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# Intro Indigenous Nations Stds GINS 101

KU

GPA 3.63

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This 5 page Class Notes was uploaded by Kylee Leannon on Monday September 7, 2015. The Class Notes belongs to GINS 101 at Kansas taught by Staff in Fall. Since its upload, it has received 26 views. For similar materials see /class/182422/gins-101-kansas in Global Indigenous Nations Stds at Kansas.

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Date Created: 09/07/15

Math 101 Name Algebra Review 2 Date Interval Notation Inequalities amp Absolute Value Interval Notation In this course we will use Interval Notation when describing inequalities in one variable To review Interval Notation and Inequalities study the material presented in Appendix Section A Q Pg A66 71 Absolute Value Equations and Inequalities The absolute ualue of a number is de ned two ways 1 The number line can be used to provide a geometric interpretation of absolute value The absolute value of a number is the distance between the number and 0 on a number line For example 5 5 and 7 5 5 because both 5 and 75 are located 5 units away from 0 Absolute value is concerned with the magnitude of a number regardless of direction to Algebraically a de nition for absolute value is 7 z ifoO 7 7m ifxlt0 That is if z is positive the is the same as m But if z is a negative number is the opposite In this way we conform to the convention that distance is always positive To solve equations or inequalities with absolute values we consider two possibilities for each situ ation For example z 5 7 means m57or m577 since both 7 and 7 are 7 units away from 0 Thinking about the geometric interpretation is especially helpful when solving absolute ualue in equalities A less than lt relationship indicates values closer to 0 while a greater than gt relationship indicates values further away from O 0 Further examples and explanations can be found in the text Section 28 Pg 170 7 173 0 Compare number line graphs and function graphs coordinate plane in Example 4 pg 172 o Caution Remember to isolate the absolute value rst 0 Pay close attention to the waming on Pg 173 Complete the following problems on a separate sheet of paper Demonstrate your understanding of the processes involved by showing all work For problems 1 67 complete the table Solve the following For the inequalities7 write the solution in interval notation and graph the solution set 1z71 2 l2y7l9 3l172wl611 4 l3z72l 4 5 lm5li4gti2 6 273427 7 l3z1l lt 72 Math 101 Name Algebra Review 1 Date Polynomials and Radicals Complete the following problems on a separate sheet of paper Demonstrate your understand ing of the processes involved by showing all work Simplify 1 5a 4b 2a 7 3b 2 21 52 3 m 4 m m 5 6m 7 NE m 6 lt3 3 3f 7 41212 4 Factor completely 8 3214 7 401y2 9 212 51 7 3 10 413 7 4x2 7 91 9 Solve 11 87317721 12 6217137z10 13 y216y640 14 127120 15 2121lz760 Math 101 Name Algebra Review 4 Date Exponent Properties and Operations Exponents are mathematical notation for repeated multiplications of some number or expression The process of working with exponents is straightforward when the exponent values are integers For example7 the meaning of 25 is shorthand notation for 2 2 2 2 2 The properties rules or laws of exponents are Example Product Rule am a amn 32 35 325 37 am 68 Quotient Rule a7 am 67 6873 657 37 7 774 3 7 W4 7 72gt 72gt 7 8 ZeroExponent Rule a0 1 30 17 60 17 760 17 5x0 1 5x0 5 Ne ative Ex onent Rule 7 7 i 9 2 7 i 7 i g 39 p a 7 a 92 81 1 1 62 P T 1 T 36 E Power Rule Powers to Powers Wm am 232 23392 26 647 1 5 is 573 7 715 y y y j Products to Powers 011 ambm 72324 724y24 724y2394 16348 a m am 3 4 794 81 Quotlents to Powers 7 him 7 m4 7 Rational exponents are de ned so that their properties are the same as the properties for integer exponents For example7 7 7 2 71 7 It is also true that 2 4 7 Thus7 it is reasonable to conclude that 1 7E Rational exponents are de ned as follows aquot and 1 quotamWm Simplifying Exponential Expressions Properties of exponents are used to simplify exponential expressions An exponential expression is simpli ed when 0 No parentheses appear 0 No powers are raised to powers 0 Each base occurs only once 0 No negative or zero exponents appear Simplify the following expressions Assume all variables represent positive numbers Show your work 10m9y5 39 78x3y7 4x5y37x2y 7 1 3x12z to Wow 16 F lt40gtlt27gtlt25gt U m72y10275 a

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