Practice - Properties of Real Numbers Simplif.. - 4.«. - 6«. ` 7 4. «- -«6 `. ` 6. 0. -6«7. 4-8«8. -0.0«` Replace each $ with the smbol R, S,or to make the sentence true. 9.!6 $!0 0. $.. 0.06 $ 0.6. 4 $ -4«. -0.4 $ 0 4. - -7«$ -7«. 0.9 $ 6.! $ Name all the sets of numbers to which each number belongs. 7. - 8. 0 9.! 0..7. 9. 0..4678 c 4. 4 7 Name the propert of real numbers illustrated b each equation.. p + = + p 6.! 0! 7. ( + ) + = + ( + ) 8. 9? 9 9. 6(t + 4v) = 48t + 64v 0.!??!. 0.0? = 0.0.?. 7 + (-7) = 0 4. () = () Graph the number on the following number line. Estimate if necessar. 4 0 4.! 6. 7. 0. 8. - Find the opposite and the reciprocal of each number. 9. 40. 4. 4. -4 9 Which set of numbers best describes the values of each variable? 4. the number of stops N a commuter train makes on a certain da! 44. the high H and low L for a certain stock during a period of n weeks 4. the average time per lap t it takes a race car to complete n laps Lesson - Practice Algebra Chapter
Practice - Algebraic Epressions Simplif b combining like terms.. 6 +. t + t -. -6a - a + b - 4. i + 7j - i. 6-4 6. - + 6 (a b) 7. (m - )+ m 8. 9. 9 4 9 b t t t t 0. 4a - (a + ). (m - n ) - 6(n + m). ( - ) + ( - ). The epression 6s represents the surface area of a cube with edges of length s. Find the surface area of a cube with each edge length. a. inches b.. meters 4. The epression 4.9 + 0.07 models a household s monthl longdistance charges, where represents the number of minutes of long-distance calls during the month. Find the monthl charges for 7 minutes. Evaluate each epression for the given value of the variable.. + + ; = 4 6. a + 6 + a; a = 7. -t - (t + ); t = 8. i - (i - i ); i = 7 9. k + - 4k - ; k =- 0. 6a - a - a ; a =. -m (m + m ); m =-4. - n - + n ; n =-. b - + b ; b = 9 4. a + b ; a =, b = 4. c( - a) - c ; a = 4, c =- 6. -a + (d - a); a =, d =- 7. Write an epression for the perimeter of the figure as the sum of the lengths of its sides. Then simplif our answer. a a b a b c c b b a c Algebra Chapter Lesson - Practice
Practice -6 Comple Numbers Find the first three output values for each function. Use z = 0 for the first input value.. f(z) = z + i. f(z) = z + + i Find the additive inverse of each of the following.. + i 4. -4 + i. i 6. - - i 7. -6i 8. - i 9. - + i 0. 4 Find each absolute value.. -i. + i. - - i 4. + i. 4 + i 6. - i 7. - i 8. - + i 9. - i 0. i. i. 4 + i. 6 - i 4. - + i. 4 Simplif each epression. 6. "40 7. "88 8. - "6 9. ( + i) + ( - i) 0. ( + i) - ( + i). 4 - ". ( + 6i) - (7 + 9i). ( + i)( - i) 4. ( + i)(6 - i). ( - 6i)(6 - i) 6. ( + 4i)( + 4i) 7. ( + i)( - i) 8. ( + i)( - i) 9. (- - i)( - i) 40. ( + i) - (4 - i) 4. "48 4. "00 4. "7 44. "6 + 4. (4 - i)(4 - i) 46. (4 + i)( - 7i) 47. ( + i)( - 7i) 48. ( + 4i)(- - i) 49. ( - i)( + i) 0. ( + i) + (-4 + i). ( + 4i) - (0 - i). ( + i)( - i). ( + 4i)( - i) 4. (6 + i)( - i). ( - i)( - i) 6. "44 7. "6 8. "8 9. ( + i)(4 + i) 60. ( + 4i) - (- - i) 6. ( + i)(- - i) 6. (- + 4i)( - i) 6. (6 + i) + ( - i) 64. ( + i)( + i) 6. (- + i) + (4 + i) 66. ( + 4i)( + i) 67. (- - i)(- + i) Solve each equation. 68. +80=0 69. + 00 = 0 70. +40=0 7. +6=0 7. +7=0 7. + 44 = 0 74. 4 + 600 = 0 7. 4 +=0 76. +0=0 77. 4 + 00 = 0 78. +9=0 79. 9 +90=0 Algebra Chapter Lesson -6 Practice 7
Practice - Relations and Functions For each function, find f( ), ƒa, f(), and f(7). b. f() = +. f() = +. f() =- +.8 Use the vertical line test to determine whether each graph represents a function. 4.. 6. O O Graph each relation. Find the domain and range. 7. e (, ), a, 8. {(-, ), (0, -), (0, 4), (, -)} 4 b, a, b, (, 9) f 9. {(-, ), (, ), (, )} 0. {(0., -), (0., 0). (0., ), (0., )} Determine whether each graph represents as a function of.... O O Make a mapping diagram for each relation, and determine whether it is a function. 4. {(, ), (, ), (, 4), (, )}. {(-, ), (0, 0), (, ), (, 4), (, 9)} Suppose f() ± and g() =. Find each value. g() ƒ() 6. ƒa 7. g(4) 8. 9. b ƒ() g() O O Algebra Chapter Lesson - Practice
Practice - Solving Equations Solve each formula for the indicated variable.. V = p r h, for h. S = L( - r), for r. S = w + wh + h, for w Solve for. State an restrictions on the variables. 4. 4 ( + ) = g. a( + c) = b( - c) 6. t = t 9 7. Two brothers are saving mone to bu tickets to a concert. Their combined savings is $. One brother has $ more than the other. How much has each saved? 8. The sides of a triangle are in the ratio ; ;. What is the length of each side of the triangle if the perimeter of the triangle is in.? 9. Find three consecutive numbers whose sum is 6. Solve each equation. 0. ( - ) + a =. w + 8 - w = 6 - w b. 7 + = 6 +..( + ) =.6( + ) 4. t - at 4 = t +. 0.(c +.8) - c = 0.6c + 0. b 6. ( + ) = ( + ) 7. 8. Mike and Adam left a bus terminal at the same time and traveled in opposite directions. Mike s bus was in heav traffic and had to travel 0 mi/h slower than Adam s bus. After hours, their buses were 70 miles apart. How fast was each bus going? 9. Two trains left a station at the same time. One traveled north at a certain speed and the other traveled south at twice the speed. After 4 hours, the trains were 600 miles apart. How fast was each train traveling? 0. Find four consecutive odd integers whose sum is 6. u u 0 u 6. The length of a rectangle is cm greater than its width. The perimeter is 8 cm. Find the dimensions of the rectangle. 4 Lesson - Practice Algebra Chapter
Practice - Linear Equations Find the slope of each line.. - = 0. - =-7. 4 4.. 6. O O O 7. through (4, -) and (-, -) 8. through (, -) and (, ) Write in point-slope form the equation of the line through each pair of points. 9. (0, ) and (, 0) 0. a and a. (-, -) and (, 6), b, b Graph each equation.. 4 + =. 6 4. Write in standard form an equation of the line with the given slope through the given point.. slope =-4; (, ) 6. slope = ;(-, ) 7. slope = 0; (, -4) Find the slope and the intercepts of each line. 8. - 4 = 9. =- 0. ƒ() 4. = 7 Write an equation for each line. Then graph the line.. through (-, ) and parallel to = +. through (, ) and perpendicular to 4. through (-, 4) and vertical. through (4, ) and horizontal Lesson - Practice Algebra Chapter
Practice - Direct Variation For each direct variation, find the constant of variation. Then find the value of when.. = when =-. when. when 4 8 8 Determine whether varies directl as. If so, find the constant of variation. 4. 4. =-. 6. + 4 = 0 7. - = 9 8. = 9. + = 0.. =-. + 7 0 For each function, determine whether varies directl as. If so, find the constant of variation and write the equation... 4.. - - - - 4 9 9 Write an equation for a direct variation with a graph that passes through each point. 6. (6, ) 7. (-., 9) 8. (-, 90) 9. (7, ) 0. a,. a. (0, ). (, 6) b, 7 b In Eercises 4 7, varies directl as. 4. If = when =, find when =.. If =-4 when =, find when =. 6. If =-4 when =-7, find when =. 7. If = when = 0, find when =. 7 8. A -minute long-distance telephone call costs $.90. The cost varies directl as the length of the call. Write an equation that relates the cost to the length of the call. How long is a call that costs $.? 9. The distance a spring stretches varies directl as the amount of weight that is hanging on it. A weight of. pounds stretches a spring 8 inches. Find the stretch of the spring when a weight of 6.4 pounds is hanging on it. - 0 - Algebra Chapter Lesson - Practice