 1.1.1.1: The fact that 2(x + 3) = 2x + 6 is because of the ______ Property. ...
 1.1.6.1: 121 = ____. (p. 19)
 1.1.4.1: True or False The principal square root of any nonnegative real num...
 1.1.2.1: Factor: x2 5x  6 (pp. 4955)
 1.1.7.1: The process of using variables to represent unknown quantities and ...
 1.1.5.1: Graph the inequality: x :2:: 2. (pp. 1 719)
 1.1: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.1: Name the integers and the rational numbers in the set  3, 0, v2, ...
 1.1.1.2: The fact that 3x = 0 implies that x = 0 is a result of the ____ Pro...
 1.1.6.2: True or False Ixl 0 for any real number x. (p. 19)
 1.1.4.2: v8 = _____. (pp. 7276)
 1.1.2.2: Factor: 2x2 x 3 (pp. 4955)
 1.1.7.2: The money paid for the use of money is _____.
 1.1.5.2: True or False 5 > 3 (pp. 1 719)
 1.2: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.2: True or False Rational numbers and irrational numbers are in the se...
 1.1.1.3: The domain of the variable in the expression x x  4 is ____. .(p.21)
 1.1.6.3: The solution set of the equation Ixl == 5 is { ____ }.
 1.1.4.3: Factor 6x3  2X2 (pp. 4955)
 1.1.2.3: The solution set of the equation (x 3)(3x + 5) = 0 is _____. (p. 13)
 1.1.7.3: Objects that move at a constant velocity are said to be in ______.
 1.1.5.3: If each side of an inequality is multiplied by a(n) ______ number, ...
 1.3: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.3: Rationalize the denominator of 3  2+ V3 (p. 74 )
 1.1.3.4: In the complex number 5 + 2i, the number 5 is called the _______ pa...
 1.1.1.4: True or False Multiplying both sides of an equation by any number r...
 1.1.6.4: The solution set of the inequality Ixl < 5 is {xl }.
 1.1.4.4: When an apparent solution does not satisfy the original equation, i...
 1.1.2.4: True or False = Ixl. (pp. 2324)
 1.1.7.4: True or False The amount charged for the use of principal for a giv...
 1.1.5.4: A( n) _____ _____, denoted [a, b], consists of all real numbers x f...
 1.4: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.5: The equation x2 = 4 has the solution set ___ _
 1.1.1.5: An equation that is satisfied for every value of the variable for w...
 1.1.6.5: True or False The equation Ixl == 2 has no solution.
 1.1.4.5: If u is an expression involving x, the equation au2 + bu + = c 0, a...
 1.1.2.5: To complete the square of the expression x2 + 5x, you would_____the...
 1.1.7.5: True or False If an object moves at an average velocity v, the dist...
 1.1.5.5: The _____ _____ state that the sense, or direction, of an inequalit...
 1.5: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.6: True or False The conjugate of 2 + 5i is 2  5i.
 1.1.1.6: An equation of the form ax + b = 0 is called a(n) equation _____ or...
 1.1.6.6: True or False The inequality Ixl 2 has the set of real numbers as ...
 1.1.4.6: True or False Radical equations sometimes have extraneous solutions.
 1.1.2.6: The quantity b2  4ac is called the_____of a quadratic equation. If...
 1.1.7.6: Suppose that you want to mix two coffees in order to obtain 100 pou...
 1.1.5.6: In 69, assume that a < b and c < o. Tl'ue 01' False a + c < b + c
 1.6: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.7: True or False All real numbers are complex numbers
 1.1.1.7: True or False The solution of the equation 3x  8 = 0 . 3 IS S .
 1.1.6.7: In 734, solve each equation. 12xl = 6
 1.1.4.7: In 740, find the real solutions of each equation. V2t=1 = 1
 1.1.2.7: True or False Quadratic equations always have two real solutions.
 1.1.7.7: In 716, translate each sentence into a mathematical equation. Be s...
 1.1.5.7: In 69, assume that a < b and c < o. Tl'Ue or False ac< bc
 1.7: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.8: True or False If 2 3i is a solution of a quadratic equation with r...
 1.1.1.8: True or False Some equations have no solution.
 1.1.6.8: In 734, solve each equation. 13xl = 12
 1.1.4.8: In 740, find the real solutions of each equation. v3t+4 = 2
 1.1.2.8: True or False If the discriminant of a quadratic equation is positi...
 1.1.7.8: In 716, translate each sentence into a mathematical equation. Be s...
 1.1.5.8: In 69, assume that a < b and c < o. Tl'Ue 01' False ac > bc
 1.8: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.9: In 946, write each expression in the standard form a + bi. (2 3i)...
 1.1.1.9: In 916, mentally solve each equation. 7 x = 21
 1.1.6.9: In 734, solve each equation. 2x + 31 = 5
 1.1.4.9: In 740, find the real solutions of each equation. v3t+4 =6
 1.1.2.9: In 928, solve each equation by factoring. x2 9x = 0
 1.1.7.9: In 716, translate each sentence into a mathematical equation. Be s...
 1.1.5.9: In 69, assume that a < b and c < o. True or False a b <C C
 1.9: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.10: In 946, write each expression in the standard form a + bi. (4 + 5i...
 1.1.1.10: In 916, mentally solve each equation. 6x = 24
 1.1.6.10: In 734, solve each equation. 13x  11 = 2
 1.1.4.10: In 740, find the real solutions of each equation. v5t+3 = 2
 1.1.2.10: In 928, solve each equation by factoring. x2 + 4x = 0
 1.1.7.10: In 716, translate each sentence into a mathematical equation. Be s...
 1.1.5.10: True or False The square of any real number is always nonnegative.
 1.10: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.11: In 946, write each expression in the standard form a + bi. (3 + 2...
 1.1.1.11: In 916, mentally solve each equation. 3x + 15 = 0
 1.1.6.11: In 734, solve each equation. 11  4tl + S = 1
 1.1.4.11: In 740, find the real solutions of each equation. VI  2x  3 =
 1.1.2.11: In 928, solve each equation by factoring. x225=O
 1.1.7.11: In 716, translate each sentence into a mathematical equation. Be s...
 1.1.5.11: In II16, express the graph shown in blue using interval notation. ...
 1.11: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.12: In 946, write each expression in the standard form a + bi. (3 4 i...
 1.1.1.12: In 916, mentally solve each equation. 6x + 18 = 0
 1.1.6.12: In 734, solve each equation. 11  2z1 + 6 = 9
 1.1.4.12: In 740, find the real solutions of each equation.  1 =
 1.1.2.12: In 928, solve each equation by factoring. x2  9 = 0
 1.1.7.12: In 716, translate each sentence into a mathematical equation. Be s...
 1.1.5.12: In II16, express the graph shown in blue using interval notation. ...
 1.12: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.13: In 946, write each expression in the standard form a + bi. (2  5i...
 1.1.1.13: In 916, mentally solve each equation. 2X  3 = 0
 1.1.6.13: In 734, solve each equation. 12xl = lsi
 1.1.4.13: In 740, find the real solutions of each equation. =2
 1.1.2.13: In 928, solve each equation by factoring. Z2 + Z  6 = 0
 1.1.7.13: In 716, translate each sentence into a mathematical equation. Be s...
 1.1.5.13: In II16, express the graph shown in blue using interval notation. ...
 1.13: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.14: In 946, write each expression in the standard form a + bi. ( 8 + ...
 1.1.1.14: In 916, mentally solve each equation. 3x + 4 = 0
 1.1.6.14: In 734, solve each equation. Ixl = 111
 1.1.4.14: In 740, find the real solutions of each equation. 2x = 3 1
 1.1.2.14: In 928, solve each equation by factoring. v2 + 7v + 6 = 0
 1.1.7.14: In 716, translate each sentence into a mathematical equation. Be s...
 1.1.5.14: In II16, express the graph shown in blue using interval notation. ...
 1.14: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.15: In 946, write each expression in the standard form a + bi. 3 (2  6i)
 1.1.1.15: In 916, mentally solve each equation. 1x = 5
 1.1.6.15: In 734, solve each equation. 121x = 4
 1.1.4.15: In 740, find the real solutions of each equation. x2 + 2x = 1
 1.1.2.15: In 928, solve each equation by factoring. 2x2  5x 3 = 0
 1.1.7.15: In 716, translate each sentence into a mathematical equation. Be s...
 1.1.5.15: In II16, express the graph shown in blue using interval notation. ...
 1.15: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.16: In 946, write each expression in the standard form a + bi. 4(2 + 8i)
 1.1.1.16: In 916, mentally solve each equation. 2 9 x =  3 2
 1.1.6.16: In 734, solve each equation. 131x = 9
 1.1.4.16: In 740, find the real solutions of each equation. \Yx2 + 16 = V
 1.1.2.16: In 928, solve each equation by factoring. 3x2 + 5x + 2 = 0
 1.1.7.16: In 716, translate each sentence into a mathematical equation. Be s...
 1.1.5.16: In II16, express the graph shown in blue using interval notation. ...
 1.16: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.17: In 946, write each expression in the standard form a + bi. 2i(2  3i)
 1.1.1.17: In 1764, solve each equation. 3x + 4 = x
 1.1.6.17: In 734, solve each equation. 3" lxl = 9
 1.1.4.17: In 740, find the real solutions of each equation. = x 8v
 1.1.2.17: In 928, solve each equation by factoring. 3t 2  48 = 0
 1.1.7.17: Financial Planning Betsy, a recent retiree, requires $6000 per year...
 1.1.5.17: In 1722, an inequality is given. Write the inequality obtained by:...
 1.17: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.18: In 946, write each expression in the standard form a + bi. 3i( 3 ...
 1.1.1.18: In 1764, solve each equation. 2x + 9 = 5x
 1.1.6.18: In 734, solve each equation. 41xl = 9
 1.1.4.18: In 740, find the real solutions of each equation. x 3vX
 1.1.2.18: In 928, solve each equation by factoring. 2/  50 = 0
 1.1.7.18: Financial Planning After 2 years, Betsy (see 17) finds that she wil...
 1.1.5.18: In 1722, an inequality is given. Write the inequality obtained by:...
 1.18: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.19: In 946, write each expression in the standard form a + bi. (3  4i...
 1.1.1.19: In 1764, solve each equation. 2t  6 = 3  t
 1.1.6.19: In 734, solve each equation. + I = 2
 1.1.4.19: In 740, find the real solutions of each equation. VIS  2x = x
 1.1.2.19: In 928, solve each equation by factoring. x(x  8) + 12 = 0
 1.1.7.19: Banking A bank loaned out $12,000, part of it at the rate of 8% per...
 1.1.5.19: In 1722, an inequality is given. Write the inequality obtained by:...
 1.19: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.20: In 946, write each expression in the standard form a + bi. (5 + 3i...
 1.1.1.20: In 1764, solve each equation. 5 Y + 6 = 18  Y
 1.1.6.20: In 734, solve each equation. I  I = 1
 1.1.4.20: In 740, find the real solutions of each equation. =x
 1.1.2.20: In 928, solve each equation by factoring. x(x + 4) = 12
 1.1.7.20: Banking Wendy, a loan officer at a bank, has $1,000,000 to lend and...
 1.1.5.20: In 1722, an inequality is given. Write the inequality obtained by:...
 1.20: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.21: In 946, write each expression in the standard form a + bi. ( 6 + ...
 1.1.1.21: In 1764, solve each equation. 6  x = 2x + 9
 1.1.6.21: In 734, solve each equation. u  21 =  2
 1.1.4.21: In 740, find the real solutions of each equation. X = 2
 1.1.2.21: In 928, solve each equation by factoring. 4x2 + 9 = 12 x
 1.1.7.21: Blending Teas The manager of a store that specializes in selling te...
 1.1.5.21: In 1722, an inequality is given. Write the inequality obtained by:...
 1.21: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.22: In 946, write each expression in the standard form a + bi. ( 3 + ...
 1.1.1.22: In 1764, solve each equation. 3  2x = 2  x
 1.1.6.22: In 734, solve each equation. 2  vi = 1
 1.1.4.22: In 740, find the real solutions of each equation. x 2V x  1
 1.1.2.22: In 928, solve each equation by factoring. 2 5x2 + 16 = 40x
 1.1.7.22: Business: Blending Coffee A coffee manufacturer wants to market a n...
 1.1.5.22: In 1722, an inequality is given. Write the inequality obtained by:...
 1.22: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.23: In 946, write each expression in the standard form a + bi. O4
 1.1.1.23: In 1764, solve each equation. 3 + 2n = 4n + 7
 1.1.6.23: In 734, solve each equation. 4  12xl = 3
 1.1.4.23: In 740, find the real solutions of each equation. yx2  X  4 = x + 2
 1.1.2.23: In 928, solve each equation by factoring. 6(p2  1) = 5p
 1.1.7.23: Business: Mixing Nuts A nut store normally sells cashews for $9.00 ...
 1.1.5.23: In 2330, write each inequality using interval notation, and illust...
 1.23: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.24: In 946, write each expression in the standard form a + bi. 13_5  12i
 1.1.1.24: In 1764, solve each equation. 6  2m = 3m + 1
 1.1.6.24: In 734, solve each equation. 5  IXI =3
 1.1.4.24: In 740, find the real solutions of each equation. Y 3  x + = X  2
 1.1.2.24: In 928, solve each equation by factoring. 2(2u2  4u) + 3 = 0
 1.1.7.24: Business: Mixing Candy A candy store sells boxes of candy containin...
 1.1.5.24: In 2330, write each inequality using interval notation, and illust...
 1.24: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.25: In 946, write each expression in the standard form a + bi. 2 7 i
 1.1.1.25: In 1764, solve each equation. 2(3 + 2x) = 3(x  4)
 1.1.6.25: In 734, solve each equation. x2  91 = 0
 1.1.4.25: In 740, find the real solutions of each equation. 3+=X
 1.1.2.25: In 928, solve each equation by factoring. 6x  5 = ..f'\x
 1.1.7.25: Physics: Uniform Motion A motorboat can maintain a constant speed o...
 1.1.5.25: In 2330, write each inequality using interval notation, and illust...
 1.25: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.26: In 946, write each expression in the standard form a + bi. 2__i1\...
 1.1.1.26: In 1764, solve each equation. 3(2  x) = 2x  1
 1.1.6.26: In 734, solve each equation. Ix2  161 = 0
 1.1.4.26: In 740, find the real solutions of each equation. 2 + V 12  2x = x
 1.1.2.26: In 928, solve each equation by factoring. x +  = 7x
 1.1.7.26: Physics: Uniform Motion A motorboat heads upstream on a river that ...
 1.1.5.26: In 2330, write each inequality using interval notation, and illust...
 1.26: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.27: In 946, write each expression in the standard form a + bi. l + i
 1.1.1.27: In 1764, solve each equation. 8x  (3x + 2) = 3x  10
 1.1.6.27: In 734, solve each equation. x2  2xl = 3
 1.1.4.27: In 740, find the real solutions of each equation. Vx+l= 1
 1.1.2.27: In 928, solve each equation by factoring. 4(x 2) 3 3 +  = x ...
 1.1.7.27: Physics: Uniform Motion A motorboat maintained a constant speed of ...
 1.1.5.27: In 2330, write each inequality using interval notation, and illust...
 1.27: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.28: In 946, write each expression in the standard form a + bi. 2 + 3i1...
 1.1.1.28: In 1764, solve each equation. 7  (2x  1) = 10
 1.1.6.28: In 734, solve each equation. x2 + xl = 12
 1.1.4.28: In 740, find the real solutions of each equation. + Vx+2=1
 1.1.2.28: In 928, solve each equation by factoring. 5 3 x+4 = 4 +x  2
 1.1.7.28: Physics: Uniform Motion Two cars enter the Florida Turnpike at Comm...
 1.1.5.28: In 2330, write each inequality using interval notation, and illust...
 1.28: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.29: In 946, write each expression in the standard form a + bi. G + iy
 1.1.1.29: In 1764, solve each equation. 3x+2 = 1 1 x
 1.1.6.29: In 734, solve each equation. Ix2 + xII = 1
 1.1.4.29: In 740, find the real solutions of each equation.  = 2
 1.1.2.29: In Proble ms 2934, so lve each eq uation by the Sq uare Root Metho...
 1.1.7.29: Moving Walkways The speed of a moving walkway is typically about 2....
 1.1.5.29: In 2330, write each inequality using interval notation, and illust...
 1.29: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.30: In 946, write each expression in the standard form a + bi. (  iy
 1.1.1.30: In 1764, solve each equation. 1 2 "3x = 2 "3x
 1.1.6.30: In 734, solve each equation. x2 + 3x  21 = 2
 1.1.4.30: In 740, find the real solutions of each equation. V3x  5 Vx+7 = 2
 1.1.2.30: In Proble ms 2934, so lve each eq uation by the Sq uare Root Metho...
 1.1.7.30: Moving Walkways The Gare Montparnasse train station in Paris has a ...
 1.1.5.30: In 2330, write each inequality using interval notation, and illust...
 1.30: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.31: In 946, write each expression in the standard form a + bi. (1 + i) 2
 1.1.1.31: In 1764, solve each equation. 1x 5 = 3x
 1.1.6.31: In 734, solve each equation. 3X  2 1 = 2 2x  3
 1.1.4.31: In 740, find the real solutions of each equation. V3  2VX = V
 1.1.2.31: In Proble ms 2934, so lve each eq uation by the Sq uare Root Metho...
 1.1.7.31: Tennis Anyone'! A regulation doubles tennis court has an area of 28...
 1.1.5.31: In 3138, write each interval as an inequality involving x, and ill...
 1.31: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.32: In 946, write each expression in the standard form a + bi. (1  if
 1.1.1.32: In 1764, solve each equation. 1 1 2:x = 6
 1.1.6.32: In 734, solve each equation. 12x + 11 = 1 3x + 4
 1.1.4.32: In 740, find the real solutions of each equation. VlO + 3 VX = VX
 1.1.2.32: In Proble ms 2934, so lve each eq uation by the Sq uare Root Metho...
 1.1.7.32: Laser Printers It takes an HP LaserJet 1300 laser printer 10 minute...
 1.1.5.32: In 3138, write each interval as an inequality involving x, and ill...
 1.32: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.33: In 946, write each expression in the standard form a + bi. i23
 1.1.1.33: In 1764, solve each equation. 2p = 1p + 1
 1.1.6.33: In 734, solve each equation. Ix2 + 3xl = Ix2  2x
 1.1.4.33: In 740, find the real solutions of each equation. (3x + 1)1/2 = 4
 1.1.2.33: In Proble ms 2934, so lve each eq uation by the Sq uare Root Metho...
 1.1.7.33: Working Together on a Job Trent can deliver his newspapers in 30 mi...
 1.1.5.33: In 3138, write each interval as an inequality involving x, and ill...
 1.33: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.34: In 946, write each expression in the standard form a + bi. il4
 1.1.1.34: In 1764, solve each equation. 1 1 4  p = 2 3 3
 1.1.6.34: In 734, solve each equation. Ix2  2xl = Ix2 + 6xl
 1.1.4.34: In 740, find the real solutions of each equation. (3x  5)1/2 = 2
 1.1.2.34: In Proble ms 2934, so lve each eq uation by the Sq uare Root Metho...
 1.1.7.34: Working Together on a Job Patrice, by himself, can paint four rooms...
 1.1.5.34: In 3138, write each interval as an inequality involving x, and ill...
 1.34: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.35: In 946, write each expression in the standard form a + bi. i15
 1.1.1.35: In 1764, solve each equation. 0.9t = 0.4 + O.1t
 1.1.6.35: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.35: In 740, find the real solutions of each equation. (5x  2) 1/3 = 2
 1.1.2.35: In 3540, what number should be added to complete the square of eac...
 1.1.7.35: Enclosing a Garden A gardener has 46 feet of fencing to be used to ...
 1.1.5.35: In 3138, write each interval as an inequality involving x, and ill...
 1.35: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.36: In 946, write each expression in the standard form a + bi. i23
 1.1.1.36: In 1764, solve each equation. 0.9t = 1 + t
 1.1.6.36: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.36: In 740, find the real solutions of each equation. (2x + 1)1/3 = 1
 1.1.2.36: In 3540, what number should be added to complete the square of eac...
 1.1.7.36: Construction A pond is enclosed by a wooden deck that is 3 feet wid...
 1.1.5.36: In 3138, write each interval as an inequality involving x, and ill...
 1.36: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.37: In 946, write each expression in the standard form a + bi. i6  5
 1.1.1.37: In 1764, solve each equation. x ; 1+x ; 2 = 2
 1.1.6.37: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.37: In 740, find the real solutions of each equation. (x2 + 9) 1/2 = 5
 1.1.2.37: In 3540, what number should be added to complete the square of eac...
 1.1.7.37: Football A tight end can run the 100yard dash in 12 seconds. A def...
 1.1.5.37: In 3138, write each interval as an inequality involving x, and ill...
 1.37: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.38: In 946, write each expression in the standard form a + bi. 4 + i3
 1.1.1.38: In 1764, solve each equation. 2x + 1 3 + 16 = 3x
 1.1.6.38: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.38: In 740, find the real solutions of each equation. (x2  16) 1/2 = 9
 1.1.2.38: In 3540, what number should be added to complete the square of eac...
 1.1.7.38: Computing Business Expense Therese, an outside salesperson, uses he...
 1.1.5.38: In 3138, write each interval as an inequality involving x, and ill...
 1.38: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.39: In 946, write each expression in the standard form a + bi. 6i3  4i5
 1.1.1.39: In 1764, solve each equation. += 3
 1.1.6.39: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.39: In 740, find the real solutions of each equation. x3/2  3xl/2 = 0
 1.1.2.39: In 3540, what number should be added to complete the square of eac...
 1.1.7.39: Mixing Water and Antifreeze How much water should be added to 1 gal...
 1.1.5.39: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.39: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.40: In 946, write each expression in the standard form a + bi. 4i3  2...
 1.1.1.40: In 1764, solve each equation. 4 5 5 =  y 2y
 1.1.6.40: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.40: In 740, find the real solutions of each equation. X3/4  9xl/4 = 0
 1.1.2.40: In 3540, what number should be added to complete the square of eac...
 1.1.7.40: Mixing Water and Antifreeze The cooling system of a certain foreign...
 1.1.5.40: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.40: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.41: In 946, write each expression in the standard form a + bi. (1 + i)3
 1.1.1.41: In 1764, solve each equation. 1 + 2 = 3
 1.1.6.41: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.41: In 4172, find the real solutions of each equation. x4  5x2 + 4 = 0
 1.1.2.41: In Proble ms 4146, solve each eq uatio n by co mpleti ng the sq ua...
 1.1.7.41: Chemistry: Salt Solutions How much water must be evaporated from 32...
 1.1.5.41: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.41: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.42: In 946, write each expression in the standard form a + bi. (3i)4 + 1
 1.1.1.42: In 1764, solve each equation. 311    =  x 3 6
 1.1.6.42: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.42: In 4172, find the real solutions of each equation. X4  10x2 + 25 = 0
 1.1.2.42: In Proble ms 4146, solve each eq uatio n by co mpleti ng the sq ua...
 1.1.7.42: Chemistry: Salt Solutions How much water must be evaporated from 24...
 1.1.5.42: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.42: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.43: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.43: In 946, write each expression in the standard form a + bi. i7 (1 +...
 1.1.1.43: In 1764, solve each equation. (x + 7)(x  1) = (x + 1)2
 1.1.6.43: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.43: In 4172, find the real solutions of each equation. 3x4  2x2  1 = 0
 1.1.2.43: In Proble ms 4146, solve each eq uatio n by co mpleti ng the sq ua...
 1.1.7.43: Purity of Gold The purity of gold is measured in karats, with pure ...
 1.1.5.43: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.44: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.44: In 946, write each expression in the standard form a + bi. 2i4(1 +...
 1.1.1.44: In 1764, solve each equation. (x + 2)(x  3) = (x + 3)2
 1.1.6.44: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.44: In 4172, find the real solutions of each equation. 2 X4  5x2  12...
 1.1.2.44: In Proble ms 4146, solve each eq uatio n by co mpleti ng the sq ua...
 1.1.7.44: Chemistry: Sugar Molecules A sugar molecule has twice as many atoms...
 1.1.5.44: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.45: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.45: In 946, write each expression in the standard form a + bi. i6 + i4...
 1.1.1.45: In 1764, solve each equation. x(2x 3) = (2x + 1)(x 4)
 1.1.6.45: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.45: In 4172, find the real solutions of each equation. x6 + 7 x3  8 = 0
 1.1.2.45: In Proble ms 4146, solve each eq uatio n by co mpleti ng the sq ua...
 1.1.7.45: Running a Race Mike can run the mile in 6 minutes, and Dan can run ...
 1.1.5.45: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.46: In 146, find all the real solution5; if any, of each equation. (Wh...
 1.1.3.46: In 946, write each expression in the standard form a + bi. P + i5 ...
 1.1.1.46: In 1764, solve each equation. x(1 + 2x) = (2x 1)(x 2)
 1.1.6.46: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.46: In 4172, find the real solutions of each equation. x6  7x3  8 = 0
 1.1.2.46: In Proble ms 4146, solve each eq uatio n by co mpleti ng the sq ua...
 1.1.7.46: Range of an Airplane An air rescue plane averages 300 miles per hou...
 1.1.5.46: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.47: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.47: In 4752, perform the indicated operations and express your answer ...
 1.1.1.47: In 1764, solve each equation. Z (Z2 + 1) = 3 + Z3
 1.1.6.47: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.47: In 4172, find the real solutions of each equation. x + 2)2 + 7(x +...
 1.1.2.47: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.47: Emptying Oil Tankers An oil tanker can be emptied by the main pump ...
 1.1.5.47: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.48: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.48: In 4752, perform the indicated operations and express your answer ...
 1.1.1.48: In 1764, solve each equation. w (4w2) = 8  w3
 1.1.6.48: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.48: In 4172, find the real solutions of each equation. (2x + 5)2  (2x...
 1.1.2.48: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.48: Cement Mix A 20pound bag of Economy brand cement mix contains 25% ...
 1.1.5.48: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.49: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.49: In 4752, perform the indicated operations and express your answer ...
 1.1.1.49: In 1764, solve each equation. x 2. . x2 +3=x2
 1.1.6.49: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.49: In 4172, find the real solutions of each equation. (3x + 4f  6(3x...
 1.1.2.49: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.49: Emptying a Tub A bathroom tub will fill in 15 minutes with both fau...
 1.1.5.49: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.50: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.50: In 4752, perform the indicated operations and express your answer ...
 1.1.1.50: In 1764, solve each equation. 2x 6 =2 x+3 x+3
 1.1.6.50: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.50: In 4172, find the real solutions of each equation. (2  x)2 + (2 ...
 1.1.2.50: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.50: Using Two Pumps A 5horsepower (hp) pump can empty a pool in 5 hour...
 1.1.5.50: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.51: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.51: In 4752, perform the indicated operations and express your answer ...
 1.1.1.51: In 1764, solve each equation. 2x 4 3., x2 4 x2 4x + 2
 1.1.6.51: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.51: In 4172, find the real solutions of each equation. 2(s + If  5(s ...
 1.1.2.51: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.51: A Biathlon Suppose that you have entered an 87mile biathlon that c...
 1.1.5.51: In 3952, fill in the blank with the correct inequality symbol. It ...
 1.52: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.52: In 4752, perform the indicated operations and express your answer ...
 1.1.1.52: In 1764, solve each equation. x 4 3 + = ? x29 x+3 r9
 1.1.6.52: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.52: In 4172, find the real solutions of each equation. 3(1  y)2 + 5(1...
 1.1.2.52: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.52: Cyclists Two cyclists leave a city at the same time, one going east...
 1.1.5.52: In 3952, fill in the blank with the correct inequality symbol. If ...
 1.53: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.53: In 5372, solve each equation in the complex number system . x2 + 4...
 1.1.1.53: In 1764, solve each equation. x = 3  x + 2
 1.1.6.53: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.53: In 4172, find the real solutions of each equation. x  4xVX = 0
 1.1.2.53: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.53: COml Jaring Olympic Heroes In the 1984 Olympics, C. Lewis of the Un...
 1.1.5.53: In 5388, solve each inequality. Express your answer using set nota...
 1.54: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.54: In 5372, solve each equation in the complex number system . x2  4...
 1.1.1.54: In 1764, solve each equation. 3x = 2 xI
 1.1.6.54: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.54: In 4172, find the real solutions of each equation. x + 8VX = 0
 1.1.2.54: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.54: Constructing a Coffee Can A 39ounce can of Hills Bros. coffee requ...
 1.1.5.54: In 5388, solve each inequality. Express your answer using set nota...
 1.55: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.55: In 5372, solve each equation in the complex number system . x2  1...
 1.1.1.55: In 1764, solve each equation. 2x5_ 3 =x ! 5
 1.1.6.55: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.55: In 4172, find the real solutions of each equation. x + VX = 20
 1.1.2.55: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.55: Critical Thinking You are the manager of a clothing store and have ...
 1.1.5.55: In 5388, solve each inequality. Express your answer using set nota...
 1.56: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.56: In 5372, solve each equation in the complex number system . x2 + 2...
 1.1.1.56: In 1764, solve each equation. 4 3 =.x+4 x+6
 1.1.6.56: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.56: In 4172, find the real solutions of each equation. x + VX = 6
 1.1.2.56: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.56: Critical Thinking Make up a word problem that requires solving a li...
 1.1.5.56: In 5388, solve each inequality. Express your answer using set nota...
 1.57: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.57: In 5372, solve each equation in the complex number system . x2  6...
 1.1.1.57: In 1764, solve each equation. 6t + 7 3t + S\ 4t = 1 2t 4
 1.1.6.57: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.57: In 4172, find the real solutions of each equation. t l/2  2tl/4 +...
 1.1.2.57: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.57: Critical Thinking Without solving, explain what is wrong with the f...
 1.1.5.57: In 5388, solve each inequality. Express your answer using set nota...
 1.58: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.58: In 5372, solve each equation in the complex number system . x2 + 4...
 1.1.1.58: In 1764, solve each equation. Sw + 5 4w  3  lOw 7 5w + 7
 1.1.6.58: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.58: In 4172, find the real solutions of each equation. ZI/2  4ZI/4 + ...
 1.1.2.58: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.58: Computing Average Speed In going from Chicago to Atlanta, a car ave...
 1.1.5.58: In 5388, solve each inequality. Express your answer using set nota...
 1.59: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.59: In 5372, solve each equation in the complex number system . x2  6...
 1.1.1.59: In 1764, solve each equation. 4 3+ 7x2 x+5 (x+5)(x2)
 1.1.6.59: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.59: In 4172, find the real solutions of each equation. 4XI/2  9XI/4 +...
 1.1.2.59: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.7.59: Speed of a Plane On a recent flight from Phoenix to Kansas City, a ...
 1.1.5.59: In 5388, solve each inequality. Express your answer using set nota...
 1.60: In 4760, solve each inequality. Express your answer using set nota...
 1.1.3.60: In 5372, solve each equation in the complex number system . x2  2...
 1.1.1.60: In 1764, solve each equation. . +1=12x+3 xI (2x+3)(x1)
 1.1.6.60: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.60: In 4172, find the real solutions of each equation. XI/2  3xl/4 + ...
 1.1.2.60: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.60: In 5388, solve each inequality. Express your answer using set nota...
 1.61: In 6164, what number should be added to complete the square of eac...
 1.1.3.61: In 5372, solve each equation in the complex number system . 8x2  ...
 1.1.1.61: In 1764, solve each equation. 2 + 3 = 5 y+3 y4 y+6
 1.1.6.61: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.61: In 4172, find the real solutions of each equation. \Y 5x2  6 = x
 1.1.2.61: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.61: In 5388, solve each inequality. Express your answer using set nota...
 1.62: In 6164, what number should be added to complete the square of eac...
 1.1.3.62: In 5372, solve each equation in the complex number system . lOx2 +...
 1.1.1.62: In 1764, solve each equation. 5 4 3 5z 11+2z  3 5 z
 1.1.6.62: In 3562, solve each inequality. Express your answer using set nota...
 1.1.4.62: In 4172, find the real solutions of each equation. \y 4  5x2 = x
 1.1.2.62: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.62: In 5388, solve each inequality. Express your answer using set nota...
 1.63: In 6164, what number should be added to complete the square of eac...
 1.1.3.63: In 5372, solve each equation in the complex number system . 5x2 + ...
 1.1.1.63: In 1764, solve each equation. x x + 3 _ 3' x2 1x2  X x2 + X
 1.1.6.63: Body Temperature "Normal" human body temperature is 9S.6F. If a tem...
 1.1.4.63: In 4172, find the real solutions of each equation. x2 + 3x + Vx2 +...
 1.1.2.63: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.63: In 5388, solve each inequality. Express your answer using set nota...
 1.64: In 6164, what number should be added to complete the square of eac...
 1.1.3.64: In 5372, solve each equation in the complex number system . 13x2 +...
 1.1.1.64: In 1764, solve each equation. x+1 x+4 3 64. 2 X + 2x x2 + X x...
 1.1.6.64: Household Voltage In the United States, normal household voltage is...
 1.1.4.64: In 4172, find the real solutions of each equation. x2  3x  Vx2 ...
 1.1.2.64: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.64: In 5388, solve each inequality. Express your answer using set nota...
 1.65: In 6574, use the complex number system and write each expression i...
 1.1.3.65: In 5372, solve each equation in the complex number system . x2 + X...
 1.1.1.65: In 6568, use a calculator to solve each equation. Round the soluti...
 1.1.6.65: Reading Books A Gallup poll conducted May 2022, 2005, found that A...
 1.1.4.65: In 4172, find the real solutions of each equation. I? =1_ + 2(x + ...
 1.1.2.65: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.65: In 5388, solve each inequality. Express your answer using set nota...
 1.1.5.66: In 5388, solve each inequality. Express your answer using set nota...
 1.66: In 6574, use the complex number system and write each expression i...
 1.1.3.66: In 5372, solve each equation in the complex number system . x2  x...
 1.1.1.66: In 6568, use a calculator to solve each equation. Round the soluti...
 1.1.6.66: SI)eed of Sound According to data from the Hill Aerospace Museum (H...
 1.1.4.66: In 4172, find the real solutions of each equation. 1 2 +  = 12(x...
 1.1.2.66: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.67: In 5388, solve each inequality. Express your answer using set nota...
 1.67: In 6574, use the complex number system and write each expression i...
 1.1.3.67: In 5372, solve each equation in the complex number system . x3  8...
 1.1.1.67: In 6568, use a calculator to solve each equation. Round the soluti...
 1.1.6.67: Express the fact that x differs from 3 by less than as an inequalit...
 1.1.4.67: In 4172, find the real solutions of each equation. 3x2  7x1  6...
 1.1.2.67: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.68: In 5388, solve each inequality. Express your answer using set nota...
 1.68: In 6574, use the complex number system and write each expression i...
 1.1.3.68: In 5372, solve each equation in the complex number system . x3 + 2...
 1.1.1.68: In 6568, use a calculator to solve each equation. Round the soluti...
 1.1.6.68: Express the fact that x differs from 4 by less than 1 as an inequa...
 1.1.4.68: In 4172, find the real solutions of each equation. 2x2  3x1  4...
 1.1.2.68: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.69: In 5388, solve each inequality. Express your answer using set nota...
 1.69: In 6574, use the complex number system and write each expression i...
 1.1.3.69: In 5372, solve each equation in the complex number system . X4 = 16
 1.1.1.69: In 6974, solve each equation. The letters a, b, and c are constant...
 1.1.6.69: In 7176, find a and b. If Ix  11 < 3, then a < x + 4 < b.
 1.1.4.69: In 4172, find the real solutions of each equation. 2x2/3  5xl/3 ...
 1.1.2.69: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.70: In 5388, solve each inequality. Express your answer using set nota...
 1.70: In 6574, use the complex number system and write each expression i...
 1.1.3.70: In 5372, solve each equation in the complex number system . X4 = 1
 1.1.1.70: In 6974, solve each equation. The letters a, b, and c are constant...
 1.1.6.70: In 7176, find a and b. If Ix + 21 < 5, then a < x  2 < b
 1.1.4.70: In 4172, find the real solutions of each equation. 3x4/3 + 5x2/3 ...
 1.1.2.70: In 4770, find the real solutions, if any, of each equation. Use th...
 1.1.5.71: In 5388, solve each inequality. Express your answer using set nota...
 1.71: In 6574, use the complex number system and write each expression i...
 1.1.3.71: In 5372, solve each equation in the complex number system . X4 + 1...
 1.1.1.71: In 6974, solve each equation. The letters a, b, and c are constant...
 1.1.6.71: In 7176, find a and b. If Ix + 41 ::; 2, then a ::; 2x  3 ::; b.
 1.1.4.71: In 4172, find the real solutions of each equation. V)2 2v  += ...
 1.1.2.71: In 7178, find the real solutions, if any, of each equatio n. Use t...
 1.1.5.72: In 5388, solve each inequality. Express your answer using set nota...
 1.72: In 6574, use the complex number system and write each expression i...
 1.1.3.72: In 5372, solve each equation in the complex number system . X4 + 3...
 1.1.1.72: In 6974, solve each equation. The letters a, b, and c are constant...
 1.1.6.72: In 7176, find a and b. If Ix  31 ::; 1, then a ::; 3x + 1 ::; b.
 1.1.4.72: In 4172, find the real solutions of each equation. (y )2 = 6(Y )...
 1.1.2.72: In 7178, find the real solutions, if any, of each equatio n. Use t...
 1.1.5.73: In 5388, solve each inequality. Express your answer using set nota...
 1.73: In 6574, use the complex number system and write each expression i...
 1.1.3.73: In 7378, without solving, determine the character of the solutions...
 1.1.1.73: In 6974, solve each equation. The letters a, b, and c are constant...
 1.1.6.73: In 7176, find a and b. If Ix + 41 ::; 2, then a ::; 2x  3 ::; b.
 1.1.4.73: In 7388, find the real solutions of each equation by factoring. x3...
 1.1.2.73: In 7178, find the real solutions, if any, of each equatio n. Use t...
 1.1.5.74: In 5388, solve each inequality. Express your answer using set nota...
 1.74: In 6574, use the complex number system and write each expression i...
 1.1.3.74: In 7378, without solving, determine the character of the solutions...
 1.1.1.74: In 6974, solve each equation. The letters a, b, and c are constant...
 1.1.6.74: In 7176, find a and b. If Ix  31 ::; 1, then a ::; 3x + 1 ::; b.
 1.1.4.74: In 7388, find the real solutions of each equation by factoring. X4...
 1.1.2.74: In 7178, find the real solutions, if any, of each equatio n. Use t...
 1.1.5.75: In 5388, solve each inequality. Express your answer using set nota...
 1.75: In 7582, solve each equation in the complex number system. x2 + x ...
 1.1.3.75: In 7378, without solving, determine the character of the solutions...
 1.1.1.75: Find he number a for which x = 4 is a solution of the equatIOn x + ...
 1.1.6.75: In 7176, find a and b. If Ix  21 ::; 7, then a ::; ::; b.x  10 x
 1.1.4.75: In 7388, find the real solutions of each equation by factoring. 4x...
 1.1.2.75: In 7178, find the real solutions, if any, of each equatio n. Use t...
 1.1.5.76: In 5388, solve each inequality. Express your answer using set nota...
 1.76: In 7582, solve each equation in the complex number system. x2  x ...
 1.1.3.76: In 7378, without solving, determine the character of the solutions...
 1.1.1.76: Find the number b for which x = 2 is a solution of the equation x +...
 1.1.6.76: In 7176, find a and b. If Ix + 11 ::; 3, then a ::;  ::; b.x + 5
 1.1.4.76: In 7388, find the real solutions of each equation by factoring. x5...
 1.1.2.76: In 7178, find the real solutions, if any, of each equatio n. Use t...
 1.1.5.77: In 5388, solve each inequality. Express your answer using set nota...
 1.77: In 7582, solve each equation in the complex number system. 2X2 + x...
 1.1.3.77: In 7378, without solving, determine the character of the solutions...
 1.1.1.77: 7782 list some formulas that occur in applications. Solve each for...
 1.1.6.77: Show that if a > 0, b > 0, and va < Vb, then a < b. [Hint: b  a = ...
 1.1.4.77: In 7388, find the real solutions of each equation by factoring. x3...
 1.1.2.77: In 7178, find the real solutions, if any, of each equatio n. Use t...
 1.1.5.78: In 5388, solve each inequality. Express your answer using set nota...
 1.78: In 7582, solve each equation in the complex number system. 3x2  2...
 1.1.3.78: In 7378, without solving, determine the character of the solutions...
 1.1.1.78: 7782 list some formulas that occur in applications. Solve each for...
 1.1.6.78: Show that a ::; lal.
 1.1.4.78: In 7388, find the real solutions of each equation by factoring. x3...
 1.1.2.78: In 7178, find the real solutions, if any, of each equatio n. Use t...
 1.1.5.79: In 5388, solve each inequality. Express your answer using set nota...
 1.79: In 7582, solve each equation in the complex number system. x2 + 3 = x
 1.1.3.79: 2 + 3i is a solution of a quadratic equation with real coefficients...
 1.1.1.79: 7782 list some formulas that occur in applications. Solve each for...
 1.1.6.79: Prove the triangle inequality la + bl ::; lal + Ibl. [Hint: Expand ...
 1.1.4.79: In 7388, find the real solutions of each equation by factoring. x3...
 1.1.2.79: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.80: In 5388, solve each inequality. Express your answer using set nota...
 1.80: In 7582, solve each equation in the complex number system. 2x2 + 1...
 1.1.3.80: 4  i is a solution of a quadratic equation with real coefficients....
 1.1.1.80: 7782 list some formulas that occur in applications. Solve each for...
 1.1.6.80: Prove that la  bl 2: lal  Ibl. [Hint: Apply the triangle inequali...
 1.1.4.80: In 7388, find the real solutions of each equation by factoring. x3...
 1.1.2.80: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.81: In 5388, solve each inequality. Express your answer using set nota...
 1.81: In 7582, solve each equation in the complex number system. x(1x)=6
 1.1.3.81: In 8184, z = 3  4i and w = 8 + 3i. Write each expression in the s...
 1.1.1.81: 7782 list some formulas that occur in applications. Solve each for...
 1.1.6.81: If a > 0, show that the solution set of the inequality x 2 < a cons...
 1.1.4.81: In 7388, find the real solutions of each equation by factoring. x3...
 1.1.2.81: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.82: In 5388, solve each inequality. Express your answer using set nota...
 1.82: In 7582, solve each equation in the complex number system. x(1 + x...
 1.1.3.82: In 8184, z = 3  4i and w = 8 + 3i. Write each expression in the s...
 1.1.1.82: 7782 list some formulas that occur in applications. Solve each for...
 1.1.6.82: If a > 0, show that the solution set of the inequality x2 > a consi...
 1.1.4.82: In 7388, find the real solutions of each equation by factoring. x3...
 1.1.2.82: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.83: In 5388, solve each inequality. Express your answer using set nota...
 1.83: Translate the following statement into a mathematical expression : ...
 1.1.3.83: In 8184, z = 3  4i and w = 8 + 3i. Write each expression in the s...
 1.1.1.83: Finance A total of $20,000 is to be invested, some in bonds and som...
 1.1.6.83: In 8390, use the results found in 81 and 82 to solve each inequali...
 1.1.4.83: In 7388, find the real solutions of each equation by factoring. 2x...
 1.1.2.83: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.84: In 5388, solve each inequality. Express your answer using set nota...
 1.84: Translate the following statement into a mathematical expression:Th...
 1.1.3.84: In 8184, z = 3  4i and w = 8 + 3i. Write each expression in the s...
 1.1.1.84: Finance A total of $10,000 is to be divided between Sean and George...
 1.1.6.84: In 8390, use the results found in 81 and 82 to solve each inequali...
 1.1.4.84: In 7388, find the real solutions of each equation by factoring. 3x...
 1.1.2.84: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.85: In 5388, solve each inequality. Express your answer using set nota...
 1.85: Banking A bank lends out $9000 at 7% simple interest. At the end of...
 1.1.3.85: Electrical Circuits The impedance Z, in ohms, of a circuit element ...
 1.1.1.85: Internet Searches In November 2005, Google and Yahoo! search engine...
 1.1.6.85: In 8390, use the results found in 81 and 82 to solve each inequali...
 1.1.4.85: In 7388, find the real solutions of each equation by factoring. 5x...
 1.1.2.85: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.86: In 5388, solve each inequality. Express your answer using set nota...
 1.86: Financial Planning Steve, a recent retiree, requires $5000 per year...
 1.1.3.86: Parallel ircuits n an ac CirCUit Wit 1 two para I el pathways, the ...
 1.1.1.86: Sharing the Cost of a Pizza Judy and Tom agree to share the cost of...
 1.1.6.86: In 8390, use the results found in 81 and 82 to solve each inequali...
 1.1.4.86: In 7388, find the real solutions of each equation by factoring. 3x...
 1.1.2.86: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.87: In 5388, solve each inequality. Express your answer using set nota...
 1.87: Lightning and Thunder A flash of lightning is seen, and the resulti...
 1.1.3.87: Use z = a + bi to show that z + z = 2a and z  z = 2bi.
 1.1.1.87: Computing Hourly Wages Sandra, who is paid timeandahalf for hours...
 1.1.6.87: In 8390, use the results found in 81 and 82 to solve each inequali...
 1.1.4.87: In 7388, find the real solutions of each equation by factoring. x(...
 1.1.2.87: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.88: In 5388, solve each inequality. Express your answer using set nota...
 1.88: Physics: Intensity of Light The intensity I (in candlepower) f .. ....
 1.1.3.88: Use z = a + bi to show that z = z.
 1.1.1.88: Computing Hourly Wages Leigh is paid timeandahalf for hours work...
 1.1.6.88: In 8390, use the results found in 81 and 82 to solve each inequali...
 1.1.4.88: In 7388, find the real solutions of each equation by factoring. 3x...
 1.1.2.88: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.89: In 8998, find a and b. If 1 < x < 1, then a < x + 4 < b.
 1.89: Extent of Search and Rescue A search plane has a cruising speed of ...
 1.1.3.89: Use z = a + bi and w = c + di to show that z + w = z + W.
 1.1.1.89: Computing Grades Going into the final exam, which will count as two...
 1.1.6.89: In 8390, use the results found in 81 and 82 to solve each inequali...
 1.1.4.89: In 8994, find the real solutions of each equation. Use a calculato...
 1.1.2.89: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.90: In 8998, find a and b. If 3 < x < 2, then a < x  6 < b.
 1.90: Extent of Search and Rescue If the search plane described in is abl...
 1.1.3.90: Use z = a + bi and w = c + di to show that z w = z w.
 1.1.1.90: Computing Grades Going into the final exam, which will count as two...
 1.1.6.90: In 8390, use the results found in 81 and 82 to solve each inequali...
 1.1.4.90: In 8994, find the real solutions of each equation. Use a calculato...
 1.1.2.90: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.91: In 8998, find a and b. If 2 < x < 3, then a < 4x < b.
 1.91: Rescue at Sea A life raft, set adrift from a sinking ship 150 miles...
 1.1.3.91: Explain to a friend how you would add two complex numbers and how y...
 1.1.1.91: Business: Discount Pricing A builder of tract homes reduced the pri...
 1.1.6.91: Solve 13x  12x + 111 = 4
 1.1.4.91: In 8994, find the real solutions of each equation. Use a calculato...
 1.1.2.91: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.92: In 8998, find a and b. If 4 < x < 0, then a < "2 x < b.
 1.92: Physics: Uni form Motion Two bees leave two locations 150 meters ap...
 1.1.3.92: Write a brief paragraph that compares the method used to rationaliz...
 1.1.1.92: Business: DiscOlmt Pricing A car dealer, at a yearend clearance, r...
 1.1.6.92: Solve Ix + 13x  211 = 2.
 1.1.4.92: In 8994, find the real solutions of each equation. Use a calculato...
 1.1.2.92: In 7992, find the real solutions, if any, of each equation. Use an...
 1.1.5.93: In 8998, find a and b. If 0 < x < 4, then a < 2x + 3 < b.
 1.93: Physics: Uniform Motion A Metra commuter train leaves Union Station...
 1.1.1.93: Business: Marking up the Price of Books A college book store marks ...
 1.1.6.93: The equation Ixl = 2 has no solution. Explain why.
 1.1.4.93: In 8994, find the real solutions of each equation. Use a calculato...
 1.1.2.93: In 9398, use the discriminant to determine whether each quadratic ...
 1.1.5.94: In 8998, find a and b. If 3 < x < 3, then a < 1  2x < b.
 1.94: Physics An object is thrown down from the top of a building 1280 fe...
 1.1.1.94: Personal Finance: Cost of a Car The suggested list price of a new c...
 1.1.6.94: The inequality /x/ > 0.5 has all real numbers as the solution. Exp...
 1.1.4.94: In 8994, find the real solutions of each equation. Use a calculato...
 1.1.2.94: In 9398, use the discriminant to determine whether each quadratic ...
 1.1.5.95: In 8998, find a and b. If 3 < x < 0, then a <  < b. x+4
 1.95: Working Together to Get a Job Done Clarissa and Shawna, working tog...
 1.1.1.95: Business: Theater Attendance The manager of the Coral Theater wants...
 1.1.6.95: The inequality Ixl > 0 has as solution set {xix =F O}. Explain why.
 1.1.4.95: If k= x + 3 and k  k = 12, fmd x. x3
 1.1.2.95: In 9398, use the discriminant to determine whether each quadratic ...
 1.1.5.96: In 8998, find a and b. If 2 < x < 4, then a <x_ 6 < b.
 1.96: Emptying a Tank Two pumps of different sizes, working together, can...
 1.1.1.96: Business: Discount Pricing A wool suit, discounted by 30% for a cle...
 1.1.4.96: If k = x + 3 and k2  3k = 2 8, find x.
 1.1.2.96: In 9398, use the discriminant to determine whether each quadratic ...
 1.1.5.97: In 8998, find a and b. If 6 < 3x < 12 , then a < < b.
 1.97: Chemistry: Salt Solutions How much water should be added to 64 ounc...
 1.1.1.97: Geometry The perimeter of a rectangle is 60 feet. Find its length a...
 1.1.4.97: Physics: Using Sound to Measure Distance The distance to the surfac...
 1.1.2.97: In 9398, use the discriminant to determine whether each quadratic ...
 1.1.5.98: In 8998, find a and b. If 0 < 2x < 6, then a < .? < b.
 1.98: Chemistry: Salt Solutions How much water must be evaporated from 64...
 1.1.1.98: Geometry The perimeter of a rectangle is 42 meters. Find its length...
 1.1.4.98: Crushing Load A civil engineer relates the thickness T, in inches, ...
 1.1.2.98: In 9398, use the discriminant to determine whether each quadratic ...
 1.1.5.99: What is the domain of the variable in the expression ?
 1.99: Geometry The hypotenuse of a right triangle measures 13 centimeters...
 1.1.1.99: Internet Users In March 2006, 152 million people in the United Stat...
 1.1.4.99: Foucault's Pendulum The period of a pendulum is the time it takes t...
 1.1.2.99: College Tuition and Fees The average annual published undergraduate...
 1.1.5.100: What Vs+2x is the domain of the variable in the expression ?
 1.100: Geometry The diagonal of a rectangle measures 10 inches. If the len...
 1.1.1.100: One step in the following list contains an error. Identify it and e...
 1.1.4.100: Make up a radical equation that has no solution.
 1.1.2.100: Women's Weekly Earnings The median weekly earnings E, in dollars, f...
 1.1.5.101: A young adult may be defined as someone older than 21, but less tha...
 1.101: Chemistry : Mixing Acids A laboratory has 60 cubic centimeters (cm3...
 1.1.1.101: The equation 5 8 + x x+3 + 3=x+3 has no solution, yet when we go...
 1.1.4.101: Make up a radical equation that has an extraneous solution.
 1.1.2.101: Dimensions of a Window The area of the opening of a rectangular win...
 1.1.5.102: Middleaged may be defined as being 40 or more and less than 60. Ex...
 1.102: Framing a Painting An artist has 50 inches of oak trim to frame a p...
 1.1.1.102: Make up an equation that has no solution and give it to a fellow st...
 1.1.4.102: Discuss the step in the solving process for radical equations that ...
 1.1.2.102: Dimensions of a Window The area of a rectangular window is to be 3 ...
 1.1.5.103: Life Expectancy The Social Security Administration determined that ...
 1.103: Using Two Pumps An 8horsepower (hp) pump can fill a tank in 8 hour...
 1.1.2.103: Geometry Find the dimensions of a rectangle whose perimeter is 26 m...
 1.1.5.104: General Chemistry For a certain ideal gas, the volume V (in cubic c...
 1.104: Pleasing Proportion One formula stating the relationship between th...
 1.1.2.104: Watering a Field An adjustable water sprinkler that sprays water in...
 1.1.5.105: Real Estate A real estate agent agrees to sell an apartment complex...
 1.105: F inance An inheritance of $900,000 is to be divided among Scott, A...
 1.1.2.105: Constructing a Box An open box is to be constructed from a square p...
 1.1.5.106: Sales Commission A used car salesperson is paid a commission of $25...
 1.106: B us iness: Determining the Cost of a Charte r A group of 20 senior...
 1.1.2.106: Constructing a Box Rework if the piece of sheet metal is a rectangl...
 1.1.5.107: Federal Tax Withholding The percentage method of withholding for fe...
 1.107: U tilizing Copying Machines A new copying machine can do a certain ...
 1.1.2.107: Physics A ball is thrown vertically upward from the top of a buildi...
 1.1.5.108: Exercising Sue wants to lose weight. For healthy weight loss, the A...
 1.108: n a 100meter race, Todd crosses the finish line 5 meters ahead of ...
 1.1.2.108: Physics An object is propelled vertically upward with an initial ve...
 1.1.5.109: Electricity Rates Commonwealth Edison Company's charge for electric...
 1.109: Physics: Uniform Motion A man is walking at an average speed of 4 m...
 1.1.2.109: Reducing the Size of a Candy Bar A jumbo chocolate bar with a recta...
 1.1.5.110: Water Bills The Village of Oak Lawn charges homeowners $28.84 per q...
 1.1.2.110: Reducing the Size of a Candy Bar Rework if the reduction is to be 20%.
 1.1.5.111: Markup of a New Car The markup over dealer's cost of a new car rang...
 1.1.2.111: Constructing a Border around a Pool A circular pool meaV\ sures 10 ...
 1.1.5.112: IQ Tests A standard intelligence test has an average score of 100. ...
 1.1.2.112: Constructing a Border arollnd a Pool Rework if the depth of the bor...
 1.1.5.113: Computing Grades In your Economics 101 class, you have scores of 68...
 1.1.2.113: Constructing a Border around a Garden A landscaper, who just comple...
 1.1.5.114: "Light" Foods For food products to be labeled "light," the U.S. Foo...
 1.1.2.114: Dimensions of a Patio A contractor orders 8 cubic yards of premixed...
 1.1.5.115: Arithmetic Mean If a < b, show that a < 2 < b. The a + b . number ...
 1.1.2.115: Comparing TVs The screen size of a television is determined by the ...
 1.1.5.116: Refer to 115. Show that the arithmetic mean of a and b is equidista...
 1.1.2.116: Comparing TVs Refer to 15. Find the screen area of a traditional 50...
 1.1.5.117: Geometric Mean If 0 < a < b, show that a < vaJj < b. The number vaJ...
 1.1.2.117: The sum of the consecutive integers 1, 2, 3, ... , n is given by 1 ...
 1.1.5.118: Refer to 115 and 1 17. Show that the geometric mean of a and b is l...
 1.1.2.118: Geometry If a polygon of n sides has n( n  3) diagonals, how many ...
 1.1.5.119: Harmonic Mean For 0 < a < b, let h be defined by ! = ! (! + !) h 2 ...
 1.1.2.119: Show that the sum of the roots of a quadratic equation is .
 1.1.5.120: Refer to 1 15, 1 17, and 1 19. Show that the harmonic mean of a and...
 1.1.2.120: Show that the product of the roots of a quadratic equation . c lS . a
 1.1.5.121: Another Reciprocal PrOI)erty Prove that if 0 < a < b, then 1 1 0< ...
 1.1.2.121: Find k such that the equation kx2 + x + k = 0 has a repeated real s...
 1.1.5.122: Make up an inequality that has no solution. Make up one that has ex...
 1.1.2.122: Find k such that the equation x2  kx + 4 = 0 has a repeated real s...
 1.1.5.123: The inequality y} + 1 < 5 has no real solution. Explain why.
 1.1.2.123: Show that the real solutions of the equation ax 2 + bx + c = 0 are ...
 1.1.5.124: Do you prefer to use inequality notation or interval notation to ex...
 1.1.2.124: Show that the real solutions of the equation ax 2 + bx + c = 0 are ...
 1.1.5.125: How would you explain to a fellow student the underlying reason for...
 1.1.2.125: Which of the following pairs of equations are equivalent? Explain. ...
 1.1.2.126: Describe three ways that you might solve a quadratic equation. Stat...
 1.1.2.127: Explain the benefits of evaluating the discriminant of a quadratic ...
 1.1.2.128: Create three quadratic equations: one having two distinct solutions...
 1.1.2.129: The word quadra tic seems to imply four (quad), yet a quadratic equ...
Solutions for Chapter 1: Equations and Inequalities
Full solutions for Algebra and Trigonometry  8th Edition
ISBN: 9780132329033
Solutions for Chapter 1: Equations and Inequalities
Get Full SolutionsAlgebra and Trigonometry was written by and is associated to the ISBN: 9780132329033. Since 813 problems in chapter 1: Equations and Inequalities have been answered, more than 53907 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. Chapter 1: Equations and Inequalities includes 813 full stepbystep solutions. This textbook survival guide was created for the textbook: Algebra and Trigonometry, edition: 8.

Cholesky factorization
A = CTC = (L.J]))(L.J]))T for positive definite A.

Covariance matrix:E.
When random variables Xi have mean = average value = 0, their covariances "'£ ij are the averages of XiX j. With means Xi, the matrix :E = mean of (x  x) (x  x) T is positive (semi)definite; :E is diagonal if the Xi are independent.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Fibonacci numbers
0,1,1,2,3,5, ... satisfy Fn = Fnl + Fn 2 = (A7 A~)I()q A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } A].

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

Graph G.
Set of n nodes connected pairwise by m edges. A complete graph has all n(n  1)/2 edges between nodes. A tree has only n  1 edges and no closed loops.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Iterative method.
A sequence of steps intended to approach the desired solution.

Markov matrix M.
All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace N (A)
= All solutions to Ax = O. Dimension n  r = (# columns)  rank.

Projection p = a(aTblaTa) onto the line through a.
P = aaT laTa has rank l.

Schwarz inequality
Iv·wl < IIvll IIwll.Then IvTAwl2 < (vT Av)(wT Aw) for pos def A.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Spectral Theorem A = QAQT.
Real symmetric A has real A'S and orthonormal q's.

Trace of A
= sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).