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This document provides an overview of solving different types of equations and inequalities, including linear equations, quadratic equations, rational equations, radical equations, linear inequalities, quadratic inequalities, and graphing methods. Key methods discussed are factoring, the quadratic formula, completing the square, manipulating fractions to get a common denominator, squaring both sides of an equation to eliminate radicals, and determining shading regions for inequalities based on a test point.
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3) The document provides steps for graphing a linear inequality in two variables: graph the line by changing the inequality to an equation, use a test point to determine which side to shade, and shade the area where the test point satisfies the inequality.
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This document defines and provides examples of different types of polygons. It explains that a polygon is a closed figure made of line segments that intersect exactly two others. It then defines regular and irregular polygons, as well as different types of triangles, quadrilaterals, pentagons, hexagons, and other polygons. Key details like the number of sides and sum of interior angles are provided. Examples of both regular and irregular shapes are shown.
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The document discusses different types of polygons. It defines a polygon as a closed shape with three or more sides and distinguishes between convex polygons, where any two interior points can be connected by a line segment staying inside the figure, and concave polygons, where the line segment may pass outside. It also distinguishes between regular polygons with equal sides and angles and irregular polygons. Finally, it classifies polygons based on the number of sides they have, such as triangles having three sides, quadrilateral four sides, and so on.
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Similar to Math Project 2ppt
0010 chapter iii
Here are the steps to solve this quadratic equation using the quadratic formula:
1. Identify the coefficients: a = 3, b = -1, c = -5/2
2. Plug the coefficients into the quadratic formula:
x = (-b ± √(b2 - 4ac)) / 2a
x = (-(-1) ± √((-1)2 - 4(3)(-5/2))) / 2(3)
3. Simplify:
x = (1 ± √(1 + 30)) / 6
4. Evaluate the square root:
x = (1 ± 5√3) / 6
Therefore, the solutions are:
Analytic Geometry Period 1
The document provides an overview of various topics in analytic geometry, including circle equations, distance equations, systems of two and three variable equations, linear inequalities, rational inequalities, and intersections of inequalities. It defines key concepts, provides examples of how to solve different types of problems, and notes things to remember when working with inequalities.
Tricks to remember the quadratic equation.ACTION RESEARCH ON MATHS
This document provides information about different methods for solving quadratic equations. It discusses factoring the equation, using the quadratic formula, and completing the square. Step-by-step explanations are provided for each method. Factoring involves finding two binomials that multiply to give the quadratic term and add to the linear term. The quadratic formula is given as x = (-b ±√(b2 - 4ac))/2a. Completing the square requires grouping like terms and completing the square of the quadratic term.
quadratic equations.pptx
The document defines quadratic equations as polynomial equations of the second degree where the highest exponent is 2. It provides the general form of a quadratic equation as ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. There are three main ways to solve quadratic equations: factoring, completing the square, and using the quadratic formula. Factoring involves finding two linear expressions whose product is the quadratic, while completing the square rewrites the equation in the form of a perfect square trinomial. The discriminant, b2 - 4ac, determines the nature of the roots.
Maths
This document discusses linear equations in two variables. It defines linear equations in two variables as equations of the form ax + by = c, where a, b, and c are real numbers and a and b are not both zero. It explains that the graph of any linear equation in two variables is a straight line. It also categorizes different types of systems of linear equations based on the relationship between the lines: intersecting lines have a unique solution; coincident lines have an infinite number of solutions; and parallel lines have no solution. Methods for solving systems of linear equations like substitution, elimination, and graphing are also covered.
quadratic equations-1
Okay, let's solve this step-by-step:
1) Given: x = 2 and x = 3 are roots of the equation 3x^2 - 2mx + 2n = 0
2) Substitute x = 2 in the equation: 3(2)^2 - 2m(2) + 2n = 0
=> 12 - 4m + 2n = 0
3) Substitute x = 3 in the equation: 3(3)^2 - 2m(3) + 2n = 0
=> 27 - 6m + 2n = 0
4) Solve the two equations simultaneously to find m and n:
12 - 4m + 2n = 0
27 - 6m +
quadraticequations-111211090004-phpapp02 (2).pdf
Quadratic equations take the form of ax^2 + bx + c = 0, where a, b, and c are constants and a is not equal to 0. There are three main ways to solve quadratic equations: factoring, completing the square, and using the quadratic formula. Factoring involves finding two linear expressions whose product is the quadratic expression. Completing the square transforms the equation into the form (x + p)^2 = q. The quadratic formula provides exact solutions for x in terms of a, b, and c. The discriminant, b^2 - 4ac, determines the nature of the roots.
quadraticequations-111211090004-phpapp02 (1).pdf
The document defines quadratic equations as polynomial equations of degree 2 in the form of ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. It provides examples of quadratic equations in standard and "hidden" forms. Methods for solving quadratics include factoring, completing the square, and using the quadratic formula. The discriminant is used to determine the number and type of roots.
Rs solving graphingquadraticequation
The document discusses quadratic equations and functions. It defines a quadratic equation as one where the variable is squared, and explains that the graph of a quadratic function is a parabola with an open U-shape. It outlines the standard form of a quadratic equation as ax2 + bx + c = 0 and describes how to find the solutions/roots by setting it equal to zero. Methods for solving quadratic equations include using the quadratic formula, factoring, or completing the square. The key steps to graph a quadratic equation are finding the standard form, solutions/roots, and y-intercept.
Quadratic equations
This document discusses quadratic equations and methods for solving them. It begins by defining quadratic equations as second degree polynomial equations of the form ax^2 + bx + c = 0, where a is not equal to 0. It then presents several methods for finding the roots or solutions of quadratic equations: factoring, completing the square, and using the quadratic formula. Examples are provided to illustrate each method. The document also discusses graphing quadratic functions and key features of parabolas such as vertex, axis of symmetry, and direction of opening.
quadraticequations-111211090004-phpapp02.pptx
Quadratic equations are polynomial equations of the second degree that take the general form of ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. They can be solved using methods like factoring, completing the square, or the quadratic formula. The discriminant, b2 - 4ac, determines whether the roots are real numbers, a repeated real root, or complex numbers.
presentation_quadraticequations-111211090004-phpapp02_1524500815_313961.pptx
Quadratic equations are polynomial equations of the second degree that can be written in the general form of ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. There are three main ways to solve quadratic equations: using the quadratic formula, factoring, or completing the square. The quadratic formula provides the exact solutions and can be used to solve any quadratic equation. Factoring and completing the square involve rewriting the equation in an equivalent form to reveal the solutions.
.
This document provides an overview of basic algebra concepts including:
1. Variables, expressions, equations, and manipulating equations through addition, subtraction, multiplication and division while maintaining equality.
2. Solving one-variable equations by isolating the variable on one side of the equation.
3. Calculating the slope of a line using the slope-intercept form given two points on the line.
Quadratic equations
The document defines quadratic equations as polynomial equations of the second degree where the highest exponent on the variable is 2. It provides the general form of a quadratic equation as ax2 + bx + c = 0 where a, b, and c are constants and a ≠ 0. Roots or solutions of a quadratic equation are the values that make the equation equal to 0. The document discusses several methods for solving quadratic equations including factoring, using the quadratic formula, and completing the square. It provides examples of solving quadratic equations using each of these methods.
DOC-20240528-WA0000..pdfcjcfnfnjcfjfnfjffjjfj
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Solving equations
The document discusses solving equations through the following key points:
1) It defines what an equation is and introduces properties of equality like addition, subtraction, multiplication, and division properties that allow equations to be solved.
2) It explains how to solve single-step equations by using the inverse operations of addition/subtraction and multiplication/division.
3) It provides examples of solving multi-step equations and proportions, as well as checking solutions.
QUADRATIC.pptx
The document defines and provides examples of quadratic equations. It begins by stating that a quadratic equation is a polynomial equation of the second degree in the general form of ax2 + bx + c = 0, where a, b, and c are constants and a ≠ 0. Roots of a quadratic equation are the values that make the equation equal to 0. There are three main methods for solving quadratic equations: factoring, completing the square, and using the quadratic formula. The discriminant can be used to determine the nature of the roots.
quadratic equation
The document provides information about quadratic equations including:
1) It defines a quadratic equation as a polynomial equation of the second degree in the form ax2 + bx + c, where a ≠ 0. The constants a, b, and c are the quadratic, linear, and constant coefficients.
2) There are three main methods to solve quadratic equations: factoring, completing the square, or using the quadratic formula.
3) The discriminant, b2 - 4ac, determines the nature of the roots - two real roots if positive, one real root if zero, or two complex roots if negative.
Equations Revision
The document outlines objectives and methods for solving linear equations, including:
1) Solving single variable linear equations using inverse operations like addition, subtraction, multiplication, and division.
2) Solving simultaneous linear equations using substitution or elimination methods.
3) Constructing linear equations to represent real-world problems.
Humaira quadratic
The document discusses various topics relating to quadratic equations including:
1) Methods for solving quadratic equations such as completing the square, factorization, and the quadratic formula.
2) The steps for using the completing the square method which involves rewriting the quadratic in the form of a perfect square trinomial.
3) Examples are provided to demonstrate how to use completing the square to solve quadratic equations.
Similar to Math Project 2ppt (20)
Tricks to remember the quadratic equation.ACTION RESEARCH ON MATHS
Tricks to remember the quadratic equation.ACTION RESEARCH ON MATHS
presentation_quadraticequations-111211090004-phpapp02_1524500815_313961.pptx
presentation_quadraticequations-111211090004-phpapp02_1524500815_313961.pptx
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