  ### Home > CAAC > Chapter 6 > Lesson 6.2.4 > Problem6-74

6-74.
1. Identify the hypothesis and conclusion for each of 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. Homework Help ✎

1. If y = − 5, then the point (6, −1) is a solution.

2. 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.

3. If (3x + 1)(x − 2) = 4, then 3x2 − 5x − 2 = 4.  Hypothesis:

$y=\frac{2}{3}x \minus 5$

Conclusion: (6, −1) is a solution

Check to see if the conclusion is true by plugging in the points into the original equation. Add 2 tiles to Figure 2 to find figure three. Repeat the process to find Figure 4.
Does the number of tiles you found for Figure 4 match the number that the problem says there should be? Hypothesis: (3x + 1)(x − 2) = 4
Conclusion: 3x2 − 5x − 2 = 4

Check by making a generic rectangle.
Does (3x + 1)(x − 2) = 3x2 − 5x − 2?