 1.1.3.1: In Exercises 1 to 10, solve each quadratic equation by factoring an...
 1.1.6.1: In Exercises 1 to 12, write an equation that represents the relatio...
 1.1: In Exercises 1 to 20, solve each equation. 4  5x = 3x + 14
 1.1.4.1: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.1: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.1: In Exercises 1 to 8, use the properties of inequalities to 10 3x  ...
 1.1.2.1: In Exercises 1 to 10, solve the formula for the specified variable....
 1.1.3.2: In Exercises 1 to 10, solve each quadratic equation by factoring an...
 1.1.6.2: In Exercises 1 to 12, write an equation that represents the relatio...
 1.2: In Exercises 1 to 20, solve each equation. 7  5(1  2x) = 3(2x + 1)
 1.1.4.2: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.2: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.2: In Exercises 1 to 8, use the properties of inequalities to 10 3x  ...
 1.1.2.2: In Exercises 1 to 10, solve the formula for the specified variable....
 1.1.3.3: In Exercises 1 to 10, solve each quadratic equation by factoring an...
 1.1.6.3: In Exercises 1 to 12, write an equation that represents the relatio...
 1.3: In Exercises 1 to 20, solve each equation. 4x3  4x  16 = 12
 1.1.4.3: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.3: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.3: In Exercises 1 to 8, use the properties of inequalities to 10 3x  ...
 1.1.2.3: In Exercises 1 to 10, solve the formula for the specified variable....
 1.1.3.4: In Exercises 1 to 10, solve each quadratic equation by factoring an...
 1.1.6.4: In Exercises 1 to 12, write an equation that represents the relatio...
 1.4: In Exercises 1 to 20, solve each equation. 3x4  2x  18 = 32
 1.1.4.4: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.4: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.4: In Exercises 1 to 8, use the properties of inequalities to 10 3x  ...
 1.1.2.4: In Exercises 1 to 10, solve the formula for the specified variable....
 1.1.3.5: In Exercises 1 to 10, solve each quadratic equation by factoring an...
 1.1.6.5: In Exercises 1 to 12, write an equation that represents the relatio...
 1.5: In Exercises 1 to 20, solve each equation. x  3 = 2
 1.1.4.5: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.5: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.5: In Exercises 1 to 8, use the properties of inequalities to 10 3x  ...
 1.1.2.5: In Exercises 1 to 10, solve the formula for the specified variable....
 1.1.3.6: In Exercises 1 to 10, solve each quadratic equation by factoring an...
 1.1.6.6: In Exercises 1 to 12, write an equation that represents the relatio...
 1.6: In Exercises 1 to 20, solve each equation. x + 5 = 4
 1.1.4.6: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.6: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.6: In Exercises 1 to 8, use the properties of inequalities to 10 3x  ...
 1.1.2.6: In Exercises 1 to 10, solve the formula for the specified variable....
 1.1.3.7: In Exercises 1 to 10, solve each quadratic equation by factoring an...
 1.1.6.7: In Exercises 1 to 12, write an equation that represents the relatio...
 1.7: In Exercises 1 to 20, solve each equation. 2x + 1 = 5
 1.1.4.7: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.7: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.7: In Exercises 1 to 8, use the properties of inequalities to 10 3x  ...
 1.1.2.7: In Exercises 1 to 10, solve the formula for the specified variable....
 1.1.3.8: In Exercises 1 to 10, solve each quadratic equation by factoring an...
 1.1.6.8: In Exercises 1 to 12, write an equation that represents the relatio...
 1.8: In Exercises 1 to 20, solve each equation. 3x  7 = 8
 1.1.4.8: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.8: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.8: In Exercises 1 to 8, use the properties of inequalities to 10 3x  ...
 1.1.2.8: In Exercises 1 to 10, solve the formula for the specified variable....
 1.1.3.9: In Exercises 1 to 10, solve each quadratic equation by factoring an...
 1.1.6.9: In Exercises 1 to 12, write an equation that represents the relatio...
 1.9: In Exercises 1 to 20, solve each equation. V = pr h2 h, for h
 1.1.4.9: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.9: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.9: In Exercises 9 to 16, solve each compound inequality. Write the sol...
 1.1.2.9: In Exercises 1 to 10, solve the formula for the specified variable....
 1.1.3.10: In Exercises 1 to 10, solve each quadratic equation by factoring an...
 1.1.6.10: In Exercises 1 to 12, write an equation that represents the relatio...
 1.10: In Exercises 1 to 20, solve each equation. P = tA1 + rt ,
 1.1.4.10: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.10: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.10: In Exercises 9 to 16, solve each compound inequality. Write the sol...
 1.1.2.10: In Exercises 1 to 10, solve the formula for the specified variable....
 1.1.3.11: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.11: In Exercises 1 to 12, write an equation that represents the relatio...
 1.11: In Exercises 1 to 20, solve each equation. A = b1h2 (b1 + b2),
 1.1.4.11: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.11: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.11: In Exercises 9 to 16, solve each compound inequality. Write the sol...
 1.1.2.11: Quarterback Rating During the 2008 season, Drew Brees, the quarterb...
 1.1.3.12: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.12: In Exercises 1 to 12, write an equation that represents the relatio...
 1.12: In Exercises 1 to 20, solve each equation. P = 2(l + w), w
 1.1.4.12: In Exercises 1 to 12, solve each polynomial equation by factoring a...
 1.1.1.12: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.12: In Exercises 9 to 16, solve each compound inequality. Write the sol...
 1.1.2.12: Quarterback Rating During the 2008 season, Peyton Manning, the quar...
 1.1.3.13: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.13: In Exercises 13 to 20, write the equation that expresses the relati...
 1.13: In Exercises 1 to 20, solve each equation. x2  5x + 6 = 0
 1.1.4.13: In Exercises 13 to 26, solve the rational equation.5x + 4  2 = 7x ...
 1.1.1.13: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.13: In Exercises 9 to 16, solve each compound inequality. Write the sol...
 1.1.2.13: The simplified measure of gobbledygook (SMOG) readability formula i...
 1.1.2.14: The simplified measure of gobbledygook (SMOG) readability formula i...
 1.1.3.14: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.14: In Exercises 13 to 20, write the equation that expresses the relati...
 1.14: In Exercises 1 to 20, solve each equation. 6x2 + x  12 = 0
 1.1.4.14: In Exercises 13 to 26, solve the rational equation. x + 4x  2+ 3 =...
 1.1.1.14: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.14: In Exercises 9 to 16, solve each compound inequality. Write the sol...
 1.1.2.15: Another reading level formula is the GunningFog Index 0.4(A P). He...
 1.1.3.15: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.15: In Exercises 13 to 20, write the equation that expresses the relati...
 1.15: In Exercises 1 to 20, solve each equation. (x  2)2 = 50
 1.1.4.15: In Exercises 13 to 26, solve the rational equation. 2 +9r  3 = 3rr...
 1.1.1.15: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.15: In Exercises 9 to 16, solve each compound inequality. Write the sol...
 1.1.2.16: Another reading level formula is the GunningFog Index 0.4(A P). He...
 1.1.3.16: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.16: In Exercises 13 to 20, write the equation that expresses the relati...
 1.16: In Exercises 1 to 20, solve each equation. 2(x + 4)2 + 18 = 0
 1.1.4.16: In Exercises 13 to 26, solve the rational equation. tt  4+ 3 = 4t  4
 1.1.1.16: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.16: In Exercises 9 to 16, solve each compound inequality. Write the sol...
 1.1.2.17: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.17: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.17: In Exercises 13 to 20, write the equation that expresses the relati...
 1.17: In Exercises 1 to 20, solve each equation. x2  6x  1 = 0
 1.1.4.17: In Exercises 13 to 26, solve the rational equation. 3x + 2 = 52x  7
 1.1.1.17: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.17: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.18: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.18: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.18: In Exercises 13 to 20, write the equation that expresses the relati...
 1.18: In Exercises 1 to 20, solve each equation. 4x2  4x  1 = 0
 1.1.4.18: In Exercises 13 to 26, solve the rational equation. 4y + 2 = 7y  4
 1.1.1.18: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.18: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.19: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.19: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.19: In Exercises 13 to 20, write the equation that expresses the relati...
 1.19: In Exercises 1 to 20, solve each equation. 3x2  x  1 = 0
 1.1.4.19: In Exercises 13 to 26, solve the rational equation. x  2x + 3x + 3...
 1.1.1.19: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.19: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.20: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.20: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.20: In Exercises 13 to 20, write the equation that expresses the relati...
 1.20: In Exercises 1 to 20, solve each equation. x2  x + 1 = 0
 1.1.4.20: In Exercises 13 to 26, solve the rational equation. 2x +3x  1 = 7...
 1.1.1.20: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.20: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.21: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.21: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.21: Charless Law Charless Law states that the volume occupied by a gas ...
 1.21: In Exercises 21 and 22, use the discriminant to determine whether t...
 1.1.4.21: In Exercises 13 to 26, solve the rational equation. 5x  3  3x  2...
 1.1.1.21: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.21: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.5.22: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.22: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.22: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.22: Hookes Law Hookes Law states that the distance a spring stretches v...
 1.22: In Exercises 21 and 22, use the discriminant to determine whether t...
 1.1.4.22: In Exercises 13 to 26, solve the rational equation. 4x  1+7x + 7 =...
 1.1.1.22: In Exercises 1 to 22, solve each equation and check your solution. ...
 1.1.5.23: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.23: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.23: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.23: Semester Hours vs. Quarter Hours A student plans to transfer from a...
 1.23: In Exercises 23 to 40, solve each equation. 3x3  5x2 = 0
 1.1.4.23: In Exercises 13 to 26, solve the rational equation. xx + 1  x + 2x...
 1.1.1.23: In Exercises 23 to 32, classify each equation as a contradiction, a...
 1.1.5.24: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.24: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.24: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.24: Pressure and Depth The pressure a liquid exerts at a given point on...
 1.24: In Exercises 23 to 40, solve each equation. 2x3  8x = 0
 1.1.4.24: In Exercises 13 to 26, solve the rational equation. 2x + 1x  3  x...
 1.1.1.24: In Exercises 23 to 32, classify each equation as a contradiction, a...
 1.1.5.25: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.25: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.25: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.25: Amount of Juice Contained in a Grapefruit The amount of juice in a ...
 1.25: In Exercises 23 to 40, solve each equation. 2x3 + 3x2  8x  12 = 0
 1.1.4.25: In Exercises 13 to 26, solve the rational equation. 4  3x2x + 1+3x...
 1.1.1.25: In Exercises 23 to 32, classify each equation as a contradiction, a...
 1.1.5.26: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.26: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.26: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.26: Motorcycle Jump The range of a projectile is directly proportional ...
 1.26: In Exercises 23 to 40, solve each equation. 3x3  2x2  3x + 2 = 0
 1.1.4.26: In Exercises 13 to 26, solve the rational equation. 5x + 33x  2  ...
 1.1.1.26: In Exercises 23 to 32, classify each equation as a contradiction, a...
 1.1.5.27: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.27: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.27: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.27: Period of a Pendulum The period of a pendulum (the time it takes th...
 1.27: In Exercises 23 to 40, solve each equation. xx + 2+14 = 5
 1.1.4.27: In Exercises 27 to 42, solve the radical equation. 1x  4  6 = 0
 1.1.1.27: In Exercises 23 to 32, classify each equation as a contradiction, a...
 1.1.5.28: In Exercises 17 to 28, use interval notation to express the solutio...
 1.1.2.28: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.28: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.28: Area of a Projected Picture The area of a projected picture on a mo...
 1.28: In Exercises 23 to 40, solve each equation. y  1y + 1  1 = 2y
 1.1.4.28: In Exercises 27 to 42, solve the radical equation. 110  x = 4
 1.1.1.28: In Exercises 23 to 32, classify each equation as a contradiction, a...
 1.1.5.29: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.29: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.29: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.29: Speed of a Bicycle Gear The speed of a bicycle gear, in revolutions...
 1.29: In Exercises 23 to 40, solve each equation. 3x +2x  2 = 4x  1x  2
 1.1.4.29: In Exercises 27 to 42, solve the radical equation. 13x  5  1x + 2...
 1.1.1.29: In Exercises 23 to 32, classify each equation as a contradiction, a...
 1.1.5.30: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.30: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.30: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.30: Vibration of a Guitar String The frequency of vibration of a guitar...
 1.30: In Exercises 23 to 40, solve each equation. x + 1x + 3+2x  1x  2 ...
 1.1.4.30: In Exercises 27 to 42, solve the radical equation. 1x + 7  2 = 1x  9
 1.1.1.30: In Exercises 23 to 32, classify each equation as a contradiction, a...
 1.1.5.31: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.31: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.31: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.31: Jet Engine Noise The sound intensity of a jet engine, measured in w...
 1.31: In Exercises 23 to 40, solve each equation. 12x + 6  1 = 3
 1.1.4.31: In Exercises 27 to 42, solve the radical equation. 12x + 11  12x ...
 1.1.1.31: In Exercises 23 to 32, classify each equation as a contradiction, a...
 1.1.5.32: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.32: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.32: In Exercises 11 to 32, use the square root procedure to solve the e...
 1.1.6.32: Illumination The illumination a source of light provides is inverse...
 1.32: In Exercises 23 to 40, solve each equation. 5x  1 + 3 = 1
 1.1.4.32: In Exercises 27 to 42, solve the radical equation. 1x + 7 + 1x  5 = 6
 1.1.1.32: In Exercises 23 to 32, classify each equation as a contradiction, a...
 1.1.5.33: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.33: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.33: In Exercises 33 to 50, solve each equation by completing the square...
 1.1.6.33: Volume Relationships The volume V of a right circular cone varies j...
 1.33: In Exercises 23 to 40, solve each equation. 12x  7 + 2x = 7
 1.1.4.33: In Exercises 27 to 42, solve the radical equation. 1x  4 + 1x + 1 = 1
 1.1.1.33: In Exercises 33 to 48, solve each absolute value equation for x. x = 4
 1.1.5.34: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.34: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.34: In Exercises 33 to 50, solve each equation by completing the square...
 1.1.6.34: Safe Load The load that a horizontal beam can safely support varies...
 1.34: In Exercises 23 to 40, solve each equation. 18x  2 + 4x = 1
 1.1.4.34: In Exercises 27 to 42, solve the radical equation. 12x  9 + 12x + ...
 1.1.1.34: In Exercises 33 to 48, solve each absolute value equation for x. x = 7
 1.1.5.35: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.35: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.35: In Exercises 33 to 50, solve each equation by completing the square...
 1.1.6.35: Ideal Gas Law The Ideal Gas Law states that the volume V of a gas v...
 1.35: In Exercises 23 to 40, solve each equation. 3x + 4 + 1x  3 = 5
 1.1.4.35: In Exercises 27 to 42, solve the radical equation. 19x  20 = x
 1.1.1.35: In Exercises 33 to 48, solve each absolute value equation for x. x ...
 1.1.5.36: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.36: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.36: In Exercises 33 to 50, solve each equation by completing the square...
 1.1.6.36: Maximum Load The maximum load a cylindrical column of circular cros...
 1.36: In Exercises 23 to 40, solve each equation. 12x + 2  1x + 2 = 1
 1.1.4.36: In Exercises 27 to 42, solve the radical equation. x = 112x  35
 1.1.1.36: In Exercises 33 to 48, solve each absolute value equation for x. x ...
 1.1.5.37: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.37: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.37: In Exercises 33 to 50, solve each equation by completing the square...
 1.1.6.37: Earned Run Average A pitchers earned run average (ERA) is directly ...
 1.37: In Exercises 23 to 40, solve each equation. x5>4  32 = 0
 1.1.4.37: In Exercises 27 to 42, solve the radical equation. 12x  1  1x  1...
 1.1.1.37: In Exercises 33 to 48, solve each absolute value equation for x. 2x...
 1.1.5.38: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.38: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.38: In Exercises 33 to 50, solve each equation by completing the square...
 1.1.6.38: Safe Load The load a horizontal beam can safely support varies join...
 1.38: In Exercises 23 to 40, solve each equation. 2x 2>3  5 = 13
 1.1.4.38: In Exercises 27 to 42, solve the radical equation. 16  x + 15x + 6...
 1.1.1.38: In Exercises 33 to 48, solve each absolute value equation for x. 2x...
 1.1.5.39: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.39: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.39: In Exercises 33 to 50, solve each equation by completing the square...
 1.1.6.39: Force, Speed, and Radius Relationships The force needed to keep a c...
 1.39: In Exercises 23 to 40, solve each equation. 6x4  23x2 + 20 = 0
 1.1.4.39: In Exercises 27 to 42, solve the radical equation. 17x + 2 + x = 2
 1.1.1.39: In Exercises 33 to 48, solve each absolute value equation for x. 2x...
 1.1.5.40: In Exercises 29 to 40, use the critical value method to solve each ...
 1.1.2.40: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.40: In Exercises 33 to 50, solve each equation by completing the square...
 1.1.6.40: Stiffness of a Beam A cylindrical log is to be cut so that it will ...
 1.40: In Exercises 23 to 40, solve each equation. 3x + 161x  12 = 0
 1.1.4.40: In Exercises 27 to 42, solve the radical equation. 19x  9 + x = 1
 1.1.1.40: In Exercises 33 to 48, solve each absolute value equation for x. 2x...
 1.1.5.41: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.41: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.41: In Exercises 33 to 50, solve each equation by completing the square...
 1.1.6.41: Keplers Third Law Keplers Third Law states that the time T needed f...
 1.41: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.41: In Exercises 27 to 42, solve the radical equation. 3 x3  2x  13 =...
 1.1.1.41: In Exercises 33 to 48, solve each absolute value equation for x. x ...
 1.1.5.42: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.42: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.42: In Exercises 33 to 50, solve each equation by completing the square...
 1.42: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.42: In Exercises 27 to 42, solve the radical equation. 23 x3  5x  17 ...
 1.1.1.42: In Exercises 33 to 48, solve each absolute value equation for x. x ...
 1.1.5.43: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.43: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.43: In Exercises 33 to 50, solve each equation by completing the square...
 1.43: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.43: In Exercises 43 to 52, solve each equation containing a rational ex...
 1.1.1.43: In Exercises 33 to 48, solve each absolute value equation for x. 2x...
 1.1.5.44: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.44: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.44: In Exercises 33 to 50, solve each equation by completing the square...
 1.44: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.44: In Exercises 43 to 52, solve each equation containing a rational ex...
 1.1.1.44: In Exercises 33 to 48, solve each absolute value equation for x. 4x...
 1.1.5.45: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.45: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.45: In Exercises 33 to 50, solve each equation by completing the square...
 1.45: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.45: In Exercises 43 to 52, solve each equation containing a rational ex...
 1.1.1.45: In Exercises 33 to 48, solve each absolute value equation for x. 2 ...
 1.1.5.46: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.46: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.46: In Exercises 33 to 50, solve each equation by completing the square...
 1.46: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.46: In Exercises 43 to 52, solve each equation containing a rational ex...
 1.1.1.46: In Exercises 33 to 48, solve each absolute value equation for x. 3 ...
 1.1.5.47: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.47: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.47: In Exercises 33 to 50, solve each equation by completing the square...
 1.47: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.47: In Exercises 43 to 52, solve each equation containing a rational ex...
 1.1.1.47: In Exercises 33 to 48, solve each absolute value equation for x. 2x...
 1.1.5.48: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.48: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.48: In Exercises 33 to 50, solve each equation by completing the square...
 1.48: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.48: In Exercises 43 to 52, solve each equation containing a rational ex...
 1.1.1.48: In Exercises 33 to 48, solve each absolute value equation for x. 3 ...
 1.1.5.49: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.49: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.49: In Exercises 33 to 50, solve each equation by completing the square...
 1.49: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.49: In Exercises 43 to 52, solve each equation containing a rational ex...
 1.1.1.49: Biology The male magnificent frigatebird inflates a red pouch under...
 1.1.5.50: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.50: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.50: In Exercises 33 to 50, solve each equation by completing the square...
 1.50: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.50: In Exercises 43 to 52, solve each equation containing a rational ex...
 1.1.1.50: Health According to one formula for lean body mass (LBM, in kilogra...
 1.1.5.51: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.51: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.51: In Exercises 51 to 70, solve by using the quadratic formula. x2  2...
 1.51: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.51: In Exercises 43 to 52, solve each equation containing a rational ex...
 1.1.1.51: Travel Ruben is driving along a highway that passes through Barstow...
 1.1.5.52: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.52: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.52: In Exercises 51 to 70, solve by using the quadratic formula. x2  5...
 1.52: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.52: In Exercises 43 to 52, solve each equation containing a rational ex...
 1.1.1.52: Automobile Gas Mileage The gas mileage in miles per gallon, obtaine...
 1.1.5.53: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.53: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.53: In Exercises 51 to 70, solve by using the quadratic formula. 12x2 ...
 1.53: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.53: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.1.53: Office Carpeting The cost to install new carpet in an office is det...
 1.1.5.54: In Exercises 41 to 54, use the critical value method to solve each ...
 1.1.2.54: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.54: In Exercises 51 to 70, solve by using the quadratic formula. 10x2 +...
 1.54: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.54: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.1.54: Wholesale Price A retailer determines the retail price of a coat by...
 1.1.5.55: Personal Finance A bank offers two checking account plans. The mont...
 1.1.2.55: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.55: In Exercises 51 to 70, solve by using the quadratic formula. x2  2...
 1.55: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.55: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.1.55: Computer Science If p% of a file remains to be downloaded using a c...
 1.1.5.56: Personal Finance You can rent a car for the day from Company A for ...
 1.1.2.56: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.56: In Exercises 51 to 70, solve by using the quadratic formula. x2 + 4...
 1.56: In Exercises 41 to 56, solve each inequality. Write the answer usin...
 1.1.4.56: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.1.56: Aviation The number of miles that remain to be flown by a commercia...
 1.1.5.57: Shipping Requirements United Parcel Service (UPS) will only ship pa...
 1.1.2.57: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.57: In Exercises 51 to 70, solve by using the quadratic formula. x2 = ...
 1.57: Rectangular Region The length of a rectangle is 9 feet less than tw...
 1.1.4.57: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.1.57: To benefit from an aerobic exercise program, many experts recommend...
 1.1.5.58: Movie Theater Attendance The attendance A, in billions of people, a...
 1.1.2.58: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.58: In Exercises 51 to 70, solve by using the quadratic formula. 2x2 + ...
 1.58: Rectangular Region The perimeter of a rectangle is 40 inches and it...
 1.1.4.58: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.1.58: To benefit from an aerobic exercise program, many experts recommend...
 1.1.5.59: Car Value Based on data from the Kelley Blue Book website, the valu...
 1.1.2.59: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.59: In Exercises 51 to 70, solve by using the quadratic formula. 4x2 = ...
 1.59: Height of a Tree The height of a tree is estimated by using its sha...
 1.1.4.59: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.5.60: Personal Finance A video store offers two rental plans. The yearly ...
 1.1.2.60: In Exercises 17 to 60, solve by using the strategies for solving ap...
 1.1.3.60: In Exercises 51 to 70, solve by using the quadratic formula. 2x = 9...
 1.60: Shadow Length A person 5 feet 6 inches tall is walking away from a ...
 1.1.4.60: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.5.61: Average Temperatures The average daily minimumtomaximum temperatur...
 1.1.3.61: In Exercises 51 to 70, solve by using the quadratic formula. 2 x2 +...
 1.61: Diameter of a Cone As sand is poured from a chute, it forms a right...
 1.1.4.61: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.5.62: Mean Weight of Women If a researcher wanted to know the mean weight...
 1.1.3.62: In Exercises 51 to 70, solve by using the quadratic formula. x2 +5x...
 1.62: Individual Price A calculator and a battery together sell for $21. ...
 1.1.4.62: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.5.63: Mean Weight of Men If a researcher wanted to know the mean weight (...
 1.1.3.63: In Exercises 51 to 70, solve by using the quadratic formula. x2 + 6...
 1.63: Maintenance Cost Eighteen owners share the maintenance cost of a co...
 1.1.4.63: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.5.64: Consecutive Odd Integers The sum of three consecutive odd integers ...
 1.1.3.64: In Exercises 51 to 70, solve by using the quadratic formula. x2 = 2...
 1.64: Investment A total of $5500 was deposited into two simple interest ...
 1.1.4.64: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.5.65: Forensic Science Forensic specialists can estimate the height of a ...
 1.1.3.65: In Exercises 51 to 70, solve by using the quadratic formula. 2x2 = ...
 1.65: Distance to an Island A motorboat left a harbor and traveled to an ...
 1.1.4.65: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.5.66: Forensic Science An inequality that is used to calculate the height...
 1.1.3.66: In Exercises 51 to 70, solve by using the quadratic formula. 9x2  ...
 1.66: Running Inez can run at a rate that is 2 miles per hour faster than...
 1.1.4.66: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.5.67: Revenue The monthly revenue R for a product is given by R = 420x  ...
 1.1.3.67: In Exercises 51 to 70, solve by using the quadratic formula. x2 + 2...
 1.67: Chemistry A chemist mixes a 5% salt solution with an 11% salt solut...
 1.1.4.67: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.5.68: Revenue A shoe manufacturer finds that the monthly revenue from a p...
 1.1.3.68: In Exercises 51 to 70, solve by using the quadratic formula. x2 + 6...
 1.68: Pharmacy How many milliliters of pure water should a pharmacist add...
 1.1.4.68: In Exercises 53 to 68, find all real solutions of each equation by ...
 1.1.5.69: Publishing A publisher has determined that if books are published, ...
 1.1.3.69: In Exercises 51 to 70, solve by using the quadratic formula. 4X2 + ...
 1.69: Alloys How many ounces of a gold alloy that costs $460 per ounce mu...
 1.1.4.69: Boating A small fishing boat heads to a point 24 miles downriver an...
 1.1.5.70: Manufacturing A company manufactures running shoes. The company has...
 1.1.3.70: In Exercises 51 to 70, solve by using the quadratic formula. 9x2 = ...
 1.70: Blends A grocer makes a snack mixture of raisins and nuts by combin...
 1.1.4.70: Running Maureen can run at a rate that is 2 miles per hour faster t...
 1.1.5.71: Height of a Projectile The equation s = 16t 2 + v0t + s0 gives the...
 1.1.3.71: In Exercises 71 to 80, determine the discriminant of the quadratic ...
 1.71: Construction of a Wall A mason can build a wall in 9 hours less tha...
 1.1.4.71: Fence Construction A worker can build a fence in 8 hours. Working t...
 1.1.5.72: Height of a Projectile A ball is thrown directly upward from a heig...
 1.1.3.72: In Exercises 71 to 80, determine the discriminant of the quadratic ...
 1.72: Parallel Processing One computer can solve a problem 5 minutes fast...
 1.1.4.72: Roof Repair A roofer and an assistant can repair a roof together in...
 1.1.3.73: In Exercises 71 to 80, determine the discriminant of the quadratic ...
 1.73: Dogs on a Beach Two dogs start, at the same time, from points C and...
 1.1.4.73: Painting a Room An experienced painter and an apprentice can paint ...
 1.1.3.74: In Exercises 71 to 80, determine the discriminant of the quadratic ...
 1.74: Constructing a Box A square piece of cardboard is formed into a box...
 1.1.4.74: Parallel Processing Parallel processing uses two or more computers,...
 1.1.3.75: In Exercises 71 to 80, determine the discriminant of the quadratic ...
 1.75: Sports In an Olympic 10meter diving competition, the height h, in ...
 1.1.4.75: In Exercises 75 and 76, the depth s from the opening of a well to t...
 1.1.3.76: In Exercises 71 to 80, determine the discriminant of the quadratic ...
 1.76: Fair Coin If a fair coin is tossed 100 times, we would expect heads...
 1.1.4.76: In Exercises 75 and 76, the depth s from the opening of a well to t...
 1.1.3.77: In Exercises 71 to 80, determine the discriminant of the quadratic ...
 1.77: Mean Height If a researcher wanted to know the mean height (the mea...
 1.1.4.77: Radius of a Cone A conical funnel has a height of 4 inches and a la...
 1.1.3.78: In Exercises 71 to 80, determine the discriminant of the quadratic ...
 1.78: Mean Waist Size If a researcher wanted to know the mean waist size ...
 1.1.4.78: Diameter of a Cone As flour is poured onto a table, it forms a righ...
 1.1.3.79: In Exercises 71 to 80, determine the discriminant of the quadratic ...
 1.79: Basketball Dimensions A basketball is to have a circumference of 29...
 1.1.4.79: Precious Metals A solid silver sphere has a diameter of 8 millimete...
 1.1.3.80: In Exercises 71 to 80, determine the discriminant of the quadratic ...
 1.80: Population Density The population density in people per square mile...
 1.1.4.80: Pendulum The period T of a pendulum is the time it takes the pendul...
 1.1.3.81: Geometry The length of each side of an equilateral triangle is 31 c...
 1.81: Physics Force F is directly proportional to acceleration a. If a fo...
 1.1.4.81: Distance to the Horizon On a ship, the distance that you can see to...
 1.1.3.82: Dimensions of a Baseball Diamond How far, to the nearest tenth of a...
 1.82: Physics The distance an object will fall on the moon is directly pr...
 1.1.4.82: As mentioned in the chapter opener, the golden mean, F , occurs in ...
 1.1.3.83: Dimensions of a Television Screen A television screen measures 54 i...
 1.83: Business The number of MP3 players a company can sell is inversely ...
 1.1.4.83: As mentioned in the chapter opener, the golden mean, F , occurs in ...
 1.1.3.84: Publishing Costs The cost, in dollars, of publishing x books is C(x...
 1.84: Magnetism The repulsive force between the north poles of two magnet...
 1.1.4.84: Providing Power A power station is on one side of a river that is 1...
 1.1.3.85: Sports The height of a kicked football during a field goal attempt ...
 1.85: Acceleration The acceleration due to gravity on the surface of a pl...
 1.1.4.85: Triathlon Training To prepare for a triathlon, a person swims acros...
 1.1.3.86: Revenue The demand for a certain product is given by p = 26  0.01x...
 1.1.3.87: Profit A company has determined that the profit, in dollars, it can...
 1.1.3.88: Quadratic Growth A plants ability to create food through the proces...
 1.1.3.89: Dimensions of an Animal Enclosure A veterinarian wishes to use 132 ...
 1.1.3.90: Construction of a Box A square piece of cardboard is formed into a ...
 1.1.3.91: Population Density of a City The population density (in people per ...
 1.1.3.92: Traffic Control Traffic engineers install flow lights at the entran...
 1.1.3.93: Daredevil Motorcycle Jump In March 2000, Doug Danger made a success...
 1.1.3.94: Dimensions of a Candy Bar A company makes rectangular solid candy b...
 1.1.3.95: Height of a Rocket A model rocket is launched upward with an initia...
 1.1.3.96: Baseball The height in feet, of a baseball above the ground t secon...
 1.1.3.97: Baseball Two equations can be used to track the position of a baseb...
 1.1.3.98: Basketball Michael Jordan was known for his hang time, which is the...
 1.1.3.99: Number of Handshakes If everyone in a group of n people shakes hand...
 1.1.3.100: Data Storage The projected data storage requirements D, in petabyte...
 1.1.3.101: Centenarians According to data provided by the U.S. Census Bureau, ...
 1.1.3.102: Automotive Engineering The number of feet that a car needs to stop ...
 1.1.3.103: Orbital Debris The amount of space debris is increasing. The number...
Solutions for Chapter 1: Equations and Inequalities
Full solutions for College Algebra  7th Edition
ISBN: 9781439048610
Solutions for Chapter 1: Equations and Inequalities
Get Full SolutionsSince 504 problems in chapter 1: Equations and Inequalities have been answered, more than 25956 students have viewed full stepbystep solutions from this chapter. Chapter 1: Equations and Inequalities includes 504 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. College Algebra was written by and is associated to the ISBN: 9781439048610. This textbook survival guide was created for the textbook: College Algebra, edition: 7.

Column space C (A) =
space of all combinations of the columns of A.

Complete solution x = x p + Xn to Ax = b.
(Particular x p) + (x n in nullspace).

Condition number
cond(A) = c(A) = IIAIlIIAIII = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A

Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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

Kirchhoff's Laws.
Current Law: net current (in minus out) is zero at each node. Voltage Law: Potential differences (voltage drops) add to zero around any closed loop.

Linear transformation T.
Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

Multiplicities AM and G M.
The algebraic multiplicity A M of A is the number of times A appears as a root of det(A  AI) = O. The geometric multiplicity GM is the number of independent eigenvectors for A (= dimension of the eigenspace).

Multiplier eij.
The pivot row j is multiplied by eij and subtracted from row i to eliminate the i, j entry: eij = (entry to eliminate) / (jth pivot).

Norm
IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

Pivot.
The diagonal entry (first nonzero) at the time when a row is used in elimination.

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Pseudoinverse A+ (MoorePenrose inverse).
The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

Semidefinite matrix A.
(Positive) semidefinite: all x T Ax > 0, all A > 0; A = any RT R.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t  k).