b g (a) 0 (b) 6 (c) 2 (d) 4

Transcription

1 ection. Linear and Absolute alue Equations Linear Equations olve. Chapter : Equations and Inequalities. x x 9 7 (b) x 7 0 (b) x (b) b g 0 (b) 6. x x Contradictions, Conditional Equations, and Identities. hich of the following equations is not an identity? b g x x (b) x x 9x 6. hich of the following equations is an identity? x x x All of the above are identities b g (b) bx g x bx g x bx gx 7. hich of the following equations is not a conditional equation? b g (b) x bxg x x bxg x x x xx (e) None of these. Find the values of a and c that make the equation an identity. b 9x axc 6x g a, c (b) a, c a, c a, c (e) None of these Absolute alue Equations olve. 9. x, (b),,, 0. x 7 69, (b) 9, 69,, 7. x, (b) 7 7, 7, 7, Copyright Houghton Mifflin Company. All rights reserved. 9

2 Chapter Equations and Inequalities. hat is the solution to the equation x 0? x 6 (b) x 6 x x. he formula C bf g 9 is used to convert degrees Fahrenheit, F, to degrees Celsius, C. Convert C to degrees Fahrenheit.. F (b) 7.0 F 0. F. F. se the formula d rt, where d is the distance, r is the rate of speed, and t is the time, to find how long it would take to travel a distance of 00 miles at a speed of 0 miles per hour. hr (b) 7 hr hr 6 hr. he sum of the angles in a convex polygon can be determined by the formula D 0 n b g where D is the total number of degrees in the angles of a convex polygon with n sides. If a convex polygon s angles have a sum of 70, find the number of sides in the polygon. 7 (b) 6 (e) None of these 6. he charge for mailing a fourth-class package through the.. Postal ervice is C 00. x 7. where C is the charge in dollars and x is the weight of the package in pounds. Find the charge to mail a package that weighs 0 pounds. (b) How many pounds can be mailed for $.97? $0.0 (b) 0 lb (b) $.9 (b) 7 lb $.07 (b) lb $.07 (b) 9 lb ection. Formulas and Formulas olve the formula for the given variable. 7. r h for h h r (b) h r h r none of these. pf H I K for p p (b) p p p F H I K 9. M m for MP m (b) P MP m m MP Mm P 0. olve the equation A h bc b g for c. A h c (b) c Ac b c c A hb c h Ab 0 Copyright Houghton Mifflin Company. All rights reserved.

3 ection. Formulas and. he perimeter of a triangle is 60 centimeters. One side is 6 centimeters shorter than the second side. he third side is 6 centimeters shorter than triple the length of the first side. Find the length of each side. cm, cm, cm (b) 6 cm, cm, cm cm, cm, 0 cm 6 cm, cm, cm. Jacob has $6.00 in dimes and quarters. He has twice as many quarters as dimes. How many of each coin does he have? 0 dimes and 0 quarters dimes and 6 quarters (b) dimes and 6 quarters 0 dimes and 0 quarters. he daily cost of renting a car is $0 plus $0.0 per mile. If Jane paid $.60 for a -day rental, how many miles did Jane travel? 6 (b) 9 6. he sum of three consecutive odd integers is 99. hat is the largest of the three integers? (b) None of these ection. Quadratic Equations olve Quadratic Equations by Factoring olve by factoring.. x x 0, (b),,, 6. x x 0, (b),,, 7. x x6 0, 6 (b) 6,,,. olve. x x, (b),,, olve Quadratic Equations by aking quare oots 9. olve. x 0 0 (b),,, 0. olve by taking the square root. 9x (b) olve. x 6, (b),. olve by extracting square roots. x 0 0 b g (b) Copyright Houghton Mifflin Company. All rights reserved.

4 Chapter Equations and Inequalities olve Quadratic Equations by Completing the quare. olve by completing the square. 9x x (b) olve by completing the square.. x 6x6 0, (b),,,. 9x 90x, (b),,, 6. olve by completing the square. x x0 0, 0 (b) 0,, 0 0, olve Quadratic Equations by sing the Quadratic Formula olve using the quadratic formula. 7. x x, (b) 7, 7, 7, 7. x x 0 6 6, (b) 6 6, 6 6, 6, 6 9. se the Quadratic Formula to solve. x 7x 7 (b) olve using the Quadratic Formula. x 9x 9 9i 0 (b) 9 0i 0 9 0i 0 9 9i 0 he Discriminant of a Quadratic Equation. Determine the nature of the roots: x x = 0. wo equal real roots (b) No real roots wo distinct real roots Cannot be determined. Determine the number of real solutions of the equation. x 6x 0 (b) 0 Copyright Houghton Mifflin Company. All rights reserved.

5 ection. Quadratic Equations. hich of the following is the discriminant and the nature of the roots for x x =0? he discriminant is 0 and there are no real roots. he discriminant is 0 and there is one real root. (b) he discriminant is and there are two real roots. he discriminant is and there is one real root.. Determine the number and nature of the roots of the equation. x x 0 one real root and one imaginary root (b) one real root two imaginary roots two real roots of Quadratic Equations. he width of a rectangular carpet is feet less than its length. If the area of the carpet is 70 square feet, find its width. 7 ft (b) ft 0 ft 6 ft 6. One integer is eight more than three times another. If the product of the integers is, find the two integers. and 7 (b) and 7 and 7 and 7 7. A sidewalk was built around a rectangular garden. If the area of the sidewalk is m, find x. (Note: Figure not drawn to scale.) x x x x 7 m (b) m m 6 m. he length of a rectangle is 7 cm less than three times its width. If the area is 0 cm, find the dimensions of the rectangle. cm cm (b) cm 6 cm 7 cm cm 0 cm 6 cm ection. Other ypes of Equations Polynomial Equations 9. olve. x x 6x6 0, (b), 6,, e j 0. olve by factoring. x x x 0. olve the polynomial equation by factoring. x 0x 7x (b), 0 0,,, 0, (b), 0,, 0,, 0,. olve: 6x 6x 0 0, 6 (b) 96 0, 6 0 Copyright Houghton Mifflin Company. All rights reserved.

6 Chapter Equations and Inequalities ational Equations olve the equation.. k (b) 7. x x x x 7 (b) 7 0. x 0 x x x 0 (b) x 9 0 (b) 0 x x 9 x 9 adical Equations olve. 7. x9 = x (b) 7, x x 7 (b) 6 No solution 9. olve. x x, 6 (b), 6, olve. x x (b) 6, 6 no solution Equations that are Quadratic in Form olve: 6. 6 x x 0 x, x (b) x, x x, x no solution 6. x x 0, (b),, 6, 6. x x 0 x, x (b) x, x x, x no solution 6. x x 0 x or x 6 (b) x or x 6 x 6 or x 6 x or x ection. Inequalities Properties of Inequalities olve: 6. 9 w mw w r (b) mw w r mw w 7r mw w 7r Copyright Houghton Mifflin Company. All rights reserved.

7 ection. Inequalities olve: m r (b) mb b 0r mb b r b b b g m r (b) mx x r mx x r mx x r 7 7 x 9x x x 7 (b) x x 9 7 x x b b 6 b b x 9x x 0 x x x none of these Compound Inequalities 69. olve. x 0 or x 7 x or x 7 (b) x 7 x 7 x or x olve. x or x x (b) x all real numbers no solution 7. olve. x and x 7 x or x 7 (b) x or x 7 x 7 x 7 7. olve the inequality and give the solution in interval notation. x 9 or x 9 b, g (b), b g b, g Absolute alue Inequalities 7. olve. x m r (b) mx x or x 0r mx x or x 0r none of these x x 0 7. olve: x x x (b) x x or x x x or x x x 7. olve. x m r (b) mx 0 x r mx 0 x r mx x or x x x 0 or x 0 r 76. olve the inequality. x 6 x, x (b) x x x, x Copyright Houghton Mifflin Company. All rights reserved.

8 Chapter Equations and Inequalities he Critical alue Method olve. b gb g x7 7x 0 x x 7 (b) x 7 x 7 xx or x7 xx 7or x x x m r (b) mx x 7r mxx or x 7 r mx x xx 7 or x 79. x x 0 x x 9 7 m r (b) mxx 9 or x r mxx or x 9 r mx x 0. olve the inequality and give the solution in interval notation. x x 0 F HG O Q P, 6 6, j (b), 6 6, F HG I KJ 6, 6 6, 6 P F HG L N M I KJ e O Q j r 9 r ational Inequalities. olve the inequality: x x x (b) x, x x, x x. olve: x x b gb g 0 x x (b) x or x x or x x or x. Identify the solution set of the inequality: x x 7 x (b) x x x or x. olve the equation or inequality. x x 6 x 6 x 6 or x ; undefined at x 6 (b) x 6; x 6 6 x or x 6 ; undefined at x 6 6 x. he daily cost of renting a car is $0 plus $0.0 per mile. Joan s budget allows her to spend a maximum of $ for a -day rental. How many miles may Joan drive the rental car in one day without exceeding her budget of $? 60 mi (b) 60 mi mi mi 6 Copyright Houghton Mifflin Company. All rights reserved.

9 ection. Inequalities 6. During a physics lab, students found that the minimum force F needed to pull a block up an incline was given by F 06. x. If the mass of the block x is.6 kilograms, what is the force needed to pull the block? 0. 0 N (b) N. N. 6 N 7. A garden is to have a perimeter of 0 feet and its area must be at least 99 square feet. ithin what bounds must the length of the rectangle lie? 6 ft l 9 ft (b) ft l ft 9 ft l ft 6 ft l ft. he area of the cross section of a round bolt must be greater than 69 mm and less than 9 mm. emember that the formula for the area of a circle is A r, where r is the radius. rite an inequality to describe the requirements for the radius of the bolt. ound to the nearest hundredth of a millimeter. 7. mm r 99. mm (b) mm r 7 mm 0.9 mm r mm.79 mm r 9.99 mm ection.6 ariation and Direct ariation 9. he total cost of gasoline varies directly with the number of gallons purchased. Mariko pays $. for gallons of gasoline. rite a direct variation equation that shows the relationship between the total cost of gasoline c and the number of gallons purchased n. n 7. c (b) n. c c. n c 7. n 90. he distance an object falls varies directly with the square of the time of the fall. On planet X, an object falls 9 feet in seconds. a. Find a mathematical model that relates the distance the object falls to time. b. How long does it take an object to fall 9 feet? ound your answer to three decimal places. a. d 6 t b..0 s (b) a. d 9 t 6 b. 7.0 s t a. d 9 b.. s a. d t 6 b..97 s 9. he amount of a person s paycheck P varies directly with the number of hours worked t. For hours of work, the paycheck is $6.00. Find the pay for 0 hours of work. $0.7 (b) $0.00 $.00 none of these 9. An enclosed gas exerts a pressure P, on the walls of a container. his pressure is directly proportional to the temperature, of the gas. If the pressure is lb per square inch when the temperature is 0 F, find the constant of variation. 70 (b) 70 Inverse ariation 9. he intensity I of light received from a source varies inversely as the square of the distance d from the source. If the light intensity is foot-candles at feet, find the light intensity at feet. 0.7 foot-candles (b).67 foot-candles. foot-candles 0. foot-candles Copyright Houghton Mifflin Company. All rights reserved. 7

10 Chapter Equations and Inequalities 9. he price per person of renting a bus varies inversely with the number of people renting the bus. It costs $ per person if 7 people rent the bus. a. rite a mathematical model representing the price p, to the number of people renting the bus n. b. How much will it cost per person if people rent the bus? a. p 9 n b. $7.07 (b) a. p n 7 b. $6. a. p n 9 b. $.9 a. p 7 n b. $ Yellows vary inversely as oranges squared. hen there are 6 yellows, there are oranges. How many yellows are present when there are oranges? 6 (b) 96. nder certain conditions, the pressure of a perfect gas varies inversely as the volume. hen the pressure of a quantity of gas is 6 pascals, the volume is 60 liters. hat would be the volume if the pressure is increased to 0 pascals? L (b) 0 L L L Joint ariation and Combined ariation 97. rite the variation and find the quantity indicated when a varies jointly as b and the square of c. If a is 7 when b is and c is, find a when b is and c is. k a kbc; (b) a kbc ; 9 a bc ; a bc ; 6 9. he horsepower that a rotating shaft can safely generate varies jointly with the cube of its diameter and its speed in revolutions per minute. A shaft with a -inch diameter turning at a speed of 700 revolutions per minute can safely transmit 0 horsepower. Find the horsepower that a shaft with a -inch diameter can safely transmit at a speed of 00 revolutions per minute. hp (b) 6 hp 0 hp 9 hp 99. If m varies directly as the square root of y, inversely as p, and directly as n, what happens to m when y is quadrupled, p is tripled, and n is multiplied by? m is multiplied by 9 (b) m is multiplied by 9 m is divided by 9 it stays the same 00. he Crystal Glass Company found that the number of windows sold, N, varies directly as their advertising budget, A, and inversely as the price of each window, P. hen $0,000 is spent on advertising and the price of a window is set at $0, 0,00 windows are sold. Determine the number of windows sold when the amount spent on advertising is increased to $60,000.,00 (b) 0, Copyright Houghton Mifflin Company. All rights reserved.

11 Chapter : Equations and Inequalities (Answer Key) ection. Linear and Absolute alue Equations Linear Equations [] [] [] (b) [] Contradictions, Conditional Equations, and Identities [] [6] [7] (e) [] (b) Absolute alue Equations [9] (b) [0] (b) [] [] [] [] [] [6] ection. Formulas and Formulas [7] (b) [] [9] (b) [0] [] [] [] [] ection. Quadratic Equations olve Quadratic Equations by Factoring [] [6] [7] (b) [] olve Quadratic Equations by aking quare oots [9] (b) [0] [] [] olve Quadratic Equations by Completing the quare [] [] (b) [] [6] olve Quadratic Equations by sing the Quadratic Formula [7] (b) [] [9] (b) [0] he Discriminant of a Quadratic Equation [] [] [] [] of Quadratic Equations [] [6] [7] (b) [] ection. Other ypes of Equations Polynomial Equations [9] [0] [] [] ational Equations [] (b) [] [] (b) [6] (b) adical Equations [7] [] [9] [60] Equations that are Quadratic in Form [6] Copyright Houghton Mifflin Company. All rights reserved. 9

12 Chapter Equations and Inequalities [6] (b) [6] [6] (b) ection. Inequalities Properties of Inequalities [6] [66] (b) [67] (b) [] [6] (b) [7] [] ection.6 ariation and Direct ariation [9] [6] [90] (b) Compound Inequalities [69] [70] [7] [9] [9] Inverse ariation [9] (b) [7] [9] Absolute alue Inequalities [7] [7] [7] [76] he Critical alue Method [77] [7] [9] (b) [96] Joint ariation and Combined ariation [97] (b) [9] (b) [99] [00] (b) [79] (b) [0] (b) ational Inequalities [] [] (b) [] [] (b) 60 Copyright Houghton Mifflin Company. All rights reserved.