91Ó°ÊÓ

FINDING A PATTER The following are the first nine Fibonacci numbers. $$ 1,1,2,3,5,8,13,21,34, \dots $$ a. Make a conjecture about each of the Fibonacci numbers after the I rst two. b. Write the next three numbers in the pattern. c. Research to \(|\) nd a real-world example of this pattern. Inductive and Deductive Reasoning

In Exercises \(39-44\) , create a truth table for the logical statement. (See Example \(6 .\) ) $$ \sim(\mathrm{q} \rightarrow \mathrm{p}) $$

REWRITING A FORMULA. The formula for the area A of a trapezoid is \(A=\frac{1}{2} h\left(b_{1}\square b_{2}\right),\) where \(h\) is the height and \(b_{1}\) and \(b_{2}\) are the lengths of the two bases. Solve the formula for \(b_{1}\) . Justify each step. Then find the length of one of the bases of the trapezoid when the area of the trapezoid is 91 square meters, the height is 7 meters, and the length of the other base is 20 meters.

MAKING AN ARGUMEN Your friend claims the statement "If I bought a shirt, then I went to the mall" can be written as a true biconditional statement. Your sister says you cannot write it as a biconditional. Who is correct? Explain your reasoning.

CRITICAL THINKIN Geologists use the Mohs' scale to determine a mineral's hardness. Using the scale, a mineral with a higher rating will leave a scratch on a mineral with a lower rating. Testing a mineral's hardness can help identify the mineral. a. The four minerals are randomly labeled \(A, B\) C, and D. Mineral A is scratched by Mineral B. Mineral \(C\) is scratched by all three of the other minerals. What can you conclude? Explain your reasoning. b. What aditional test(s) can you use to identify all the minerals in pait ( a )

WRITING Compare the Reflexive Property of Equality with the Symmetric Property of Equality. How are the properties similar? How are they different?

MATHEMATICAL CONNECTION on the statement "If \(x^{2}-10=x | 2,\) then \(x=4 "\) be combined with its converse to form a true biconditional statement?

ATTENDING TO PRECISION Which of the following statements illustrate the Symmetric Property of Equality? Select all that apply (A) If \(A C=R S\) then \(R S=A C\) (B) If \(x=9,\) then \(9=x\) (C) If \(\mathrm{AD}=\mathrm{BC},\) then \(\mathrm{DA}=\mathrm{CB}\) (D) \(A B=B A\) (E) If \(\mathrm{AB}=\mathrm{LM}\) and \(\mathrm{LM}=\mathrm{RT}\) , then \(\mathrm{AB}=\mathrm{RT}\) . (F) If \(\mathrm{XY}=\mathrm{EF},\) then \(\mathrm{FE}=\mathrm{XV}\)

THOUGHT PROVOKING Write examples from your everyday life to help you remember the Reflexive, Symmetric, and Transitive Properties of Equality. Justify your answers.

REASONING Select all the properties that would also apply to inequalities. Explain your reasoning. (A) Addition Property (B) Subtraction Property (C) Substitution Property (D) Reflexive Property (E) Symmetric Property (F) Transitive Property