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Identify the hypothesis and conclusion for the following statements. Then decide if the statement is true or false. Justify your decision. You may want to review the meanings of hypothesis and conclusion from problem 6–31.
If Figure 2 of a tile pattern has 13 tiles and Figure 4 of the same pattern has 15 tiles, then the pattern grows by 2 tiles each figure.
How does the pattern grow? Explain how you know.
Copy the pattern, shown in your textbook, and continue the pattern for successive powers of 3.
In a sentence or two, describe a pattern formed by the units digits (the "ones") of the numbers in the pattern.
The camp council is designing a patio floor for an outdoor cafeteria. They have chosen the pattern shown in figure. What is the area of the section with the pattern(b) ?
Find a rule that represents the number of tiles in the tile pattern in the figure.
Study the figures below, find a pattern, and sketch the next four figures. State the pattern's rule in a sentence or two.
Figure 2 of a tile pattern is shown. If the pattern grows linearly and if Figure 5 has 15 tiles, then find a rule for the pattern.
Multiply.
(2x – 3)^{2}
Start with the number 6. Double it. Then double this result. Continue to double each new number until you find a pattern in the unit (one's) digits. Describe the pattern. You may want to make an organized table (list).
Write the given numbers and continue each pattern on your paper.
^{1}/_{8}, , ^{3}/_{8}, ____, _____, _____, _____, _____
Here is a famous number pattern called Fibonacci Numbers:
1, 1, 2, 3, 5, 8, ...
a) Copy the pattern on your paper, then list the three numbers that would appear next.
The camp council is designing a patio floor for an outdoor cafeteria. They have chosen the pattern shown in figure. What is the area of the section with the pattern (a) ?
Write the given numbers and continue each pattern on your paper.
^{1}/_{6},^{1}/_{3}, _____, _____, ^{5}/_{6}, _____
John figures he can make each pen larger if he places the squares in a square pattern instead of in a row. Is he right? Justify your answer.
Write the given numbers and continue each pattern on your paper.
0.25, _____, 0.75, _____, 1.25, _____, _____
Here is a famous number pattern called Fibonacci Numbers:
1, 1, 2, 3, 5, 8, ...
Copy the pattern on your paper, then list the three numbers that would appear next.
Marisa wanted to investigate some patterns. She wrote out some of them for you to complete.
27, 9, 3, 1, ___, ___, ___
Parts DS–94a and DS–94d of DS–94 represent a general pattern known as the sum and difference of cubes. Use this pattern to factor of the following polynomial:
x^{3} + y^{3}
Cami has a different tile pattern. She decided to represent the number of tiles of her pattern in a table, as shown below. Can you use the table to predict how many tiles would be in Figure 5 of her tile pattern? How many tiles would Figure 8 have? Explain how you know.
Marisa wanted to investigate some patterns. She wrote out some of them for you to complete.
16, 4, 1, ___, ___, ___