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Mathematics

factoring

Subject: 
Algebra
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Mathematics
Elementary algebra
Polynomials
Corporate finance
Working capital management
Algebra
Trinomial
Factoring
Binomial
Quadratic equation
Factor

Section 4.3: Solve by Factoring Vocabulary ? Monomial: OA 4?ct&in j?W ? Binomial: cuij e'ICS 1uX i-ewis Trinomial: CLAA Cc(.1 tJ9 :!2i *ermS *Some binomials and trinomials will have a Greatest Common Factor (GCF) that we will factor ou7 when factoring ? Solutions to a Quadratic Equation: X-'zef1 (O*5 so W )(-V 0 Greatest Common Factoring Ex1: Factor 3x2 +9x QCF? Ex 2: Factor 4x + 6 .. 3x(*-s x+3) Factoring a Trinomial with a leading coefficient of 1 (iejjx2 + bx + c) -Iind luy 'f&r&c -mc** Ex 3: Factor X2 - 9x+ 20 C, (x-5 I X-4 ) Ex 5: Factor x2 - 3x ?18 (-)(x+3) (14-C oxILt Ex4: Factor x2_3x+93 a tb :: -3 - 01 rj -.t - - - - Special Factoring Patterns ? Difference of Perfect Squares: a2 - - b)(a + b) Ex 6: Factor x2 - 9 xX 3

graphing quadratic equations

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Algebra
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Mathematics
Elementary algebra
Algebra
Geometry
Parabolas
Equations
Conic sections
Polynomial functions
Quadratic function
Quadratic equation
Parent function
Graph

Name: Date: Section 4-2 Notes Graphing Quadratic Functions in ird For Standard form of a quadratic function is E ax - A The parent function of the family of all quadratic functions is f(x) The graph of a quadratic function is a DaYWO01 IA. The vertex of a parabola is the or point on the parabola. .-.J 00 The axis of jcnY1LeA-rJ7 divides the parabola into mirror images and passes through the Graph the function y = CoWare to Graph the function y = (_--x)2. Compare it to -1 '/q 00 Thej X~'M The graph of a parabola is more vertically stretched than the parent function if 1 1k 1 > I The graph of a parabola is more vertically compressed than the parent function if The graph of a parabola is more horizontally stretched than the parent function if" I

relation and functions notes

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Algebra
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Function
Mathematical notation
General relativity

Section 2-1: Relations and Functions Goal: Write the domain and range of afunction in interval notation, inequalities, and set notation. ? Domain (Independent variable, InputvaIue,x)? ?- Of 4) OO't t '? x: (iI)(3)(5 ? Range (dependent variable, output value, y)? ?* oj,,l L4- 00r7J1 4i V' x: (t, I) (3,)?, ) ? Set Notation? ?TE 4 f - s c coIIeq, o ,ftM~, ? Relation? k 4 &QA "V ? Vertical Line Test? Function- L i\ ecA'l xqvf &9rn-M (c) I Cam t- Ivt t ac, Cs). - \ MOM 4\PdY\OVU- *j t it on Me. I \uI I k t yt -rwt c, Onto Function? ea (L44Ul1 or k-nfn nc DomBIt arre i__i__ YZWiclfl ecWcpwi _iIiJ ? flJMM Li. -- Continuous Relation? ?'-.-- k efrvrj l0 wt ?.+ick st t v - ? One-to-One Function? ? tflqt iii o(vlav f1.c$

Absolute value notes

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Algebra
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Equations
Inequality
Absolute value
Equation solving
Equation
E
Linear equation

1-4, 1-6 Solving Absolute Value Equations and Inequalities Absolute value: distance from zero on a number line. Since distance in a nonnegative, the absolute value of a number is always positive. The symbol lxi is used to represent the absolute value of a number x. I units 4 units I I I I 1 I 3 4 5 Solving Absolute Value Equations: For any real numbers a and b, where b ~! 0, if Jal = then a = b or ?a = b. The second case is often written as a = ?b. Steps 1. Isolate the Absolute Value expression 2. Rewrite equation without the I I symbols. a. One with positive answer b. One with negative answer Ex 1: Jx-51=7 x-c3- ?t-3 k'3 + 3. Solve each equation '7 2\: flL1 - '7 I 2 - \ - 4. Check your answers (plug back into I T

transformation and compositions notes

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Algebra
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Functions and mappings
Function
Differentiation rules
Differential calculus
Algebraic geometry
Chain rule
L'Hôpital's rule

I?. Ei- Pre-AP Algebra 2 Day 3 Notes: Transformations and Compositions Date Transformations y=?af[?b(x?c)](+c? c H &1M s C) t ( c) o &A \ \ on j. vri (G vv I I Graph and state the transformation y = f(x) to y = f(x - 3) + 2 y = 2f(x) y = f(2x) (, ::; 91 dt L j-vcLLNc I - VI aizA. pxvawc' 10 ticw ti a 0 10 y = f(x)to y = f(4x) 9 OY7.A4'iit cWrcc1 It C, 10 y=f(x) to y= ?f(x+2) y=f(?x) y=f(x) onicrt Cftc4ioj k horl SkICkI 10~ of O-i CtWi&'\ [r1 C,-& Lmi1z H- y = f(x) - 2 _& y = 2f(3x) + 3 -7-- - V ho?i\ cecA s\'\E4' b 3 o'iziA 1;S aN C_ Yify Compositon of functions: Putting one function into another. Ex. Given f(x) and gf4piS would be f(g(x))?"f of g of x'. **When

12

Subject: 
Algebra
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Mathematics
Algebra
Polynomials
Computer algebra
Factorization
Multiplicity
Degree of a polynomial
Ruffini's rule

Nishat? ?Ahmed ? ?? ?? ?? ?? ?Test? ?Date:? ?9/19/17 TEST? ?1? ?REVIEW? ?SHEET - A? ?polynomial? ?written? ?in? ?standard? ?form? ?has? ?the? ?greatest? ?exponent? ?in? ?the? ?beginning? ?and? ?the constant? ?(or? ?the? ?smallest? ?exponent)? ?at? ?the? ?end.? ?Therefore,? ?the? ?exponents? ?are? ?organized? ?in descending? ?manner. - The? ?degree? ?of? ?a? ?polynomial? ?is? ?equivalent? ?to? ?the? ?value? ?of? ?the? ?greatest? ?exponent? ?in? ?the polynomial. - The? ?leading? ?coefficient? ?in? ?a? ?polynomial? ?is? ?the? ?coefficient? ?of? ?the? ?variable? ?with? ?the? ?greatest exponent. - The? ?constant? ?in? ?a? ?polynomial? ?does? ?not? ?have? ?a? ?variable,? ?it? ?simply? ?a? ?number.

Calculus 1 Exam 3 4of4

Subject: 
Calculus
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Mathematical analysis
Mathematics
Geometry
Conic sections
Elementary algebra
Exponentials
Ellipse
Calculus
Equation
E

18) Find the center, foci, and vertices of the ellipse, and determine the length of the major and minor axes. Then sketch the graph. a) b) Center: Foci: Vertices: 19) Find the solutions of the system of equation. 20) The population of a certain city was 112,000 in 2006, and the observed doubling time for the population in 18 years. a) Find an exponential model for the population t years after 2006. b) Find an exponential model for the population t years after 2006. 21) Find the for the given system of equations.
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Calculus 1 Exam 3 2of4

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Calculus
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Algebra
Numerical linear algebra
Equations
Linear algebra
Gaussian elimination
System of linear equations
E
Calculus
Carl Friedrich Gauss
GAUSS

8) Find the inverse function of f. 9) Find the exact solution and rounded to four decimal places solution of the exponential equation. 10) Find the solution using Gaussian elimination or Gauss ? Jordan elimination. 11) Determine whether the system of linear equations is inconsistent or dependent. If it is dependent, find the complete solution. Find the solution using Gaussian elimination or Gauss ? Jordan elimination 12) Graph the solution set of the system of inequality. 13) Use Cramer?s Rule to solve the system.
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The 1 Percent Rule: Why a Few People Get Most of the Rewards

Subject: 
Psychology
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Vilfredo Pareto
Adages
Pareto principle
Percentage
Knowledge
Mathematics
Sociology

9/30/2018 The 1 Percent Rule: Why a Few People Get Most of the Rewards https://jamesclear.com/the-1-percent-rule 1/13 JAMES CLEAR The 1 Percent Rule: Why a Few People Get Most of the Rewards by James Clear (staging.jamesclear.com/about)????| ???? Continuous Improvement (https://jamesclear.com/continuous-improvement), Featured (https://jamesclear.com/featured), Habits (https://jamesclear.com/habits) Sometime in the late 1800s?nobody is quite sure exactly when?a man named Vilfredo Pareto was fussing about in his garden when he made a small but interesting discovery. Pareto noticed that a tiny number of pea pods in his garden produced the majority of the peas. Now, Pareto was a very mathematical fellow. He worked as an economist and one

Inversion: The Crucial Thinking Skill Nobody Ever Taught You

Subject: 
Psychology
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Linguistics
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Syntax
Voicing
Harmony
Inversion
Melody
Musical symmetry
Question
English subjunctive
English conditional sentences

9/30/2018 Inversion: The Crucial Thinking Skill Nobody Ever Taught You https://jamesclear.com/inversion 1/11 JAMES CLEAR Inversion: The Crucial Thinking Skill Nobody Ever Taught You by James Clear (staging.jamesclear.com/about)????| ???? Mental Models (https://jamesclear.com/mental-models) The ancient Stoic philosophers like Marcus Aurelius (https://jamesclear.com/marcus-aurelius), Seneca, and Epictetus regularly conducted an exercise known as?a premeditatio malorum, which translates to a ?premeditation of evils.? The goal of this exercise was to envision the negative things that could happen in life. For example, the Stoics would imagine what it would be like to lose their job and become homeless or to suffer an injury and become paralyzed or to have their

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