiPath training and certification
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TrustArc Webinar - Building your DPIA/PIA Program: Best Practices & Tips
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DevNexus - Building 10x Development Organizations.pdf
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Developer Experience is Dead! Long Live Developer Experience!
In this keynote-style session, we¡¯ll take a detailed, granular look at the barriers to productivity developers face today and modern approaches for removing them. 10x developers may be a myth, but 10x organizations are very real, as proven by the influential study performed in the 1980s, ¡®The Coding War Games.¡¯
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But which of these approaches works? DORA? SPACE? DevEx? What should we invest in and create urgency behind today so we don¡¯t have the same discussion again in a decade?Geometry dots & lines
- 1. Geometry Dots & Lines Made by Listening Daisy, based on notes from her Geometry Class (with permission from her instructor).
- 2. Table of Contents ? ºÝºÝߣ 3: What is a Point? ? ºÝºÝߣ 4: Mini Lesson: What Letters Not To Use When Naming Points ? ºÝºÝߣ 5: What Is A Line? ? ºÝºÝߣ 6: How To Name A Line ? ºÝºÝߣ 7: What Is A Line Segment? ? ºÝºÝߣ 8: What Is A Ray? ? ºÝºÝߣ 9: Name That Ray! ? ºÝºÝߣ 11: Mini Lesson: Additional Way to Name A Line ? ºÝºÝߣ 12: What Is Collinear? ? ºÝºÝߣ 13: What Is A Plane? ? ºÝºÝߣ 14: What Is Intersection? ? ºÝºÝߣ 16: Mini Lesson: Lines & Intersection ? ºÝºÝߣ 17: What Is Space?
- 3. What is a Point? ? Points have no dimension they are ¡°a place in space¡±. ? When you name a point, use capital letters (usually the Roman Alphabet is used, but sometimes Greek letters are used). A
- 4. Mini Lesson: What Letters Not To Use When Naming Points When naming points, try not to use letters like T and S due to the fact they could be easily confused with something else. For example, S and 5 look very similar.
- 5. What Is A Line? B A AB Symbol for the line: ? It has no end points ? It has an infinite number of points ? It is straight and not curved ? Lines go off towards infinity in two directions
- 6. How To Name A Line ? Now I¡¯m sure you saw the symbol on the top right corner of the slide before this. is the abbreviation for a line, it is the name of the line. To make this symbol there must be at least two points on a line. Let¡¯s use the line below as an example. ? Since it has over two points, we can name it. You can only use two letters in the name however. ? It is preferred that the letters of the name are read left to right as in the names AB, BC, & AC. It is also possible to use names like BA, CB & CA though. AB B A C
- 7. What Is A Line Segment? ? Straight ? Made up of points ? To name it, you use the end points, not the points on the line. A B AB Symbol for the line:
- 8. What Is A Ray? ? Ray: half a line, on one end it has a finite end point and on the other end it goes off infinitely ? Straight ? Needs two points to name: when naming, always start with the end point. It can¡¯t be BA because BA is: A B AB Symbol for the line: B A
- 9. Name That Ray! Where are the rays? A B C
- 10. Name That Ray! A B C The rays that are located here are BA, BC & AC A B B C A C
- 11. Mini Lesson: Additional Way to Name A Line ? An additional way to name a line is to use a lower case cursive letter.
- 12. What is Collinear? ? When there are more then three points on the same line. ? Ex 1: A, B & C are collinear ? Ex 2: A, B & C are not collinear A B C A B C
- 13. What Is A Plane? ? Flat ? 2-dimensional ? Named using its four points or a single cursive letter. or A B C D Note: The cursive letters must always be capitalized
- 14. What Is Intersection? ? When lines cross, it¡¯s in the form of a point ? When planes cross it¡¯s a line segment ? When a line crosses a plane it¡¯s a point.
- 15. What Is Intersection? ? When three planes intersect, it¡¯s a point.
- 16. Mini Lesson: Lines & Intersection ? A line can only intersect at one point. ? For example, due to the fact that the line is straight, it cannot curve to create another point inside the shape.
- 17. What Is Space? ? A set of all possible points