The golden ratio is a solution to a quadratic equation. a. Find the precise value for Φ by solving Φ2 − Φ − 1 = 0.

b. Which method of solving a quadratic equation did you use? Explain your reasoning.

c. What type of number is Φ? Why can it only be approximated by a decimal value?

The table shows a pattern of exponents. what is the pattern as the exponents decrease?

Which equation represents the partial sum of the geometric series?

According to the 2008 u.s. census, california had a population of approximately 4 × 10^7 people and florida had a population of approximately 2 × 10^7 people. which of the following is true? a. the population of florida was approximately two times the population of california. b. the population of florida was approximately twenty times the population of california. c. the population of california was approximately twenty times the population of florida. d. the population of california was approximately two times the population of florida.