Algebra Supplement Homework Packet #1

Algebra Supplement Homework Packet #1Day 1:Fill in each blank with one of the words or phrases listed below.Distributive RealReciprocals Absolute valueOppositeAssociativeInequalityCommutative WholeAlgebraic expressionExponentVariable1) A(n) is formed by numbers and variables connected by the operations ofaddition, subtraction, multiplication, division, raising to powers, and/or taking roots.2) The of a number a is –a.3) 3(x – 6) 3x – 18 by the property.4) The of a number is the distance between that number and 0 on thenumber line.5) A(n) is a shorthand notation for repeated multiplication of the samefactor.6) A letter that represents a number is called a .7) The symbols and are called symbols.8) If a is not 0, then a and 1/a are called .9) A B B A by the property.10) (A B) C A (B C) by the property.11) The numbers 0, 1, 2, 3, 4 are called numbers.12) If a number corresponds to a point on the number line, we know that number is anumber.𝟐 𝟖𝟓List the elements of the set 𝟓, 𝟑 , 𝟐 , 𝟗, 𝟎. 𝟑, 𝟕, 𝟏 𝟖 , 𝟏, 𝝅 that are also elements of each given set.13) Whole Numbers15) Rational Numbers17) Real Numbers14) Natural Numbers16) Irrational Numbers18) IntegersSimplify without the assistance of a calculator.319) -5 7 – 3 – (-10)23) 3 2 68420) 3(4 – 5)24) 23 32 5 728225) 23 32 5 721) 22)615825153 Simplify each expression.29) 5xy – 7xy 3 – 2 xy30) 4x 10x – 19x 10 – 1931) 6x2 2 – 4(x2 1)26)27)28)4 9 4 910 12 4 8254 3 78 10 3 4 22 8 2 432) -7(2x2 – 1) – x2 – 133) (3.2x – 1.5) – (4.3x – 1.2)34) (7.6x 4.7) – (1.9x 3.6)Translate each statement using mathematical symbols.35) Twelve is the product of x and negative 4.42) The opposite of four is less than the36) The sum of n and twice n is negativeproduct of y and seven.fifteen.43) Two-thirds is not equal to twice the sum of37) Four times the sum of y and three is -1.n and one-fourth.38) The difference of t and five, multiplied by44) The sum of t and six is not more thansix is four.negative twelve.39) Seven subtracted from z is six.40) Ten less than the product of x and nine isfive.41) The difference of x and 5 is at least 12.

Name the property illustrated from the list provided.Distributive Property Associative Property of Commutative Property ofof MultiplicationAddition/Multiplication Addition/Multiplication45)46)47)48)(M 5) P M (5 P)5(3x – 4) 15x – 20(-4) 4 0(3 x) 7 7 (3 x)Inverse Property ofAddition/Multiplication49) (XY)Z (YZ)X50)3 55 3Identity Zero ProductProperty Property53) A 0 A54) 8(1) 8 151) 𝑇 0 052) (ab)c a(bc)Complete each equation using the given property.55) Distributive Property: 5x – 15x 56) Commutative property: (7 y) (3 x) 57) Additive Inverse Property: 0 58) Multiplicative Inverse Property: 1 59) Associative Property: [(3.4)(0.7)]5 60) Additive Identity Property: 7 Use , , or to make each statement true.61) -9 -1263) -3 -162) 0 -664) 7 -7 65) -5 -(-5)66) –(-2) -2Simplify without the assistance of a calculator.7167) 11 1169)68)70)3 52 11 2 3 132139𝑥 3𝑦 4𝑥 1 4𝑦36 2 3Day 2:Solve each linear equation.1) 4 𝑥 5 2𝑥 142) 𝑥 7 2 𝑥 83) 3 2𝑦 1 8 6 𝑦4) – 𝑧 12 5 2𝑧 15) 𝑛 8 4𝑛 2 3𝑛 46) 4 9𝑣 2 6 1 6𝑣 10𝑥7) 3 4 𝑥 28)9)10)11)12)92𝑦 3𝑦43𝑛𝑛 1 3 862𝑥8 𝑥332𝑡 13𝑡 2 1533𝑎 34𝑎 1 15 26Solve each equation for the specified variable.13) 𝑉 𝐿𝑊𝐻 for W.14) 5𝑥 4𝑦 12 for y.15) 𝑦 𝑦1 𝑚 𝑥 𝑥1 for x.16) 𝑆 𝑣𝑡 𝑔𝑡 2 for g.17) 𝐼 𝑃𝑟𝑡 𝑃 for P.Solve each absolute value equation.18) 𝑥 7 919) 3𝑥 2 6 1020) 5 4𝑥 321) 6𝑥 1 15 4𝑥22) 4 223) 5 2 6𝑥 1 153𝑥 7

Solve the following application problems.24) Twice the difference of a number and 3 is the same as 1 added to three times the number. Findthe number.25) In 2000, a record number of music CDs were sold by manufacturers in the US. By 2005, thisnumber had decreased to 205.4 million. If this represented a decrease of 25% find the numberof music CDs sold in 2000.26) The length of a rectangular playing field is 5 meters less than twice its width. If 230 meters offencing goes around the field, find the dimensions of the field.27) A car rental company charges 19.95 per day for a compact car plus 12 cents per mile for everymile over 100 miles driven per day. If Mr. Woo’s bill for 2 days use is 46.86, find how manymiles he drove.Day 3:Write inequalities.1) Connie takes at least 54 seconds to recite a poem. Write and graph an inequality to describe thisinterval.2) Tina can type at least 50 words per minute. Write and graph an inequality to describe thisstatement.3) Jack can run a mile in less than 7 minutes. Write and graph an inequality to describe thisstatement.4) The width, w, of a piece of wood ranges from 70 mm to 79 mm. Write and graph an inequalityto describe this interval.5) The cost of a box of stationery ranges from 2.25 to 2.95. Write and graph an inequality todescribe this statement.6) The cost of a 5 pound bag of dog food ranges from 5.25 to 5.95. Write and graph an inequalityto describe this statement.Solve and graph the inequality.7) 3𝑓 118) 6𝑥 5 259) 2𝑥 5 2 𝑥 910) 3 1 𝑥 1 5𝑥11) 5𝑥 4 3 𝑥 7Solve and graph the compound inequality12) 3𝑥 8 𝑜𝑟 4𝑥 413) 𝑥 5 𝑥 7 𝑜𝑟 𝑥 3 3𝑥 414) 𝑥 5 10 𝑎𝑛𝑑 3𝑥 17515) 𝑥 5 6 𝑜𝑟 6𝑥 5416) 5𝑥 6 16 𝑜𝑟 13𝑥 2617) 2𝑥 8 𝑜𝑟 2𝑥 1 13Solve and graph the absolute value inequality.18) 2𝑥 5 119) 3𝑥 2 520) 2𝑥 3 521) 3𝑥 4 522) 5 𝑥 8 1023) 2𝑥 3 824) 4𝑥 5 7 4

Day 4Determine whether each ordered pair is a solution of the given equation.1) y 3x – 5; (-1, -8) (0, 5)3) y 2 x ; (-1, 2) (0, 2)2) -6x 5y -6; (1, 0) (2, 6/5)4) y x4; (-1, 1) (2, 16)Determine whether each equation is linear or not. Then graph the equation by finding and plottingordered-pair solutions.5) 𝑥 𝑦 38) 𝑦 2𝑥 39) 𝑦 𝑥 2 6) 𝑦 4𝑥 – 210) 𝑦 𝑥3 – 27) 𝑦 𝑥 2Match each description with the graph that best illustrates it.11) Moe worked 40 hours per week until thefall semester started. He quit and didn’t workagain until he worked 60 hours a week during theholiday season starting mid-December.12) Kawana worked 40 hours a week for herfather during the summer. S he slowly cut backher hours to not working at all during the fallsemester. During the holiday season inDecember, she started working again andincreased her hours to 60 hours per week.13) Wendy worked from July throughFebruary, never quitting. She worked between10 and 30 hours per week.14) Bartholomew worked from July throughFebruary. T he rest of the time, he workedbetween 10 and 40 hours per week. During theholiday season he worked 40 hours per week.Answer questions using a graph.For income tax purposes, Jason Verges, owner of CopyServices, uses a method called straight-line depreciationto show the loss in value of a copy machine he recentlypurchased. Jason assumes that he can use the machine for7 years. The following graph shows the value of themachine over the years.15) What was the purchase price of the copy machine?16) What is the depreciated value of the machine in 7years?17) What loss in value occurred during the first year?18) What loss in value occurred during the secondyear?19) Why is the line tilted downward?Find the domain and the range of each relation. Also determine whether the relation is a function.20) {(-1, 7), (0, 6), (-2, 2), (5, 6)}22) {(6, 6), (5, 6), (5, -2), (7, 6)}21) {(4, 9), (-4, 9), (2, 3), (10, -5)}23) {(1, 2), (1, 3), (1, 1), (1, 4)}

25)26)24)Look at each graph and determine whether or not it is a function. Write Yes or No.

State the domain and range from each graph.If 𝒇 𝒙27)28)29) 𝟑𝒙 𝟑, 𝒈 𝒙 𝟒𝒙𝟐 𝟔𝒙 𝟑, 𝒂𝒏𝒅 𝒉 𝒙 𝟓𝒙𝟐 𝟕, find the following:𝑓(4)30) 𝑓( 1) ( 3)31) (0)𝑔(2)32) 𝑔(1)

Use the graphs to the right to answer questions 33 - 39.33) If g(4) 56, write the correspondingordered pair.34) Find g(2)35) Find f(-1)36) Find g(-4)37) Find all values of x such that f(x) -238) Find all positive values of x such that g(x) 439) Find all values of x such that g(x) 0Answer the following questions regarding functions.40) What is the greatest number of x-intercepts a function may have?41) What is the greatest number of y-intercepts a function may have?42) The function f(x) 0.42x 10.5 can be used to predict diamond production, in billions of dollars,for all years after 2000. What is the predicted diamond production in 2012? 2015?Day 5:Graph the following functions.1) y -2x2) y ½ x3) y 1/3 x – 24) y 5x 35) –x 2y 66) 2x 3y 67) x -18)9)10)11)12)13)14)y 0y 7 0x–3 0x – 3y 5x 8y 8y x4x y 5Find the slope between the given points or of the given line.22) (3, 2), (8, 11)26) (-2, -4), (-6, -4)23) (3, 1), (1, 8)27) (3, -2), (-1, -6)24) (4, 2), (4, 0)28) x 125) (5, 2), (0, 5)29) y -315)16)17)18)19)20)21)y 4/3x 2x 3/2y -3y -4x 2y 4x – 54 x – 3y–x 9 -y30)31)32)33)-6x 5y 302y – 7 xx–7 02y 4 7Determine which line has greater slope.34)35)36)37)38)39)

Determine if the lines are parallel, perpendicular, or neither.40) y -3x 6;y 3x 543) 2x – y -10;41) -4x 2y 5;2x – y 744) -2x 3y 1;42) y 5x – 6;y 5x 245) x 4y 7;2x 4y 23x 2y 122x – 5y 0Answer the following application questions46) The annual average income y of an American man over 25 years with an associate’s degree isapproximated by the linear equation y 694.9x 43,884.9, where x is the number of years after2000.a. Predict the average income of a man in 2009b. Find and interpret the slope of the equation.c. Find and interpret the y-intercept of the equation.47) With WiFi gaining popularity, the number of public wireless Internet access points, in thousands,is projected to grow from 2003 to 2008 according to the equation -66x 2y 84, where x is thenumber of years after 2003.a. Find the slope and y-intercept of the linear equation.b. What does the slope mean in this context?c. What does the y-intercept mean in this context?Graph the following piecewise functions.2𝑥, 𝑥 048) 𝑓 𝑥 𝑥 1, 𝑥 049) 𝑓 𝑥 50) 𝑓 𝑥 51) 𝑓 𝑥 52) 𝑓 𝑥 4, 𝑥 3𝑥 2, 𝑥 33𝑥, 𝑥 0𝑥 2, 𝑥 053) 𝑓 𝑥 𝑥, 𝑥 12𝑥 1, 𝑥 15𝑥 4 𝑥 2 1, 𝑥 254) 𝑓 𝑥 𝑥, 𝑥 12𝑥 1, 𝑥 11𝑥3 4𝑥, 𝑥 03𝑥 2, 𝑥 0Day 6Write an equation of a line in slope-intercept form using the given information.1. slope of – ½ ; y-intercept of -92. through (0, 4) and (-1, 3)3. slope of ¼ ; value of f(0) 74. slope of -5; through (1, 2) 5 5. through 12 , 1 and 3, 26. values f(-5) 3 and f(4) -5Write an equation of a line in point-slope form using the given information.7. slope of – ⅖; through (3, -7)8. through (5, -6) and (1, -7)9. through (6, -3) and (-1, 9)