MAT 135In Class AssignmentsFall 20071MAT135In-Class AssignmentChapter 11. Simplify each expression:2 2)2 3 5 )3 2(5 2) )3 4 2 3 )30 6 4 2a b c d+ � + - � - � � + �2. a)Factor 4,356 into the product of prime factors b) Reduce 4,3565,148 to lowest terms.3. Translate each statement into an equivalent inequality:a) x is at least 4 b) x is between 0 and 8 c) x is no more than 54. Which property or properties of the real numbers is illustrated by each expression?) 3 3 )5 0 5 )5 ( 5) 0)5 ( ) (5 ) )3(1) 3 )3( ) 3 3a x x b cd x y x y e f x y x y+ = + + = + - == = + = +5. Write in scientific notation:a) 376,000 b) 4,520 c) 0.00000676. Write in expanded form:5 4 3)1.94x10 )5.4x10 )3.53x10a b c-7. Simplify each expression. Write all answers with positive exponents only. Assume allvariables are nonzero.4 3 3 42 -5 3 2 3 4 -310( ) ( ))( y ) )(2 ) (5y ) )x xa x b y cx- --2MAT135In-Class AssignmentSection 2.1 Solving Linear Equations1. Solve the following equations:5) 4 8 3 7 ) 3 23 3 1 1 1 5)7 3( 2) 4( 1) ) 2 4 3 4 ) (3 2) 26 )2 3(3 5) 6a a a b tc x x d x xe x x f x x- - =- + - + =+ + = - + = ++ + = - - =-2. The taxi meter was invented in 1891 by Wilhelm Bruhn. Chicago charges $1.80 plus$0.40 per mile for a taxi ride.a) If the fare is $6.60, write an equation that shows how the fare is calculated.b) How many miles were traveled if the fare was $6.60?3. In 1992, twice as many people visited their doctor because of a cough than an earache.The total number of doctor’s visits for these two ailments was reported to be 45 million.a) Let x represent the number of earaches reported in 1992. Write an expression for thenumber of coughs reported in 1992.b) Write an equation that related 45 million to the variable x.c) How many people visited their doctor in 1992 to report an earache?3MAT135In-Class AssignmentSection 2.3 Solving Linear Inequalities1. Solve the inequalities, graph each solution, and write the solution in interval notation:1) y>4 ) 12 2 3 1)5 115 )10 y 36 2 )2(3 1) 10 )1 3 4(3 1)a b xc x de x f a- ��- - �+ �- < - -2. A store selling art supplies finds that they can sell x sketch pads each week at a priceof p dollars each according to the formula x=900-300p. What price should they charge isthey want to sell:a) at least 300 pads each week?b) fewer than 525 pads each week?c) more than 600 pads each week?d) at most 375 pads each week?4MAT135In-Class AssignmentSection 2.4 Solving Compound Inequalities1. Solve the following inequalities. Use a line graph and interval notation to write each solution set.) 60 20 20 60 )7 5 2 or 3 2 3 1 2)5 x+1<9 )8 12 and x>1 4 3 )3 1 2 4 or 5 2 3 4 a a b x xc d xe x x x x- < + < - �- + >< � - -- > + - < + ) 2 5 2f m- � - �2. A factory’s quality control department randomly selects a sample of 5 lightbulbs totest. In order to meet quality control standards, the lightbulbs in the sample must last anaverage of at least 950 hours. Four of the selected bulbs lasted 925 hours, 1000 hours,950 hours, and 900 hours. How many hours must the fifth lightbulb last for the sample tomeet quality control standards?3. A worker earns $12 per hour plus $16 overtime pay for every hour over 40 hours.How many hours of overtime are needed to make between $600 and $800 per week?5MAT135In-Class AssignmentSection 3.1 The Rectangular Coordinate System1. Identify the quadrant in which each point is located, and place it on the graph below. Label the axes on the graph.a) (1,2) b) (-1,-2) c) (5,0) d) (0,2)e) (-5,-5) f) (1/2,2) g)(-8,3) h) ( 6,-2)2. The x-axis on the graph below represents number of hours worked and the y-axis represents pay, in dollars. Approximately what is the pay for working 10, 20, 30, and 40 hours? Create a table that displays the data shown on the graph.6MAT135In-Class AssignmentSection 3.2 Slope1. Find the slope of the line from the given graphs: 2. Find the slope of the line through the given points. Then plot each pair of points and draw the line through them.a) (2,1) (4,4) b) (2, -5) (3, -2) c) (1,5) (-4,-5)3. A line, l, contains the points (3,4) and (-3,1). Give the slope of any line perpendicularto l.4. Determine if the line through the points (7,2) and (-9,2) and the line through the points(4,-4) and (1, -4) are parallel, perpendicular, or neither.5. Solve for y: 0y bmx-=-7MAT135In-Class AssignmentSection 3.3 Graphing Linear Equations1. Find the slope, x-intercept, and y-intercept of each equation. Sketch the graph using this information.) 3 2 )3 2 12 )4 5 203) 2 ) 3 34a y x b x y c x yd y x e y x= - - = + == - =- +2. Give the slope and y-intercept of y = -2.3. For the line x = -3, sketch the graph, give the slope, and find any intercepts.4. Find the x- and y-intercepts of the graph of the equation 4 16x- =-.5. Find the equation of a line with an x-intercept of (2,0) and a y-intercept of (0,3).6. In an aerobics class, the instructor tells her students that exercise heart rate is 60% ofthe maximum heart rate, where maximum heart rate is 220 minus their age. Determinethe equation that gives exercise heart rate, E, in terms of age, A. Find the exercise heartrate of a 22 year old student.8MAT135In-Class AssignmentSection 3.4 More on Graphing Linear Equations1. Complete the table:Equation Slope,m x-intercept y-intercept3 5y x=- +2y x=4 6 24x y+ =1y =3x =2. Write each equation in slope-intercept form:)6 4 1 ) 1 3( 5) )4 3 2 0a x y b y x c x y+ = + = + - - =3. Find the equation of a line with slope -3 that passes through the point (0,7).4. Find the equation of a line parallel to y=5x-1 and has x-intercept (4,0).5. What is the equation of a line perpendicular to the graph of y=2x and passes through ( -2,5)?6. What is the equation of a line that passes through (2,1) and (1,2)?7. A salesperson earns a salary of $1500 per month plus a 3% commission of the totalmonthly sales. Write a linear equation giving the salesperson’s total monthly income I interms of the sales, s. Sketch a graph of the equation, clearly labeling two points on thegraph.9MAT135In-Class AssignmentSection 3.6 Introduction to Functions1. For each of the following relations, give the domain and range, and state which are functions:){(1,3)(2,5)(4,1)}