81, 27, 9, 3, ... Find the common ratio of the given sequence and write an exponential function which represents the sequence. Use n=1,2,3,...

Which multiplicative property is being illustrated below? (type commutative, associative, or identity) 5 × 2 × 4 = 2 × 5 × 4

Imogene invested $8,000 in a bank account that pays 8 percent simple interest at the end of each year. her friend invested the same amount in stocks where the growth of the investment is represented as 2,000 times the square root of 2 less than the time lapsed in years. if y1 and y2 represent the amount earned in dollars and t is the time lapsed in years, which system of equations correctly represents the situation?

Prove the converse of the pythagorean theorem using similar triangles. the converse of the pythagorean theorem states that when the sum of the squares of the lengths of the legs of the triangle equals the squares length of the hypotenuse, the triangle is a right triangle. be sure to create and name the appropriate geometric figures.