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Example 1-3a

ALGEBRA Solve. Write the equation. Take the square root of each side. Notice that. The equation has two solutions,. Answer:. Example 1-3a. ALGEBRA Solve. Example 1-3b. Answer:. Splash Screen. Ch. 3-4 The Pythagorean Theorem. Vocabulary. Pythagorean Theorem: describes the

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Example 1-3a

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  1. ALGEBRA Solve Write the equation. Take the square root of each side. Notice that The equation has two solutions, Answer: Example 1-3a

  2. ALGEBRA Solve Example 1-3b Answer:

  3. Splash Screen

  4. Ch. 3-4 The Pythagorean Theorem

  5. Vocabulary Pythagorean Theorem: describes the relationship between the lengths of the legs and the hypotenuse for any right triangle C² = a² + b² Hypotenuse: the side opposite the right angle. It is the longest side of the triangle. c a b Legs Legs

  6. Pythagorean Theorem Example 4-1a KITES Find the length of the kite string. The kite string forms the hypotenuse of a right triangle. The vertical and horizontal distances form the legs. c = 13 Answer: The string of the kite is 13 ft.

  7. Example 4-1b KITES Find the length of the kite string. Answer: 26 ft

  8. Pythagorean Theorem Replace c with 33 and b with 28. Subtract 784 from each side. Simplify. Take the square root of each side. Example 4-2a The hypotenuse of a right triangle is 33 centimeters long and one of its legs is 28 centimeters. Find the length of the other leg. Answer: The length of the other leg is about 17.5 cm.

  9. Example 4-2b The hypotenuse of a right triangle is 26 centimeters long and one of its legs is 17 centimeters. Find the length of the other leg. Answer: about 19.7 cm

  10. Example 4-3a MULTIPLE–CHOICE TEST ITEMA 10–foot ramp is extended from the back of a truck to the ground to help movers load furniture onto the truck. If the ramp touches the ground at a point 9 feet behind the truck, how high off the ground is the top of the ramp? A about 1 foot B about 4.4 feet C about 13.5 feet D about 19 feet

  11. Example 4-3a Read the Test ItemYou know the length of the ramp and the distance from the truck to the bottom of the ramp. Make a drawing of the situation including the right triangle.

  12. Pythagorean Theorem Replace c with 10 and b with 9. Evaluate Subtract 81 from each side. Simplify. Take the square root of each side. Simplify. Example 4-3a Solve the Test Item The top of the ramp is about 4.4 feet off the ground. Answer: B

  13. Example 4-3b MULTIPLE–CHOICE TEST ITEMThe base of a 12–foot ladder is 5 feet from the wall. How high can the ladder reach? A about 7 feet B about 10.9 feet C about 11.8 feet D about 13 feet Answer: B

  14. Pythagorean Theorem Replace a with 7, b with 24, and c with 25. Evaluate Simplify. Example 4-4a The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle. Answer: The triangle is a right triangle.

  15. Example 4-4b The measures of three sides of a triangle are 13 inches, 5 inches, and 12 inches. Determine whether the triangle is a right triangle. Answer: yes

  16. Ch.3-5 Distance on the Coordinate Plane

  17. Let the distance between the two points, , Example 6-1a Graph the ordered pairs (0, –6) and (5, –1). Then find the distance between the points. a c² = a² + b² c² = 5² + 5² c² = 25 + 25 c² = 50 c = √50 ≈ 7.07 c b Answer: The points are about 7.1 units apart.

  18. Example 6-1b Graph the ordered pairs (0, –3) and (2, –6). Then find the distance between the points. Answer: about 3.6 units

  19. Let the distance between McCormickville and Lake Shore Park. Then a = 3 and b = 4. Example 6-2a TRAVEL Melissa lives in Chicago. 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).

  20. Replace a with 3 and b with 4. Pythagorean Theorem Take the square root of each side. Example 6-2a The distance between McCormickville and Lake Shore Park is 5 units on the map. Answer: Since each unit equals 0.08 mile, the distance is 0.08  5 = 0.4 mile.

  21. Example 6-2b 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 (–1, 1). Answer: 0.4 mile

  22. Ch. 3-3 The Real Number System

  23. Real numbers: rational numbers + irrational numbers. So, all numbers are real numbers. Rational numbers: has terminated decimal or repeating decimal. E.g. 1/6 =0.1666… or 1/8 = 0.125 Irrational numbers: no terminated decimal or repeating decimal. E.g. √2 = 1.4142135… Integers: …,-2,-1,0, 1,2,… Whole numbers: 0,1,2,3,… Natural Numbers: 1,2,3,…

  24. Name all sets of numbers to which belongs. Answer: Since it is a whole number, an integer, and a rational number. Example 3-1a

  25. Name all sets of numbers to which belongs. Example 3-1b Answer: whole, integer, rational

  26. Name all sets of numbers to which belongs. … Example 3-2a Answer: Since the decimal does not repeat or terminate, it is an irrational number.

  27. Name all sets of numbers to which belongs. Example 3-2b Answer: irrational

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

  29. Example 3-3b Name all sets of numbers to which 0.1010101010… belongs. Answer: rational

  30. 5-Minute Check

  31. Explore online information about the information introduced in this chapter. Click on the Connect button to launch your browser and go to the Mathematics: Applications and Concepts, Course 3 Web site. At this site, you will find extra examples for each lesson in the Student Edition of your textbook. When you finish exploring, exit the browser program to return to this presentation. If you experience difficulty connecting to the Web site, manually launch your Web browser and go to www.msmath3.net/extra_examples. Online

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