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1 . Sample answer: The height of the water decreases at a constant rate, remains the same, decreases at a constant rate, remains the same, and then decreases at a constant rate. a. Sample answer: The Demand curve remains constant. The Supply curve decreases at an increasing rate. b. The left side represents a surplus. The right side represents a shortage. Sample answer: On the left side supply is greater than the demand. On the right side demand is greater than the supply. c. Sample answer: The equilibrium point moves up and left, so a shortage occurs sooner. 6. Enrichment and Extension 6. Sample answers are given.. discrete data; Only integers between and make sense.. discrete data; There will be one fixed amount of money each year.. discrete data; Only positive integers make sense.. continuous data; It makes sense to use any number for the weight of people. continuous data; It makes sense to use any number for the distance. 6. Puzzle Time PIANO Technology Connection. Sample answer: Yes, the point (, ) disappears and is replaced by the point (, 8 ).. Sample answer: Yes, the point (, 8 ) disappears and is replaced by the point (, ).. Sample answer: The graph does not add the new value. You must make a new graph to incorporate the new data point. Sample answer: no; You must select the data you want for a new graph. 6. Sample answer: A scatter plot using color for ( x, y) and another for ( x, y ). The second set of points is units above the first set.. Sample answer: Scatter plots that connect the points with smooth curves or straight lines are a good choice of xy-plots. Chapter. Start Thinking! For use before Activity. Sample answer: no; The lengths of the sides can be any two lengths that have the given product; Yes; because the sides of a square are the same length, the area is the square of the side length. For example, if the area is 6 square meters, then the length of each side would be 8 meters.. Warm Up For use before Activity Start Thinking! For use before Lesson. Shelley; the solutions are 0 and 0.. Warm Up For use before Lesson.. in.. cm. yd.. m. Practice A. s = in.. r = 6 m. ± ± >. 0.6 < 0.. r = ft. x = widgets s = 0 in.. Practice B. s = cm. r = yd. ±. ± 0 6. ± ± s = m >. =. r = m A

2 . Enrichment and Extension. p =±. a =± 0. r =±. j =± d =± 6. y =±. x =± 8. s =±. t =± 0. p =±. r = ft. Puzzle Time EATING SWORDFISH. Start Thinking! For use before Activity. 6 = ; Sample answer: Square roots are positive unless there is a negative in front of the radical sign.. Warm Up For use before Activity Start Thinking! For use before Lesson. Sample answer: To find the square root of a number, you are determining what number when multiplied by itself, equals the given number. For example, =. To find the cube root of a number, you are determining what number when multiplied by itself, and multiplied by itself again, equals a given number. For example, 8 =.. Warm Up For use before Lesson Practice A. s = 0 cm. s = in >. Practice B a. ft b. 86 ft c. ft. >. > Sample answer: 8 and 8; and 6. m. x = 8. x =. Enrichment and Extension. n r n x r=n x Check... = 6 6 = 6 = 6 = 6 6. ;,000 is the least multiple of 000 that is a perfect cube.. 6; is the greatest factor of 0 that is a perfect cube.. Puzzle Time COAT OF PAINT. Start Thinking! For use before Activity. right triangle; yes, any lengths a, b, and c such that a + b = c. Warm Up For use before Activity.... ± 0.. ± > 6. 6π 8.8 in.. 8π m cube B; ft A8

3 . Start Thinking! For use before Lesson. Sample answer: In a gymnastics floor routine, the gymnasts must stay within a -meter-by--meter square. Often they perform tumbling passes in which they start in one corner of the square and end up in the opposite corner. You can use the Pythagorean Theorem to find how far they traveled from one corner to the other. Also, in baseball, the bases form a square with 0-foot sides. You can use the Pythagorean Theorem to find how far the catcher must throw the ball to throw out a runner at second base.. Warm Up For use before Lesson.. c = 0 cm. c = in.. c = 6 m. c = ft. Practice A. c = 0 ft. b = cm. a = m. b = 0 yd 6 in. 6. x = yd. x = 6. cm 8. no; The other leg would be 0 meters long, which is impossible.. x =. Practice B. c = mm. a = ft. b = in.. a = cm 6 in. 6. in.. x = 6 cm 8. 8 fewer blocks. Enrichment and Extension. 8 mi. 6 mi. 6,,.,80,8,00,80 mi 6.. Puzzle Time STOP HOUNDING ME. Start Thinking! For use before Activity. 60 m Sample answer: π, some square roots, like and. Warm Up For use before Activity Start Thinking! For use before Lesson. Sample answer: First find the area,. in.. Ask yourself, What number times itself is.? Because = 8 and 0 = 00, you know that the number must be between and 0. Try squaring values between and 0 to find the number that produces the value closest to. A square with sides of about. inches has the same area as an 8.-inch-by--inch sheet of paper.. Warm Up For use before Lesson.. yes. no. no. yes yes 6. no. Practice A. yes. no. irrational. rational rational 6. rational. irrational; The area is π square feet and π is irrational. 8. a. 6 b.. a. b. 0. a. b..8. a. b... 8 ft. 0; 8 = 6 < 0. ; A positive number is greater than a negative number. 6 ; 0 < = 6. ; = = 0. < a < ; Sample answer: a = yes; =. no; is not a perfect square. A

4 0. yes;. Practice B = = 8. no. yes. rational. rational rational 6. irrational. irrational; The circumference is 0 π meters and π is irrational. 8. a. b.. a. 0 b.. 0. a. b. 0.. a. b... a. c = 0 = 0 < 0 < 0 = 00 b. ( ) ( ) c.. ft. 0;. =.6. ; <, so < 6. ; = > ; = 0.. < a < b < 6; Sample answer: a = 0, b = 60. Enrichment and Extension. 6 and ; The numbers are very close. 6. ; The square of the estimate is about 0.00, which is very close to 0.. Puzzle Time THE LOBSTER THAT BECAME A POLICEMAN BECAUSE HE BELIEVED IN CLAW AND ORDER Extension. Start Thinking! For use before Extension. Sample answer: You determine a decimal is a repeating decimal if a given set of numbers repeats itself consistently. Extension. Warm Up For use before Extension.. terminating. repeating. repeating. terminating repeating 6. repeating Extension. Practice Start Thinking! For use before Activity a + b = c ; Sample answer:,, and ; No, the lengths must form a right triangle.. Warm Up For use before Activity... in.. cm. 8 ft. m. Start Thinking! For use before Lesson. will vary. Check students problems and sketches.. Warm Up For use before Lesson.. If a = a, then a is a negative number; false; a = 0. If two lines are perpendicular, then one line is vertical and the other line is horizontal; false; y = xis perpendicular to y = x and the lines are not vertical or horizontal.. If a is a positive number, then a is a negative number; false; a = and a =. If a is an even number, then a is an odd number; true; Adding to an even number creates an odd number. A0

5 If a triangle is a right triangle, then the side lengths of the triangle are,, and ; false; A right triangle can have side lengths,, and. 6. If the y-intercept of a graph is, then the line is given by the equation y = x ; false; y = x has a y-intercept of.. Practice A. If a is an even number, then a is an odd number; false; 8 a = is an even number and a equals.. If is negative, then a is negative; true; a Reciprocals have the same sign.. not a right triangle. right triangle yes. yes 0. no. yes. a. 8.8 ft b. 8.6 ft c. your friend. 0. ft. Practice B. right triangle. not a right triangle The x-coordinate was incorrectly substituted into the distance formula. ( ) ( ) d = + = =. no 8. yes. no 0. a. b. c. yes; The square of a positive value is the same as the square of its negative. d. Sample answer:. $ ( ) ( ), and 6, ; distance = 0 ( ) ( ), and 6, ; distance = 0. Enrichment and Extension. right. obtuse. obtuse. right acute 6. acute. obtuse 8. right. acute 0. right. acute. obtuse. Puzzle Time A D-HORSE Technology Connection. c =. c = 6.. b =. b = 0. Chapter 8 8. Start Thinking! For use before Activity 8. Sample answer: filling cylindrical jars with homemade jam 8. Warm Up For use before Activity Start Thinking! For use before Lesson 8. Sample answer: Find the area of the base by finding the radius and squaring it, then multiplying that number by π. Find the measure of the height and multiply that number by the area of the base. 8. Warm Up For use before Lesson 8.. π 6.6 in.. 600π 06. ft. 6π 08. m. 8. Practice A π 60. in.. π 6.8 in.. 6π. m. π. cm. π 00. in. 6..,8 gal 8.. times more volume 600π 880 ft 88π 0.8 mm 08π cm A