1. Splash Screen

2. Chapter Menu Lesson 3-1Lesson 3-1Square Roots Lesson 3-2Lesson 3-2Estimating Square Roots Lesson 3-3Lesson 3-3Problem Solving Investigation: Use a Venn Diagram Lesson 3-4Lesson 3-4The Real Number System Lesson 3-5Lesson 3-5The Pythagorean Theorem Lesson 3-6Lesson 3-6Using the Pythagorean Theorem Lesson 3-7Lesson 3-7Distance on the Coordinate Plane

3. Lesson 3-1 Menu Five-Minute CheckFive-Minute Check (over Chapter 2) Main Idea and Vocabulary Targeted TEKS Example 1: Find Square Roots Example 2: Find Square Roots Example 3: Find Square Roots Example 4: Use Square Roots to Solve an Equation Example 5:Use Square Roots to Solve a Problem

4. Lesson 3-1 Ideas/Vocabulary Find square roots of perfect squares. Perfect square –Squares of integers square root –OPPOSITE of squaring a number –Means “what number times itself” radical sign –The square root symbol

5. Lesson 3-1 TEKS Square Roots  √ X means “What number times itself = X”  Every POSITIVE number has TWO square roots!!  EX: √64 = +8 and – 8  EX: √100 = +10 and –10  To find the square roots of fractions, find the square root of the numerator and denominator.  EXAMPLE: √(16/64)  = √16 / √64 = 4/8 = ½ and – ½  Remember: Whatever I do to one side of an equation  I MUST DO THE SAME THING TO THE OTHER SIDE!  If they ask me to solve an algebra equation with a squared term, THEY WANT BOTH THE POSITIVE AND NEGATIVE SOLUTIONS!!

6. Lesson 3-1 Example 1 Find Square Roots Answer: indicates the positive square root of 81. Interactive Lab: Square Roots Find

7. A. A B. B C. C D. D Lesson 3-1 Example 1 CYP A.4 B.6 C.8 D.16 Find

8. Lesson 3-1 Example 2 Answer: indicates the negative square root of Find Square Roots Find

9. A. A B. B C. C D. D Lesson 3-1 Example 2 CYP A. B. C. D. Find

10. Lesson 3-1 Example 3 Find Square Roots Answer: Since (1.2) 2 = 1.44 and (–1.2) 2 = 1.44, = ±1.2, or 1.2 and –1.2. indicates both the positive and negative square roots of 1.44. Find

11. A. A B. B C. C D. D Lesson 3-1 Example 3 CYP A.±1.2 B.±1.25 C.±1.5 D.±1.75 Find

12. x 2 =225Write the equation. Lesson 3-1 Example 4 ALGEBRA Solve x 2 = 225. Answer: The equation has two solutions, 15 and –15. Use Square Roots to Solve an Equation x=15 and x = –15Check 15  15 = 225 and (–15)  (–15) = 225 x=Definition of square root

13. A. A B. B C. C D. D Lesson 3-1 Example 4 CYP A.–9 B.9 C.–9 and 9 D.–8 and 8 ALGEBRA Solve x 2 = 81.

14. Area is equal to the square of the length of a side. Lesson 3-1 Example 5 MUSIC The art work on the square picture in a compact disc case is approximately 14,161 mm 2 in area. Find the length of each side of the square. Words Variable Equation Let s represent the length of a side. 14,161 = s 2 Use Square Roots to Solve a Problem

15. Lesson 3-1 Example 5 Answer: The length of a side of a compact disc case is about 119 millimeters since distance cannot be negative. 14,161=s 2 Write the equation. =sDefinition of square root ENTER = 2nd c 14161Use a calculator. 119=s Use Square Roots to Solve a Problem

16. A. A B. B C. C D. D Lesson 3-1 Example 5 CYP A.85 inches B.93 inches C.95 inches D.105 inches ART A piece of art is a square picture that is approximately 11,025 square inches in area. Find the length of each side of the square picture.

17. End of Lesson 3-1

18. Lesson 3-2 Menu Five-Minute CheckFive-Minute Check (over Lesson 3-1) Main Idea Targeted TEKS Example 1:Estimate Square Roots Example 2:Estimate Square Roots Example 3:Estimate Square Roots to Solve a Problem

19. Lesson 3-2 Ideas/Vocabulary Estimate square roots.

20. Lesson 3-2 TEKS  Estimating Square Roots – PART 1 To Estimate a NON-PERFECT square root: 1.Find the nearest perfect square LOWER 2.Find the nearest perfect square HIGHER 3.Graph them on a number line 4.“Guesstimate” the square root.  When estimating square roots, IT IS VERY USEFUL TO PLOT NUMBERS ON A NUMBER LINE.

21. Lesson 3-2 Example 1 Estimate Square Roots The first perfect square greater than 54 is 64. The first perfect square less than 54 is 49. Estimate to the nearest whole number. Plot each square root on a number line. Then plot.

22. Lesson 3-2 Example 1 Estimate Square Roots 49 < 54 < 64Write an inequality. 7 2 < 54 < 8 2 49 = 7 2 and 64 = 8 2 Find the square root of each number. 7 < < 8Simplify. Answer: So, is between 7 and 8. Since 54 is closer to 49 than 64, the best whole number estimate for is 7.

23. A. A B. B C. C D. D Lesson 3-2 Example 1 CYP A.5 B.6 C.7 D.8 Estimate to the nearest whole number.

24. Lesson 3-2 Example 2 Estimate Square Roots The first perfect square greater than 41.3 is 49. The first perfect square less than 41.3 is 36. Estimate to the nearest whole number. Plot each square root on a number line. Then plot

25. 6 < < 7Simplify. Find the square root of each number. Lesson 3-2 Example 2 Estimate Square Roots 36 < 41.3 < 49Write an inequality. 6 2 < 41.3 < 7 2 36 = 6 2 and 49 = 7 2 Answer: So, is between 6 and 7. Since 41.3 is closer to 36 than 49, the best whole number estimate for is 6.

26. Estimate to the nearest whole number. A. A B. B C. C D. D Lesson 3-2 Example 2 CYP A.3 B.4 C.5 D.6

27. Lesson 3-2 Example 3 FINANCE If you were to invest $100 in a bank account for two years, your investment would earn interest daily and be worth more when you withdrew it. If you had $120 after two years, the interest rate, written as a decimal, would be found using the expression. Estimate this value. Estimate Square Roots to Solve a Problem

28. Lesson 3-2 Example 3 100 < 120 < 121100 and 121 are the closest perfect squares. 10 2 < 120 < 11 2 100 = 10 2 and 121 = 11 2 10 < < 11Find the square root of each number. First estimate the value of Estimate Square Roots to Solve a Problem

29. Lesson 3-2 Example 3 Answer: The approximate interest rate is 0.10 or 10%. Since 120 is closer to 121 than 100, the best whole number estimate for is 11. Use this to evaluate the expression. Estimate Square Roots to Solve a Problem

30. Lesson 3-2 Example 3 CYP FINANCE If you were to invest $100 in a bank account for two years, your investment would earn interest daily and be worth more when you withdrew it. If you had $150 after two years, the interest rate, written as a decimal, would be found using the expression. Estimate this value.

31. A. A B. B C. C D. D Lesson 3-2 Example 3 CYP A.0.10 B.0.15 C.0.20 D.0.25 FINANCE Estimate the value of.

32. End of Lesson 3-2

33. Lesson 3-3 Menu Five-Minute CheckFive-Minute Check (over Lesson 3-2) Main Idea Targeted TEKS Example 1:Use a Venn Diagram

34. Lesson 3-3 Ideas/Vocabulary Use a Venn diagram to solve problems.

35. Lesson 3-3 TEKS  A Venn Diagram usually consists of 2 or 3 circles that intersect each other.  Area that intersects represents number of people involved in BOTH circles!  To create Venn Diagrams do the following: 1)Figure out how many people go in the intersecting areas. – START IN THE MIDDLE! 2)Subtract to find out how many ppl are in the non-intersecting areas.  REMEMBER: THE TOTAL NUMBER OF PEOPLE IN EACH CATEGORY IS THE TOTAL NUMBER IN THE CIRCLE!!!

36. Lesson 3-3 Example 1 LANGUAGES Of the 40 foreign exchange students attending a middle school, 20 speak French, 23 speak Spanish, and 22 speak Italian. Nine students speak French and Spanish, but not Italian. Six students speak French and Italian, but not Spanish. Ten students speak Spanish and Italian, but not French. Only 4 students speak all three languages. Use a Venn diagram to find how many exchange students do not speak any of these languages. Use a Venn Diagram

37. Lesson 3-3 Example 1 ExploreYou know how many students speak each of the different languages. You want to organize the information. Use a Venn Diagram PlanMake a Venn diagram to organize the information. SolveDraw three overlapping circles to represent the three different languages. Since 4 students speak all 4 languages, place a 4 in the section that represents all three languages. Use the other information given in the problem to fill in the other sections as appropriate.

38. Solve Lesson 3-3 Example 1 Use a Venn Diagram Add the numbers in each region of the diagram: 1 + 9 + 6 + 4 + 10 + 2 = 32 Since there are 40 exchange students altogether, 40 – 32 = 8 of them do not speak French, Spanish, or Italian.

39. CheckCheck each circle to see if the appropriate number of students is represented. Lesson 3-3 Example 1 Use a Venn Diagram Answer:Eight of the exchange students do not speak French, Spanish, or Italian.

40. Lesson 3-3 Example 1 CYP SPORTS Of the 30 students in Mr. Hall’s gym class, 14 students play basketball, 9 students play soccer, and 11 students play volleyball. Three students play basketball and soccer, but not volleyball. One student plays soccer and volleyball, but not basketball. Six students play basketball and volleyball, but not soccer. Only 2 students play all three sports. Use a Venn diagram to organize this information and then answer the question on the next slide.

41. A. A B. B C. C D. D Lesson 3-3 Example 1 CYP A.6 students B.8 students C.9 students D.10 students How many students in Mr. Hall’s gym class do not play basketball, soccer, or volleyball?

42. End of Lesson 3-3

43. Lesson 3-4 Menu Five-Minute CheckFive-Minute Check (over Lesson 3-3) Main Idea and Vocabulary Targeted TEKS Key Concept: Irrational Numbers Example 1:Classify Numbers Example 2:Classify Numbers Example 3:Classify Numbers Concept Summary: Real Number Properties Example 4:Graph Real Numbers Example 5:Compare Real Numbers Example 6:Compare Real Numbers Example 7: Compare Real Numbers to Solve a Problem

44. Rational Numbers –Numbers that can be written as a fraction –Includes all WHOLE numbers and INTEGERS –Whole numbers = 0, 1, 2, 3 … –Integers = …, -3, -2, -1, 0, 1, 2, 3 … Irrational Number –Any number that CAN NOT be written as a fraction –IT NEVER REPEATS AND NEVER ENDS! Real Numbers –All rational and irrational numbers Lesson 3-4 Ideas/Vocabulary Identify and classify numbers in the real number system.

45. Lesson 3-4 TEKS  CLASSIFYING NUMBERS  There are two kinds of Irrational Numbers A. Constants like PI B. Square Roots of NON-PERFECT squares (and other roots of non-perfect numbers, but that’s for Algebra 2!)  EVERYTHING ELSE IS A RATIONAL NUMBER!!

46. Lesson 3-4 TEKS NOTES – CONT. ESTIMATING NON-PERFECT SQUARE ROOTS – Part 2  To Estimate a NON-PERFECT square root: 1.Find the nearest perfect square LOWER 2.Find the nearest perfect square HIGHER 3.Graph them on a number line 4.“Guesstimate” the square root.  COMPARING REAL NUMBERS – I can only compare things in math that ????  To compare a rational and irrational number, SQUARE BOTH OF THEM!

47. Lesson 3-4 Key Concept 1

48. Name all sets of numbers to which 0.090909… belongs. The decimal ends in a repeating pattern. Lesson 3-4 Example 1 Classify Numbers Answer: It is a rational number because it is equivalent to

49. A. A B. B C. C D. D Lesson 3-4 Example 1 CYP A.rational B.irrational C.whole, rational D.integer, rational Name all sets of numbers to which 0.1010101010… belongs.

50. Lesson 3-4 Example 2 Classify Numbers Name all sets of numbers to which belongs. Answer: Since, it is a whole number, an integer, and a rational number.

51. A. A B. B C. C D. D Lesson 3-4 Example 2 CYP A.integer B.integer, rational C.integer, whole D.integer, rational, whole Name all sets of numbers to which belongs.

52. Lesson 3-4 Example 3 Classify Numbers Answer: Since the decimal does not repeat or terminate, it is an irrational number. Name all sets of numbers to which belongs.

53. A. A B. B C. C D. D Lesson 3-4 Example 3 CYP A.rational B.irrational C.integer D.integer, irrational Name all sets of numbers to which belongs.

54. Lesson 3-4 Concept Summary 1

55. Lesson 3-4 Example 4 Graph Real Numbers Answer: Estimate and to the nearest tenth. Then graph and on a number line. or about 2.8 or about –1.4

56. Lesson 3-4 Example 4 CYP Estimate and to the nearest tenth. Then graph and on a number line. Answer:

57. Lesson 3-4 Example 5 Compare Real Numbers Write each number as a decimal. Replace  with, or = to make a true sentence. Answer:Since 3.875 is greater than 3.872983346…,

58. Lesson 3-4 Example 5 CYP 1.A 2.B 3.C A.< B.> C.= Replace  with, or = to make a true sentence.

59. Lesson 3-4 Example 6 Compare Real Numbers Replace  with, or = to make a true sentence. Write as a decimal. Answer:Since is less than 3.224903099…,

60. Lesson 3-4 Example 6 CYP 1.A 2.B 3.C A.< B.> C.= Replace  with, or = to make a true sentence.

61. Lesson 3-4 Example 7 BASEBALL The time in seconds that it takes an object to fall d feet is How many seconds would it take for a baseball that is hit 250 feet straight up in the air to fall from its highest point to the ground? Replace d with Answer: It will take about 4 seconds for the baseball to fall to the ground. Compare Real Numbers to Solve a Problem ≈ 3.95 or about 4Simplify. ≈ 0.25  15.81Use a calculator. ≈ 15.81

62. A. A B. B C. C D. D Lesson 3-4 Example 7 CYP A.about 4.9 seconds B.about 5.3 seconds C.about 5.6 seconds D.about 6.2 seconds BASEBALL The time in seconds that it takes an object to fall d feet is How many seconds would it take for a baseball that is hit 450 feet straight up in the air to fall from its highest point to the ground?

63. End of Lesson 3-4

64. Lesson 3-5 Menu Five-Minute CheckFive-Minute Check (over Lesson 3-4) Main Idea and Vocabulary Targeted TEKS Key Concept: Pythagorean Theorem Example 1: Find the Length of a Side Example 2:Find the Length of a Side Key Concept: Converse of Pythagorean Theorem Example 3:Identify a Right Triangle

65. Legs –The shorter sides of a RIGHT triangle –The sides that form the RIGHT angle Hypotenuse –The LONGEST side of a RIGHT triangle Pythagorean Theorem –Describes the relationship between the legs and hypotenuse of RIGHT triangles! –ONLY APPLIES TO RIGHT TRIANGLES!! Converse –“The opposite of” Lesson 3-5 Ideas/Vocabulary Use the Pythagorean Theorem.

66. Lesson 3-5 TEKS  In a Right triangle:  A 2 + B 2 = C 2  Can be used to find the third side of any right triangle if I know the other two sides.

67. Lesson 3-5 Example 1 Write an equation to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth, if necessary. Find the Length of a Side

68. c 2 =a 2 + b 2 Pythagorean Theorem Lesson 3-5 Example 1 Answer: The equation has two solutions, 20 and –20. However, the length of a side must be positive. So, the hypotenuse is 20 inches long. Find the Length of a Side c 2 =12 2 + 16 2 Replace a with 12 and b with 16. c 2 =144 + 256Evaluate 12 2 and 16 2. c 2 =400Add 144 and 256. c= 20 or –20Simplify. c= Definition of square root

69. A. A B. B C. C D. D Lesson 3-5 Example 1 CYP A.17 in. B.19 in. C.20 in. D.21 in. Write an equation to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth, if necessary.

70. Lesson 3-5 Example 2 The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. What is a, the length of the other leg? Find the Length of a Side c 2 =a 2 + b 2 Pythagorean Theorem 33 2 =a 2 + 28 2 Replace c with 33 and b with 28. 1,089=a 2 + 784Evaluate 33 2 and 28 2. 1,089 – 784=a 2 + 784 – 784Subtract 784 from each side. 305=a 2 Simplify. =aDefinition of square root 17.5≈aUse a calculator.

71. Lesson 3-5 Example 2 Answer: The length of the other leg is about 17.5 centimeters. Find the Length of a Side

72. A. A B. B C. C D. D Lesson 3-5 Example 2 CYP A.about 16.2 cm B.about 18.5 cm C.about 19.7 cm D.about 21.4 cm The hypotenuse of a right triangle is 26 centimeters long and one of its legs is 17 centimeters. What is a, the length of the other leg?

73. Lesson 3-5 Key Concept 2

74. Lesson 3-5 Example 3 The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle. Identify a Right Triangle c 2 =a 2 + b 2 Pythagorean Theorem 25 2 =7 2 + 24 2 Replace a with 7, b with 24, and c with 25. ? ? 625=49 + 576Evaluate 25 2, 7 2, and 24 2. 625=625Simplify. Answer: The triangle is a right triangle.

75. Lesson 3-5 CYP 3 1.A 2.B 3.C A.It is a right triangle. B.It is not a right triangle. C.Not enough information to determine. The measures of three sides of a triangle are 13 inches, 5 inches, and 12 inches. Determine whether the triangle is a right triangle.

76. End of Lesson 3-5

77. Lesson 3-6 Menu Five-Minute CheckFive-Minute Check (over Lesson 3-5) Main Idea Targeted TEKS Example 1:Use the Pythagorean Theorem to Solve a Problem Example 2:Test Example

78. Lesson 3-6 Ideas/Vocabulary Solve problems using the Pythagorean Theorem.

79. Lesson 3-6 TEKS  To Solve problems with the Pythagorean Theorem: 1.Draw and Label a picture 2.Write down the Pythagorean Theorem 3.“Plug in what you know, and solve for what you don’t!” 1.Be CAREFUL to plug the hypotenuse in for C!!!!

80. Lesson 3-6 Example 1 RAMPS A ramp to a newly constructed building must be built according to the guidelines stated in the Americans with Disabilities Act. If the ramp is 24.1 feet long and the top of the ramp is 2 feet off the ground, how far is the bottom of the ramp from the base of the building? Notice the problem involves a right triangle. Use the Pythagorean Theorem. Use the Pythagorean Theorem to Solve a Problem

81. Lesson 3-6 Example 1 Answer: The end of the ramp is about 24 feet from the base of the building. 24.1 2 =a 2 + 2 2 Replace c with 24.1 and b with 2. 580.81=a 2 + 4Evaluate 24.1 2 and 2 2. 580.81 – 4=a 2 + 4 – 4Subtract 4 from each side. 576.81=a 2 Simplify. 24.0≈aSimplify. =aDefinition of square root Use the Pythagorean Theorem to Solve a Problem

82. A. A B. B C. C D. D Lesson 3-6 Example 1 CYP A.about 30.4 feet B.about 31.5 feet C.about 33.8 feet D.about 35.1 feet RAMPS If a truck ramp is 32 feet long and the top of the ramp is 10 feet off the ground, how far is the end of the ramp from the truck?

83. Lesson 3-6 Example 2 The cross-section of a camping tent is shown below. Find the width of the base of the tent. A.6 ft B.8 ft C.10 ft D.12 ft Use the Pythagorean Theorem

84. Lesson 3-6 Example 2 Read the Test Item From the diagram, you know that the tent forms two congruent right triangles. Let a represent half the base of the tent. Then w = 2a. Use the Pythagorean Theorem

85. Lesson 3-6 Example 2 Solve the Test Item c 2 =a 2 + b 2 Write the relationship. 10 2 =a 2 + 8 2 c = 10 and b = 8 100=a 2 + 64Evaluate 10 2 and 8 2. 100 – 64=a 2 + 64 – 64Subtract 64 from each side. 36=a 2 Simplify. Use the Pythagorean Theorem. =aDefinition of square root 6=aSimplify. Use the Pythagorean Theorem

86. Lesson 3-6 Example 2 Answer: The width of the base of the tent is 2a or (2)6 = 12 feet. Therefore, choice D is correct. The cross-section of a camping tent is shown below. Find the width of the base of the tent. A.6 ft B.8 ft C.10 ft D.12 ft Use the Pythagorean Theorem

87. A. A B. B C. C D. D Lesson 3-6 Example 2 CYP A.15 ft B.18 ft C.20 ft D.22 ft This picture shows the cross-section of a roof. How long is each rafter, r?

88. End of Lesson 3-6

89. Lesson 3-7 Menu Five-Minute CheckFive-Minute Check (over Lesson 3-6) Main Ideas and Vocabulary Targeted TEKS Example 1:Name an Ordered Pair Example 2:Name an Ordered Pair Example 3:Graphing Ordered Pairs Example 4:Graphing Ordered Pairs Example 5:Find Distance on the Coordinate Plane Example 6: Use a Coordinate Plane to Solve a Problem

90. coordinate plane – TURN TO PAGE 173 AND DRAW A COORDINATE PLANE Lesson 3-7 Ideas/Vocabulary Graph rational numbers on the coordinate plane. origin y-axis x-axis quadrants ordered pair x-coordinate abscissa y-coordinate ordinate Find the distance between two points on the coordinate plane.

91. Lesson 3-7 TEKS  To graph a point on a coordinate  Move LEFT or RIGHT on the X axis FIRST  Move UP or DOWN on the Y axis SECOND  Remember “RUN BEFORE YOU JUMP!”  To Find the Distance between two points do the following: 1.DRAW a right triangle connecting the dots using the gridlines on the graph 2.FIND the lengths of the legs (count or subtract) 3.USE the Pythagorean Theorem to find the distance.

92. Start at the origin. Lesson 3-7 Example 1 Name the ordered pair for point A. Name an Ordered Pair Move right to find the x-coordinate of point A, which is 2. Move up to find the y-coordinate, which is Answer: So, the ordered pair for point A is

93. A. A B. B C. C D. D Lesson 3-7 Example 1 CYP A. B. C. D. Name the ordered pair for point A.

94. Start at the origin. Lesson 3-7 Example 2 Name the ordered pair for point B. Name an Ordered Pair Move down to find the y-coordinate, which is –2. Move left to find the x-coordinate of point B, which is Answer: So, the ordered pair for point B is

95. A. A B. B C. C D. D Lesson 3-7 Example 2 CYP A. B. C. D. Name the ordered pair for point B.

96. Start at the origin and move 3 units to the left. Then move up 2.75 units. Draw a dot and label it J(–3, 2.75). Lesson 3-7 Example 3 Graph and label point J(–3, 2.75). Graphing Ordered Pairs Answer:

97. A. A B. B C. C D. D Lesson 3-7 Example 3 CYP Graph and label point J(–2.5, 3.5). A. B. C. D.

98. Lesson 3-7 Example 4 Graphing Ordered Pairs Answer: Graph and label point K Start at the origin and move 4 units to the right. Then move down units. Draw a dot and label it K

99. A. A B. B C. C D. D Lesson 3-7 Example 4 CYP Graph and label point K A. B. C. D.

100. Let c = the distance between the two points, a = 5, and b = 5. Lesson 3-7 Example 5 Graph the ordered pairs (0, –6) and (5, –1). Then find the distance between the points. Find Distance in the Coordinate Plane

101. Lesson 3-7 Example 5 Find Distance in the Coordinate Plane Answer: The points are about 7.1 units apart. c 2 =a 2 + b 2 Pythagorean Theorem c≈7.1Simplify. =Definition of square root c 2 =5 2 + 5 2 Replace a with 5 and b with 5. c 2 =505 2 + 5 2 = 50

102. A. A B. B C. C D. D Lesson 3-7 Example 5 CYP A.about 3.1 units B.about 3.6 units C.about 3.9 units D.about 4.2 units Graph the ordered pairs (0, –3) and (2, –6). Then find the distance between the points.

103. Lesson 3-7 Example 6 TRAVEL Melissa lives in Chicago, Illinois. A unit on the grid of her map shown below is 0.08 mile. Find the distance between McCormickville at (–2, –1) and Lake Shore Park at (2, 2). Let c = the distance between McCormickville and Lake Shore Park. Then a = 3 and b = 4. Use a Coordinate Plane to Solve a Problem

104. Lesson 3-7 Example 6 Answer: Since each unit equals 0.08 mile, the distance is 0.08  5 or 0.4 mile. c 2 =a 2 + b 2 Pythagorean Theorem c=5Simplify. c 2 =3 2 + 4 2 Replace a with 3 and b with 4. c 2 =253 2 + 4 2 = 25 =Definition of square root The distance between McCormickville and Lake Shore Park is 5 units on the map. Use a Coordinate Plane to Solve a Problem

105. A. A B. B C. C D. D Lesson 3-7 Example 6 CYP A.about 0.1 mile B.about 0.2 mile C.about 0.3 mile D.about 0.4 mile TRAVEL Sato lives in Chicago. A unit on the grid of his map shown below is 0.08 mile. Find the distance between Shantytown at (2, –1) and the intersection of N. Wabash Ave. and E. Superior St. at (–3, 1).

106. End of Lesson 3-7

107. Resources Menu Five-Minute Checks Image Bank Math Tools Square Roots The Pythagorean Theorem

108. Lesson 3-1Lesson 3-1 (over Chapter 2) Lesson 3-2Lesson 3-2(over Lesson 3-1) Lesson 3-3Lesson 3-3(over Lesson 3-2) Lesson 3-4Lesson 3-4(over Lesson 3-3) Lesson 3-5Lesson 3-5(over Lesson 3-4) Lesson 3-6Lesson 3-6(over Lesson 3-5) Lesson 3-7Lesson 3-7(over Lesson 3-6) Five-Minute Menu

109. Image Bank 1 To use the images that are on the following three slides in your own presentation: 1.Exit this presentation. 2.Open a chapter presentation using a full installation of Microsoft ® PowerPoint ® in editing mode and scroll to the Image Bank slides. 3.Select an image, copy it, and paste it into your presentation.

110. Image Bank 2

111. Image Bank 3

112. Image Bank 4

113. A. A B. B C. C D. D (over Chapter 2) 5 Min 1-1 A.1.2... B.0.911 C.0.8181... D.0.11 Write the fraction as a decimal.

114. A. A B. B C. C D. D (over Chapter 2) 5 Min 1-2 A.7.6 B.6.625 C.5.375 D.3.75 Write the mixed number as a decimal.

115. A. A B. B C. C D. D (over Chapter 2) 5 Min 1-3 A. B. C. D. Multiply. Write in simplest form.

116. A. A B. B C. C D. D (over Chapter 2) 5 Min 1-4 A.–27 B.–18 C.–16 D.–4.5 Divide. Write in simplest form. –9 ÷

117. A. A B. B C. C D. D 5 Min 1-5 Mercury is the closest planet to the Sun. Mercury is 3.6 × 10 7 miles away from the Sun. Write the distance from Mercury to the Sun in standard form. A.360,000 miles B.3,600,000 miles C.36,000,000 miles D.360,000,000 miles (over Chapter 2)

118. A. A B. B C. C D. D 5 Min 1-6 A.3/12 cup B.2/7 cup C.3/7 cup D.11/12 cup Samuel used 1/4 cup of regular sugar and 2/3 cup of brown sugar to make molasses cookies. How much sugar did Samuel use to make the molasses cookies? (over Chapter 2)

119. A. A B. B C. C D. D 5 Min 2-1 A.81 B.18 C.9 D.3 (over Lesson 3-1) Find

120. A. A B. B C. C D. D 5 Min 2-2 A.–14 B.–12 C.12 D.14 (over Lesson 3-1) Find –

121. A. A B. B C. C D. D 5 Min 2-3 Solve the equation q 2 = 16. (over Lesson 3-1) A.± B.± C.± 4 D.± 8

122. A. A B. B C. C D. D 5 Min 2-4 (over Lesson 3-1) Solve the equation. A. B. C. D.

123. A. A B. B C. C D. D 5 Min 2-5 Find the positive square root of 36. A.6 B.9 C.12 D.18 (over Lesson 3-1)

124. A. A B. B C. C D. D 5 Min 2-6 A.13 B.14 C.15 D.25 The chairs in the multi-purpose room of a school need to be arranged in a square. If there are 225 chairs, how many should be in each row? (over Lesson 3-1)

125. A. A B. B C. C D. D 5 Min 3-1 A.5 B.6 C.7 D.8 (over Lesson 3-2) Estimate to the nearest whole number.

126. A. A B. B C. C D. D 5 Min 3-2 A.6 B.7 C.8 D.9 (over Lesson 3-2) Estimate to the nearest whole number.

127. A. A B. B C. C D. D 5 Min 3-3 Estimate the solution of x 2 = 102 to the nearest integer. A.± 4 B.± 5 C.± 10 D.± 11 (over Lesson 3-2)

128. A. A B. B C. C D. D 5 Min 3-4 Estimate the solution of p 2 = 62 to the nearest integer. A.± 3 B.± 4 C.± 7 D.± 8 (over Lesson 3-2)

129. A. A B. B C. C D. D 5 Min 3-5 Choose the two numbers that have square roots between 9 and 10. A.82, 87 B.80, 87 C.79, 101 D.82, 101 (over Lesson 3-2)

130. A. A B. B C. C D. D 5 Min 3-6 Which of the following is in order from least to greatest? (over Lesson 3-2) A. B. C. D.

131. A. A B. B C. C D. D 5 Min 4-1 PETS The table shows the pets of students in the 8 th grade. How many students have a dog? A.7 B.11 C.18 D.29 (over Lesson 3-3)

132. A. A B. B C. C D. D 5 Min 4-2 CONCESSIONS One evening at a movie concession stand, 80 customers bought popcorn, 55 customers bought a soft drink, and 35 bought a box of candy. Of those who bought exactly two items, 35 bought popcorn and a soft drink, 10 bought a soft drink and candy, and 5 bought popcorn and candy. Three customers bought all three. How many customers bought only popcorn? A.20 B.37 C.42 D.50 (over Lesson 3-3)

133. A. A B. B C. C D. D 5 Min 4-3 A.3 B.10 C.6 D.4 Mrs. Jenkins conducted a survey of her student’s favorite type of book. Of the 28 students in her class, 14 said fiction was their favorite, and 7 said nonfiction was their favorite. Of her students, 3 said that both types of books were their favorite. How many students said that neither fiction nor nonfiction was their favorite? (over Lesson 3-3)

134. A. A B. B C. C D. D 5 Min 5-1 Name all sets of numbers to which the real number 286 belongs. A.rational, integer, whole number, real B.integer, irrational, rational, real C.integer, irrational, real D.irrational, real (over Lesson 3-4)

135. A. A B. B C. C D. D 5 Min 5-2 A.rational, real B.integer, real C.whole number, real D.irrational, real (over Lesson 3-4) Name all sets of numbers to which the real number belongs.

136. A. A B. B C. C D. D 5 Min 5-3 A.6 B.5.8 C.5 D.2.9 (over Lesson 3-4) Estimate to the nearest tenth.

137. A. A B. B C. C D. D 5 Min 5-4 A.16.6 B.17 C.17.9 D.18 (over Lesson 3-4) Estimate to the nearest tenth.

138. 5 Min 5-5 1.A 2.B 3.C A.always B.sometimes C.never (over Lesson 3-4) Are irrational numbers sometimes, always, or never rational numbers?

139. A. A B. B C. C D. D 5 Min 5-6 A.real B.rational C.fractions D.negative integers (over Lesson 3-4) To which set does not belong?

140. A. A B. B C. C D. D 5 Min 6-1 Write an equation you could use to find the length of the missing side of the right triangle in the figure. Then find the missing length. Round to the nearest tenth if necessary. A.x 2 + 4 2 = 3 2 ; 5 cm B.x 2 + 3 2 = 4 2 ; 3.6 cm C.3 2 + 4 2 = x 2 ; 5 cm D.3 2 + 4 2 = x 2 ; 25 cm (over Lesson 3-5) cm

141. A. A B. B C. C D. D 5 Min 6-2 Write an equation you could use to find the length of the missing side of the right triangle in the figure. Then find the missing length. Round to the nearest tenth if necessary. A.15 2 + x 2 = 25 2 ; 20 B.25 2 + x 2 = 15 2 ; 24.7 C.15 2 + 25 2 = x 2 ; 25.3 D.15 2 + 25 2 = x 2 ; 29.2 (over Lesson 3-5)

142. A. A B. B C. C D. D 5 Min 6-3 Write an equation you could use to find the length of the missing side of the right triangle in the figure. Then find the missing length. Round to the nearest tenth if necessary. A.12 2 + 13 2 = x 2 ; 17.7 B.12 2 + 13 2 = x 2 ; 13.5 C.x 2 + 12 2 = 13 2 ; 12.5 D.x 2 + 12 2 = 13 2 ; 5 (over Lesson 3-5)

143. 5 Min 6-4 1.A 2.B (over Lesson 3-5) Is a triangle with side lengths of 18, 25, and 33 a right triangle? A.yes B.no

144. A. A B. B C. C D. D 5 Min 6-5 A.33 B.50 C.35 D.12 A man drives 33 miles east and 12 miles south. Approximately how many miles is the man from his starting point? (over Lesson 3-5)

145. A. A B. B C. C D. D 5 Min 7-1 In the figure, a plane is traveling from point A to point B. How far will the plane have flown when it reaches its destination? Write an equation that can be used to answer the question and solve. Round to the nearest tenth if necessary. A.300 2 – 200 2 = p 2 ; 223.6 km B.300 – 200 = p; 100 km C.300 + 200 = p; 500 km D.300 2 + 200 2 = p 2 ; 360.3 km (over Lesson 3-6) km

146. A. A B. B C. C D. D 5 Min 7-2 Refer to the figure. A girl is pinning ribbon to a 3’ × 4’ bulletin board. How long will the ribbon have to be to stretch from corner to corner diagonally? Write an equation that can be used to answer the question and solve. Round to the nearest tenth if necessary. A.4 2 + 3 2 = r 2 ; 5 ft B.4 + 3 = r; 7 ft C.4 2 – 3 2 = r 2 ; 3.6 ft D.r 2 – 3 2 = 4 2 ; 2.6 ft (over Lesson 3-6)

147. A. A B. B C. C D. D 5 Min 7-3 A.42 in. B.58 in. C.72 in. D.84 in. In the figure, triangle ABC is a right triangle. What is the perimeter of the triangle? (over Lesson 3-6)

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