Elementary Algebra. Toby Wagner. Math 70 Spring 2018 Corrections

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1 Corrections are listed by section then page number. There is a small description of the mistake followed by the correct text highlighted in yellow. Wagner Elementary Algebra aff, f this Math 70 Spring 018 Corrections Elementary Algebra Toby Wagner

2 Section 1.1 Page 13 In Example 10, step 3 had an incorrect fraction of 7 Example 10 A rectangle that is 14 feet long has an area of 91 square feet. What is the width of the rectangle? Solution Step 1: Let x = the width of the rectangle. We are given the length of the rectangle and the area. The width is unknown. Step : We know that for a rectangle, Length Width = Area. 14x = 91 In this problem, the length is 14, and the area is 91. Step 3: Now solve the equation using the properties in 14x = 91 this chapter. 14x 14 = x = 6.5 Step 4: = 91 Step 5: The width of the rectangle is 6.5 feet. 14 Then translate the solution into a written sentence. Section.7 Page 156 In the Turning Off the Plotting Feature box the graphing calculator buttons were showing up incorrectly. Turning Off the Plotting Feature If the plotting feature of your calculator is turned on but there aren t any numbers in your lists, the calculator will give you an error message any time you try to graph anything. For this reason, it s a good idea to turn the plotting feature off when you re finished creating scatterplots. To turn the plotting feature off: 1. Access the, menu by pressing y and then o.. Press Í and then toggle Plot 1 to Off.

3 Section.8 Page 170 The solution to question 5 in Example 4 was incorrectly stated as y = 3 _ x x + 6y = 8 Once again, we need to solve for y first. 9x + 6y = 8 + 9x + 9x 6y = 9x + 8 6y 6 = 9x y = 3 x Because both slopes are positive, the slope of this line is not the opposite-reciprocal of the slope of the given line. They are not perpendicular. Section 4.1 Page 31 The first form of the distributive property in the beginning paragraph of section C was incorrectly stated as a(b + c) = ab + bc C. Simplifying Expressions Containing Parentheses When parentheses occur in an expression, they should be removed before the like terms are combined. To remove the parentheses, we use the distributive property: a(b + c) = ab + ac and a(b c) = ab ac

4 Page 34 On the second-to-last line of Example 8, the expression was written incorrectly as 3 x + 7x x + 5x Example 8 Add 4 x + x 8 to 3 x 7x 10. Solution The phrase add A to B implies that we begin with B and then add A. In this case, we begin our expression with 3 x 7x 10. ( 3 x 7x 10) + ( 4 x + x 8) Both of the polynomials are written with parentheses. 3 x - 7x x + x 8 Remove the parentheses. Leave the sign of each term the same. 7 x 5x 18 Combine the like terms. Section 4.4 Page 6 In The Power Rule for Powers box, the exponents on the right side of the equation were incorrectly labelled with an addition sign. The Power Rule for Powers If A is a real number, and if m and n are natural numbers, then ( A m ) n = A m n n.

5 Section 4.6 Page 86 On the top line of page 86, in Example, the numerator of the second fraction was incorrectly missing a zero. In the last line of the paragraph following the Example, the conversion fraction was incorrectly missing a zero as well. = 3 m 1 10,000 cm Multiply the numbers, and use the product rule for ( 1 m ) exponents to combine units. = 3 m 10,000 cm Now we can cancel the m. 1 1 m = 30,000 cm 1 = 30,000 cm Finish simplifying the result. When converting square units or cubic units, we can shorten the process slightly by writing a single conversion fraction and then squaring (or cubing) all of the numbers and units in that fraction. By doing this, we avoid writing multiple conversion fractions. In the previous example, we could have written a single conversion fraction, 100 cm, instead of the two conversion fractions that we wrote. 1 m Section 5.1 Page 308 In the second paragraph it incorrectly stated that 4x + 5 is the same as 1(4x 5). Sometimes the only common factor of all the terms in a polynomial is 1, but there s no benefit to factoring 1 out of a polynomial. 4x + 5 is the same as 1(4x x + 5), and the new expression isn t any different than the original. It is thus trivial to write this polynomial in factored form. In some cases, however, it may be possible to produce a non-trivial factored form for the polynomial.

6 Section 5. Page In the 5. Exercise section, questions 16 and 30 both had two questions combined. Below is a corrected section. Exercises 5. For the following problems, factor the trinomials when possible. You may have to factor out a GCF as the first step. 1. x + 4x y 8y y 70y x + 6x x + 7x x + 6x y + 8y y 5y y 5y a + a 6 9. a + 3a x + 4x x 4x 1 1. c 8c y + 10y x + 6x n + n t 5t y 5y a + a a 3a + 1. a 1a + 0. y 4y 3 3. x + 13x x + x x + 13x y + 6y 7 7. b 5b x + 7x b + 15b a + 4a x + 1x a 18a x 54x x x + 8x 36. x 3 8 x + 15x 37. x + x y 4y x x x 40. a 3 1 a 10a a a 84a 4. 3x m 33xm 54x 43. y n + 10 y n + 48 y x 4 4 x x 45. y y y x a 6 48 x a x a 4 Section 6.1 Page 349 In Exercise 59, the equation given incorrectly had an addition sign. 59. The height of a ball thrown into the air can be modeled by the equation h = t 16 t, here h represents the ball s height in feet, and t represents the number of seconds that elapse after the ball is thrown.

7 Section 6. Page 35 In the second paragraph following Example 1, the letter C was incorrectly used. In the expression x, the root symbol,, is called a radical sign. The value within the radical sign, x, is called the radicand. The horizontal bar of the radical sign acts as a grouping symbol that shows what the radicand is. When we put the radical and radicand together, the expression, x, is called a radical expression. These terms are derived from the Latin word radix, which means root. Page 360 The answer for Practice question 18 was incorrectly stated as 4 3. Practice C Answers Section 6.6 Page 403 The graph in Example 6 was incorrect. Example 6 Use the given graph to help you solve the equation: 3 x + 30x 7 = 0

8 Odd Numbered Exercises Page 416 Answer 13 was incorrectly stated as 19,500 fish..1 Introduction to Linear Models 1. a) The total cost is $7.30. b) Your friends can afford to purchase 4 burritos. 3. a) $40 was available at the beginning of the month. b) $84 was available after three weeks. 5. a) It takes 7 weeks. b) The boxer weighs pounds after three weeks. c) The boxer will be in the super middleweight weight class after 6 weeks. 7. a) The cost is $ b) About 5.45 gallons of gasoline can be purchased. 9. a) 95 gallons of water will be in the tank. b) 600 gallons of water will remain after 5 minutes. c) The tank will be empty after minutes. 11. a) Andre will be,40 miles from his destination. b) After 1 days of riding, he will be 1,540 miles from his destination. c) He will reach his destination after 6 days of riding. 13. a) 19,000 fish will be in Loch Lake. b),000 fish will be in the lake after 8 years. 15. Table Table Table 5 1. Graph 4 3. Graph 3 5. Graph 6 7. Graph 8

9 Page 418 Answer 17 was using an incorrect graph..4 Slope-Intercept Form

10 Page 40 Answer 35 was using the incorrect variable..6 Ordered Pairs and Equations 1. y = 3x y = 8x y = 6x 1 7. y = 3 x 9. y 1 = (x 5) 11. y 3 = 5(x + 10) 13. y + 6 = 3 (x + 1) y + 10 = 8 (x 3) y = x y = 8x 3 1. y = x y = x y = 6 7 x y = 5 x y = 1 9 x y = y = x = y = 8 5 x 39. y = x y = 3x y = x = y = 4x y = 9 5 x y = 9 7 x Variables: x = number of party guests (people), y = number of cookies baked. Equation: y = 3x Variables: x = number of police officers parked on the side of the highway (people), y = number of passing drivers who are speeding (people per minute). Equation: y = 8x Variables: x: temperature (degrees), y = number of athletes who complain (people). Equation: y = 1 3 x 18 Page 47 The title for section 5. was labelled incorrectly. 5. Factoring Trinomials of the Form x² + bx + c