1 ft 1 ft border tile

Transcription

1 Application 1. a. How many 1-foot-quare border tile do you need to urround a pool that i 10 feet long and 5 feet wide? b. Write an equation for the number of border tile needed to urround a pool L feet long and W feet wide. c. Write a different but equivalent equation for the number of tile needed in part (b). Explain why your equation are equivalent. W L 2. A quare hot tub ha ide of length feet. A tiler create a border by placing 1-foot-quare tile along the edge of the tub and triangular tile at the corner, a hown. The tiler make the triangular tile by cutting the quare tile in half along a diagonal. 1 ft 1 ft border tile a. Suppoe the hot tub ha ide of length 7 feet. How many quare tile doe the tiler need for the border? b. Write an expreion for the number of quare tile N needed to build thi border for a quare tub with ide of length feet. c. Write a different but equivalent expreion for the number of tile N. Explain why your expreion for the number of border tile are equivalent. d. I the relationhip between the number of tile and ide length linear, exponential, quadratic, or none of thee? Explain. 12 Say It With Symbol

2 3. A rectangular pool i L feet long and W feet wide. A tiler create a border by placing 1-foot-quare tile along the edge of the pool and triangular tile on the corner, a hown. The tiler make the triangular tile by cutting the quare tile in half along a diagonal. W For: Help with Exercie 3 Web Code: ape-6103 L a. Suppoe the pool i 30 feet long and 20 feet wide. How many quare tile doe the tiler need for the border? b. Write two equation for the number of quare tile N needed to make thi border for a pool L feet long and W feet wide. c. Explain why your two equation are equivalent. 4. Below are three more expreion tudent wrote for the number of border tile needed to urround the quare pool in Problem Q 1 ( 1 2) Q R + 2Q + 1.5R 4 c d 2 4 R 2 a. Ue each expreion to find the number of border tile N if = 0. b. Do you think the expreion are equivalent? Explain. c. Ue each expreion to find the number of border tile if = 12. Ha your anwer to part (b) changed? Explain. d. What can you ay about teting pecific value a a method for determining whether two or more expreion are equivalent? Invetigation 1 Equivalent Expreion 13

3 5. A quare urround a circle with a radiu r. Each expreion repreent the area of part of thi figure. Decribe the hape or region each area repreent. a. 4r 2 - pr 2 b. 4r 2 pr r 6. The dimenion of a pool are hown below diving ection wimming ection Each expreion repreent the urface area for part of the pool. i. (3-10) ii. ( - 10) 2 iii ( - 10) iv a. Which expreion() could repreent the urface area of the diving ection? b. Which expreion() could repreent the urface area of the wimming ection? c. If you choe more than one expreion for part (a) and (b), how that they are equivalent. d. Write an equation that repreent the total urface area A of the pool. e. What kind of relationhip doe the equation in part (d) repreent? 14 Say It With Symbol

4 For Exercie 7 9, complete part (a) (c). a. For each expreion, write an equation of the form y = expreion. Make a table and a graph of the two equation. Show x value from -5 to 5 on the graph. b. Baed on your table and graph, tell whether you think the two expreion are equivalent. c. If you think the expreion are equivalent, ue the propertie you have learned in thi invetigation to verify their equivalence. If you think they are not equivalent, explain why x x and 6 + 2x x and 5x (3x + 4) + (2x - 3) and 5x Ue the Ditributive Property to write each expreion in expanded form. a. 3(x + 7) b. 5(5 - x) c. 2(4x - 8) d. (x + 4)(x + 2) 11. Ue the Ditributive Property to write each expreion in factored form. a. 2x - 10x b. 2x + 6 c. 14-7x 12. Ue the Ditributive and Commutative propertie to determine whether each pair of expreion i equivalent for all value of x. a. 3x + 7x and 10x b. 5x and 5x - 10x c. 4(1 + 2x) - 3x and 5x + 4 d. 5-3(2-4x) and x 13. Here i one way you might prove that 2( + 2) + 2 i equivalent to 4 + 4: (1) 2( + 2) + 2 = (2) = (3) = (2 + 2) + 4 (4) = What propertie of number and operation jutify each tep? 14. Find three equivalent expreion for 6x + 3. For Exercie 15 17, copy the tatement. Inert parenthee on the left ide of the equation, if neceary, to make the tatement true for all value of p p - p = 11p p - p = p - p = 7 + 4p Invetigation 1 Equivalent Expreion 15

5 Connection In Exercie 18 23, each expreion repreent the area of a rectangle. Draw a divided rectangle for each expreion. Label the length and area. For Exercie 18 20, write an equivalent expreion in expanded form. For Exercie 21 23, write an equivalent expreion in factored form. 18. x(x + 6) 19. x(x - 6) 20. x(5 + 1) 21. x 2 + 4x 22. x 2-2x 23. 3x + 4x 24. A circular pool with a radiu of 4 feet ha a 1-foot border. a. What i the urface area of the circular pool? b. What i the urface area of the border? c. Write an expreion for the urface area of a circular pool with a radiu of r feet. d. Write an expreion for the area of a 1-foot border around a circular pool with a radiu of r feet. 1 ft 4 ft 25. Multiple Choice Which of the following expreion i equivalent to m + m + m + m + m? A. m + 5 B. 5m C. m 5 D. 5(m + 1) 26. Multiple Choice Which of the following expreion i equivalent to a - b, where a and b are any number? F. b - a G. a + b H. -a + b J. -b + a For Exercie 27 32, draw and label a rectangle whoe area i repreented by the expreion. For Exercie 27 29, write an equivalent expreion in expanded form. For Exercie 30 32, write an equivalent expreion in factored form. 27. (x + 1)(x + 4) 28. (x + 5)(x + 6) 29. 3x(5 + 2) 30. x 2 + x + 2x x 2 + 7x x x + 49 Find each um or difference x 2 x 3 x 2 x For: Multiple-Choice Skill Practice Web Code: apa Say It With Symbol

6 Find each um, difference, product, or quotient (-14) (-14) (-11) (3x) x x 4 3 Find the greatet common factor for each pair of number and and and and Below i a diagram of Otter Middle School outdoor track. The hape of the interior region (haded green) i a rectangle with two half circle at each end. 2x 2x 4x a. Find an expreion that repreent the area of the interior region. b. Find the perimeter of the interior region a if you wanted to put a fence around it. Explain how you found your anwer. c. Write an expreion equivalent to the one in part (b). Invetigation 1 Equivalent Expreion 17

7 51. For Problem 1.2, Percy wrote the expreion 8 + 4( - 1) to repreent the number of border tile needed to urround a quare pool with ide length. a. I thi expreion equivalent to the other expreion? Explain. b. Four tudent ued Percy expreion to calculate the number of border tile needed for a pool with a ide length of 6 feet. Which tudent performed the calculation correctly? Stella 8 + 4(6 1) = = 31 tile Hank 8 + 4(6 1) = 8 + 4(5) = = 28 tile Takahi 8 + 4(6 1) = 12 + (6 1) = = 17 tile Jackie 8 + 4(6 1) = 12(6 1) = 12(5) = 60 tile 52. Lily invet D dollar in a money-market account that earn 10% interet per year. She doe not plan on taking money out during the year. She write the expreion D D to repreent the amount of money in the account at the end of one year. a. Explain why thi expreion i correct. b. Write an equivalent expreion in factored form. c. Suppoe Lily inveted $1,500. How much money will he have in her account at the end of one year? 18 Say It With Symbol

8 For Exercie 53 and 54, ue thi information: The ki club i planning a trip for winter break. They write the equation C 200 ± 10N to etimate the cot in dollar C of the trip for N tudent. 53. Duncan and Corey both ue the equation to etimate the cot for 50 tudent. Duncan ay the cot i $10,500, and Corey ay it i $700. a. Whoe etimate i correct? Show your work. b. How do you think Duncan and Corey found uch different etimate if they both ued the ame equation? 54. a. Suppoe 20 tudent go on the trip. What i the cot per tudent? b. Write an equation for the cot per tudent S when N tudent go on the trip. c. Ue your equation to find the cot per tudent when 40 tudent go on the trip. 55. The pyramid and rectangular prim have the ame bae and height. a. Find the volume of the pyramid. b. Draw a pyramid with a volume of Q 1 cubic unit. 3 R Q8R Hint: You might find it eaier to draw the related prim firt. c. Draw a pyramid with a volume of Q 1 cubic unit. 3 R Q27R 6 unit 4 unit 6 unit d. Find a poible height of a pyramid whoe volume i 9x 3 cubic unit. Invetigation 1 Equivalent Expreion 19

9 56. Below are two tudent calculation for writing an equivalent expreion for 10-4(x - 1) a. Which tudent performed the calculation correctly? b. What mitake did the other tudent make? Sarah 10 4(x 1) = 10 4x = 10 4x = 10 4x + 37 = x = 47 4x Emily 10 4(x 1) = 10 4x = 10 4x = 25 4x 3 = 25 12x Extenion 57. Percy want to write an equation for the number of tile needed to urround a quare pool with ide of length feet. He make a table for pool with ide of length 1, 2, 3, 4, and 5 feet. Then he ue the pattern in hi table to write the equation N = 8 + 4( - 1). Border Tile Side Length Number of Tile a. What pattern doe Percy ee in hi table? b. I Percy expreion for the number of tile equivalent to 4( + 1), Stella expreion in Problem 1.2? Explain. 20 Say It With Symbol

10 58. Two expreion for the number of border tile for the pool at the right are given. 2( + 0.5) + 2( + 1.5) 1 ( 1 2) 4 c d 2 Sketch a picture that illutrate each expreion. 1 ft 1 ft border tile 59. The Expreion Puzzle below all tart with the original expreion 2n n + 6n + 1. Each one end with a different expreion. a. Solve each puzzle by inerting one et of parenthee in the original expreion o that it i equivalent to the deired reult. b. Show that your expreion i equivalent to the deired reult. Jutify each tep. Expreion Puzzle Puzzle Original Expreion 2n 3 4n 6n 1 2n 3 4n 6n 1 2n 3 4n 6n 1 2n 3 4n 6n 1 Deired Reult 12n 5 12n 3 12n 2 n 1 Invetigation 1 Equivalent Expreion 21