5.. HOMEWORK 1.1
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1106
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Mathematics
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Apr 3, 2024
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Uploaded by SargentFang8306
HOMEWORK 1.1 Use inductive reasoning to predict the next line in the pattern. 2x4=8 3Ix4=12 4x4=16 5x4=20 The nextlineis 6 x 4 = 24 . Use inductive reasoning to predict the next line in the pattern. 1000 = 10° 10,000 = 10° 100,000 = 10° 1,000,000 = 10° The next line is 10,000,000 = 10" . Identify a pattern in the sequence of figures. Then use the pattern to find the next figure in the sequence. Choose the correct shape for the next figure. Identify the next figure in the pattern. Lo OO Choose the correct answer below. S) O
Use inductive reasoning to predict the next three numbers in the pattern. 12,14,16, 18, ... Predict the next three numbers in the pattern. 12,14,16,18, 20, 22, 24 Use inductive reasoning to predict the next three numbers in the pattern. 8, -88 -8, .. Predict the next three numbers in the pattern. 8 -88 -8 8, -8, 8 (Simplify your answers.) Use inductive reasoning to predict the next three numbers in the pattern. 1 . 1 1 Predict the next three numbers in the pattern. 1 1 1 25 31 37 (Type integers or fractions.) Use inductive reasoning to predict the next three numbers in the pattern. 3, -12, 48, -192, .. Predict the next three numbers in the pattern. 3, -12,48, -192, 768, -3,072, 12,288
Use inductive reasoning to predict the next three numbers in the pattern. 4,7,11,18,29, 47, .. Predict the next three numbers in the pattern. 4,7,11,18,29, 47, 76, 123, 199 Find the letter that will be entry #51 in the sequence. Z,G GG GGZGGG,G,GgG,. Entry #51is G.. An ancient culture labeled certain numbers as square numbers. The numbers 1, 4, 9, 16, 25, and so on are square numbers. Complete parts a through c below. 1 4 9 16 25 a) Determine the next three square numbers. 36, 49, 64 b) Describe a procedure to determine the next five square numbers without drawing the figures. Double the previous square number and then subtract half of the previous from that. Square 6, 8, 10, 12, and 14. Add the last two square numbers together to get the next one. ¥ 1) Square6,7,8, 9 and 10. c) Is 72 a square number? Explain how you determined your answer. ¥ /.. No, because it falls between two square numbers, 8 squared and 9 squared, and there is no natural number between 8 and 9. Yes, because you can make a square shape with 72 dots. No, because it is an even number. Yes, because it is 9 squared.
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The ancient Greeks labeled certain numbers as triangular numbers. The numbers 1, 3, 6, 10, 15, 21, and so on are triangular numbers. Complete parts a) through c) below. 1 3 10 15 21 a) Determine the next two triangular numbers. 1,3,6,10,15,21, 28, 36 b) Describe a procedure to determine the next five triangular numbers without drawing the figures. Choose the correct answer below. Square 6, 8, 10, 12, and 14. ¥ . To obtain the 8th triangular number, add 8 to the 7th triangular number. To obtain the 9th triangular number, add 9 to the 8th triangular number, and so on. Add the last two triangular numbers together to get the next one. Double the previous triangular number and then subtract half of the previous from that. c) Is 72 a triangular number? Explain how you determined your answer. Choose the correct answer below. ¥ /. No, because it falls between two triangular numbers, 66 and 78. Yes, because it is 9 squared. Yes, because you can make a triangular shape with 72 dots. No, because it is an even number. The pattern shown is taken from a quilt design known as a triple Irish chain. Complete the color pattern by indicating the color assigned to each square. N I . N 1[2]3 I A|5](67 Bl . 8 [ 9 [10[11]12]
Four rows of a triangular figure are shown to the right. Complete parts a) and b) below. a) If you added six additional rows to the bottom of this triangle, using the same pattern displayed, how many triangles would appear in the 10th row? There would be 19 triangles in the 10th row. (Type an integer or a decimal.) b) If the triangles in all 10 rows were added, how many similarly sized triangles would appear in the entire figure? There would be 100 triangles in the entire figure. (Type an integer or a decimal.) The graph to the right shows the amount of money spent in a country on video games played on mobile devices in 2013 and the projected amount for the years 2014-2018. The graph passes through the points Spending on Video Games on Mobile Devices (2013,1109) and (2018,1534). Complete parts a) and b) below. p ) > > - > - - > > - - VB DO B D ®C - E-R-R-N-R-E-R-R-N- Spending, milliors of dollars coooo 13 2014 2015 2016 2017 2018’ Year > a) Assuming this trend continues, use the graph to predict the amount spent in the country on video games played on mobile devices in 2020. The predicted amount spent in the country on video games played on mobile devices in 2020 is about $ 1697 million. (Type a whole number.) b) Explain how you are using inductive reasoning to determine your answer. In this case, specific cases are being used to make a prediction. Identify the next figure in the pattern. oo |G Choose the correct shape for the next figure.