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Chapter 1 Introduction to Real Numbers and Algebraic Expressions Exercise Set 1.1 RC2. Multiplication RC4. Division 46. P−0.3P 2. Substitute 34 for n: 600(34) = 20,400, so $20,400 is col- lected if 34 students enroll. Substitute 78 for n: 600(78) […]

y ⫺4⫺224 ⫺4 ⫺2 ⫺5 ⫺3 f(x)  2  x  1 t(4) = −√2·4+1=−√9=−3 t(0) = −√2·0+1=−√1=−1 t(−1) = −2(−1)+1=−√−1; 2 4 1 3 5 20. p2−10 22. a2−b b ⫺5⫺3⫺1135 ⫺1 x y ⫺4⫺224 ⫺4 ⫺2 2 […]

Chapter 10 Summary and Review: Study Guide 281 104. 6x=−12 106. (4.1×10−2)(6.5×106)=26.65 ×104 =(2.665 ×10) ×104 =2.665 ×105 108. 1 1−i 10 −1−i 10 2=1 1−i 10 −−2i 100 = 1 1−i 10 +i 50 =1 1−i 10 +i 50 […]

Chapter 11 Summary and Review: Discussion and Writing Exercises 329 35. a) We look for a function of the form N(x)=ax2+ bx +cwhere N(x) represents the number of live births per 1000 women and xrepresents the age of 36. x2−10x+25=0 […]

Chapter 11 Quadratic Equations and Functions Exercise Set 11.1 2. a) 5×2=35 x2=7 x=±√7 b) (−√7,0), (√7,0) 4. a) 36×2+49 =0 36×2=−49 x2=−49 36 x=±7 6i b) The equation 36×2+ 49 = 0 has no real-number solutions, so f(x)=36×2+ 49 […]

Exercise Set 11.7 315 b) The solutions of x2 8+x 4−3 8= 1 are the first coor- dinates of the points of intersection of the graph of f(x)=x2 8+x 4−3 8and y= 2. From the graph we see that they […]

y 6 5 7 8 9 x ⫺4⫺224 ⫺3⫺113 ⫺1 0 1 1 3 2 9 x ⫺4⫺224 2 ⫺3⫺113 ⫺1 1 3 f(x) 6x 2 4 6 3 5 7 8 9 f(x)  6x4 y 4 6 5 […]

x f ⴚ1 (x) ⴝ 兹 苵苵苵 苵苵苵 3 x ⴚ 1 y x f(x) ⴝ 3 x ⴚ 1 1. Replace g(x)byy:y=2x−3 7 2. Interchange xand y:x=2y−3 7 3. Solve for y:7x=2y−3 7x+3=2y 7x+3 2=y 4. Replace yby g−1(x): […]

Chapter 2 Solving Equations and Inequalities Exercise Set 2.1 6. 8y=−72 8(−9)?−72 −72  TRUE −9 is a solution. y=10 12 +9 12 y=19 8. y 8=6 49 8?6   61 8    FALSE 49 is not […]

Chapter 2 Summary and Review: Review Exercises 33 18. 4(x+3)=36 19. 3(5x−7) = −66 15x−21 = −66 15x−21+21=−66 + 21 15x=−45 y≥− 2 The solution set is yy≥− 1 2. 15x 15 =−45 15 x=−3 The solution is −3. 9x […]

⫺5 ⫺4⫺224 ⫺4 ⫺2 2 ⫺5⫺3⫺1135 ⫺5 ⫺3 ⫺1 1 x 5·0−3·5?15 −15  FALSE No 4 3 5 y 18. IV 20. I 22. III or IV 24. II or IV 26. A: (4,1), B: (0,−5),C: (−4,0),D: (−3,−2),E: (3,0) […]

y y x 2 2 4 4 2 442 x  2 of A are (−5,−1). 5. Point B is 2 units left and 5 units up. The coordinates of B are (−2,5). 6. Point C is 3 units right […]

88 Chapter 4: Polynomials: Operations 26. x−3 x−3×2−6x+9 28. x+4 x+4 x2+8x−16 x2+4x 4x−16 4x+16 −32 The answer is x+4+ −32 x+4. y3+3y2 −5y−15 −5y−15 0 The answer is y2−5. 30. x+7 x−2×2+5x−9 x2−2x 7x−9 7x−14 5 The answer is […]

Chapter 4 Polynomials: Operations Exercise Set 4.1 2. 4·4·4 4. (87.2)(87.2)(87.2)(87.2)(87.2)(87.2) 6. −5 8−5 8−5 8 8. (11c)(11c)(11c) 64. 37 66. 737 68. y10 10. 17 ·x·x 12. −1·q·q·q·q·q 14. 1 16. c 18. 1 72. (2t)25 74. 8x 76. […]

9 ft 12 ft 24 ft To find w, solve: 92+12 2=w2 w=−15 or w =15 2. A factor of a polynomial Pis a polynomial that can be used to express Pas a product. 3. A factorization of a polynomial […]

Chapter 5 Polynomials: Factoring Exercise Set 5.1 75 = 3 ·5·5 Each number has a factor of 3 and a factor of 5. The GCF is 3 ·5, or 15. −x7y5=−1·x7·y5 x4y4=x4·y4 4. 90 = 2 ·3·3·5 135 = 3 […]

Chapter 6 Rational Expressions and Equations Exercise Set 6.1 common. 2. −8y=0 y=0 The expression is not defined for 0. 36. t2−1 t+1 =(t+ 1)✏(t−1) t+1✏=t−1 4. y+6=0 y=−6 The expression is not defined for −6. 38. m2+9 m+3 cannot […]

Exercise Set 6.9 153 26. V=k P 28. P=k W 440 = k 2.4 1056 = k p=1056 W 275 = 1056 W W=1056 275 =3.84 ft W=1 5d3 W=1 5·83 W=512 5,or 1022 5lb 42. d=kr2 30. y=kx2 6=k·32 […]

4 5 y Chapter 7 Graphs, Functions, and Applications Exercise Set 7.1 RC2. f(0) = 3 RC4. f(3) = 0 2. Yes; each member of the domain is matched to only one member of the range. d) f(10) = 3 […]

y We find some ordered pairs that are solutions, using mul- tiples of 2 to avoid fractions. Then we plot these points and draw and label the line. When x=0,y=5 2·0−3=0−3=−3. When x=2,y=5 2·2−3=5−3=2. When x=4,y=5 2·4−3=10−3=7. x y (x, […]

x y 1—1—3 3254—2—4—5 —1 1 2 3 4 5 x + y = 5 (4, 1) —3 —4 —5 Consistent; independent x y 1—1—33254—2—4—5 —1 —2 —3 —4 —5 x – 2 y = 4 x 1—1—33254—2—4—5 —1 1 […]

y 4 5 x + y = 3 1. Graph both lines on the same set of axes. 2(−2) + 3y= 5 Using Equation (1) −4+3y=5 3y=9 y=3 The solution is (−2,3). 2 3 x + 3 y = 1 […]

Chapter 9 Summary and Review: Study Guide 253 Find the vertices as follows: System of equations Vertex From (1) and (4) (2,3) From (1) and (5) (5,6) From (2) and (4) (2,5) From (2) and (5) (5,8) belonging to A […]

60 {y|y<6},or(−∞,6) y≥−0.7 {y|y≥−0.7},or[−0.7,∞) 0⫺10⫺20 RC2. (h) RC4. (a) {a|a≤−20},or(−∞,−20] 100 25 −5: 3(−5)+5≤−10, or −10 ≤−10 is true. −5 is a solution. −10 : 3(−10) + 5 ≤−10, or −25 ≤−10 is true. −10 is a solution. x≤25 {x|x≤25},or(−∞,25] […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all the factors of the number. 1) 30 A) 1, 2, 3, 5, 6, 10, 20, 30 B) 1, 2, 3, 5, […]

125) 7x + 4y – z =50 x – 2y + 6z =47 5x + y + z =40 A) (5, -6, -9) B) (6, 9, 6) C) (6, 4, 9) D) (5, 6, 9) 126) 6x – 2y + […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Substitute to find the value of the expression. 1) Traveling at r kilometers per hour for t hours, a driver will travel rt […]

180) 13 + (-14) +15 + (-19) +13 + (-8) A) -30 B) 0 C) -2 D) –82 181) 3.1 – (-16.1) – (-17.0) A) 4.0 B) -36.2 C) 36.2 D) -30.0 Answer: C 182) 1 4– – 5 16 […]

276) 52xy 39xy A) 4 3 B) 4xy 3 C) – 4 3 D) –4xy 3 277) 7xy 12xy A) 7x 12x B) 7 12 C) y 12y D) 1 12 Answer: B 278) 12yz 13z A) –y 8z B) […]

219) 947x x3 A) 947 x B) 947x x C) 423 x D) 9x 47 220) 34x 35y A) 100x 5y B) 3100y2 5y C) 3100y 5y D) 3500y2 5y Answer: B 221) 2 7–10 A) 14 + 2 10 […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the square roots. 1) 361 A) 21, –21 B) 19, –19 C) 20, –20 D) 38, –38 2) 1089 A) 34, –34 […]

126) 514p56q A) 520pq B) 584pq C) 520(p + q) D) 584(p + q) 127) 413 35 A) 7133·54 B) 12 134·53 C) 7134·53 D) 12 133·54 Answer: D 128) 3310 A) 532·103 B) 533·102 C) 633·102 D) 632·103 Answer: […]

C) D) 133) f(x) =– 3 8 (x + 2)2– 1 A) B) 21 Answer: D C) D) 134) f(x) =-3(x – 1)2+ 5 A) B) 22 Answer: A C) D) 135) f(x) =-3(x + 8)2+ 5 A) B) 23 […]

185) f(x) =4×2+ 12x + 7 A) -3 ±2 8, 0 , (0, -7) B) -3 ±1 2, 0 , (0, -7) C) -12 ±2 2, 0 , (0, 7) D) -3 ±2 2, 0 , (0, 7) 186) f(x) […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve. Give exact solutions. 1) y2=21 A) 21 B) ±21 C) 10.5 D) 441 2) x2=16 A) 8 B) ±5 C) 4 D) […]

44) {(-8, -5), (5, 8), (9, 9), (–9, -9)} A) B) C) D) Find an equation of the inverse of the relation. 45) y =6x + 5 A) x =5y + 6 B) y =5x + 6 C) y =-6x […]

Express as a single logarithm. 143) log 410 –log 4y A) log 4 10 y B) log 8 10 y C) log 4(10 – y) D) log 4 y 10 144) log ba–log bb A) log 2b a b B) […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Graph. 1) f(x) =3x A) B) C) D) Answer: B 1 2) f(x) =1 2 x A) B) C) D) Answer: A 2 […]

C) D) 200) f(x) =3e-0.5x A) B) 53 Answer: B C) D) 201) f(x) = ln(x – 1) A) B) 54 Answer: C C) D) 202) f(x) =5ln x A) B) 55 Answer: A C) D) 203) f(x) = ln […]

157) Sarah left a 15% tip of $10.20 for a meal. What was the cost of the meal before the tip? A) $78.20 B) $20.40 C) $68.00 D) $1.53 158) Andy left a 15% tip for a meal that cost […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide if the given number is a solution to the given equation. 1) 5x =40; 7 A) No B) Yes 2) x 5=9; […]

A) B) C) D) 83) -3y = – 10 38 Answer: D A) B) C) D) 84) -4x =-9 39 Answer: C A) B) C) D) 85) 6x – 13 = 0 40 Answer: D A) B) C) D) Write […]

Exam Name___________________________________ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Plot the ordered pairs on the rectangular coordinate system provided. 1) A(2, 4), B(-3, 4) Answer: 1 2) A(4, -3), B(-6, 4) […]

45) y = 1 8x + 3 8 A) B) C) D) Answer: B 21 46) y =-6x A) B) C) D) Answer: B 22 47) 2x – y = 0 A) B) C) D) Answer: D 23 48) 6x […]

143) The height H (in feet) of a ball thrown into the air from the top of a building after t seconds is given by H = – 16t2+62t +209. Use the graph below to estimate the height of the […]

Draw and label rectangles to illustrate the given product. 259) x(x + 3) A) B) C) D) Answer: D 40 260) (2x + 5)(2x + 5) A) B) C) D) Multiply. 261) (x2– x +9)(x +4) A) x3+36 B) x3+5×2+13x […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. What is the meaning of the expression? 1) 52 A) 5·5 B) 2 ·5 C) 3 D) 7 2) 152 A) 15 ·15 […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the GCF. 1) 6×6, -24×3 A) 6×6 B) 2×3 C) 6×3 D) -24×6 2) –x2, –5x, –15×5 A) –5×2 B) –x2 C) […]

155) 15×2+ 16x + 4 A) (3x + 2)(5x + 2) B) (15x + 1)(x + 4) C) (3x – 2)(5x – 2) D) (15x + 2)(x + 2) 156) 75×3+ 70×2– 40x A) 5(5×2– 2)(3x + 4) B) x(5x […]

117) 4+2 x x 4+1 8 A) x 16 B) 16 C) 16 x D) 1 118) 5+1 3 4–2 27 A) 216 53 B) 144 53 C) 72 53 D) 108 53 Answer: C 119) 1 7–1 y 7– […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all numbers for which the rational expression is not defined. 1) 2 a – 5 A) None B) a = 0 C) […]

56) Find the range. A) {x|2  x 5} B) {2, 3, 4, 5} C) {–5, –3, –1, 1, 3} D) {x|–5 x 3} The graph of a function f is provided. Determine the requested function value. 57) f(–2) A) […]

A) B) C) D) 117) 17x =-17 52 Answer: C A) B) C) D) 118) 2 · f(x) +2x =2+2x 53 Answer: B A) B) C) D) If possible, determine the slope. 119) x =3 A) Not defined B) 1 […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Is the following correspondence a function? 1) A) Yes B) No 2) A) No B) Yes Answer: B 3) A) No B) Yes […]

A) B) C) D) 106) f(x) = – 1 4x +2 41 Answer: A A) B) C) D) 107) x –3y =9 42 Answer: A A) B) C) D) 108) 7x +5y =35 43 Answer: C A) B) C) D) […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve graphically. 1) 3x + y =-6 2x + 4y =6 A) (-3, 3) B) (-1, -3) C) (-3, -4) D) (3, 3) […]

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Choose the number that is a solution of the inequality. 1) a – 5 <-15 A) 11 B) -6 C) -11 D) -8 […]

192) 4x –7y >-5 A) B) C) D) 193) 3–3x > y 40 Answer: C A) B) C) D) 194) –7x <3–6y 41 Answer: B A) B) C) D) Answer: C 42 Graph the system of inequalities, and find the […]

134) 7x + 2 =7 A) 5 2, – 9 2 B) –5 7, 9 7 C) 5 7, – 9 7 D)  135) x+8=17 A) {–17, 17} B) {9} C) {–9, 9} D) {–17} Answer: C 136) 9x […]