Suppose that you have two different algorithms for solving a problem. to solve a problem of size n, the first algorithm uses exactly n(log(n)) operations and the second algorithm uses exactly n3=2 operations. as n grows, which algorithm uses fewer operations? justify your answer using definitional proof.

Juliana says that she can use the patterns of equivalent ratios in the multiplication table below to write an infinite number of ratios that are equivalent to 6: 10. which statement explains whether juliana is correct? she is correct because she can multiply 6 and 10 by any number to form an equivalent ratio. she is correct because 6: 10 can be written as 1: 2 and there are an infinite number of ratios for 1: 2. she is not correct because the multiplication table does not include multiples of 10. she is not correct because 6: 10 is equivalent to 3: 5 and there are only 9 ratios in the multiplication table that are equivalent to 3: 5.

The multiplicative property of equality states that for real numbers a, b, c, and d, if a = b and c = d, then ac = bd. true false

The areas of two similar triangles are 72dm2 and 50dm2. the sum of their perimeters is 226dm. what is the perimeter of each of these triangles?