Below is a proof showing that the sum of a rational number and an irrational number is an irrational number.

let a be a rational number and b be an irrational number.
assume that a + b = x and that x is rational.
then b = x – a = x + (–a).
x + (–a) is rational because
however, it was stated that b is an irrational number. this is a contradiction.
therefore, the assumption that x is rational in the equation a + b = x must be incorrect, and x should be an irrational number.
in conclusion, the sum of a rational number and an irrational number is irrational.

which of the following best completes the proof?
it is the sum of two rational numbers.
it is the sum of two irrational numbers.
it represents a non-terminating, non-repeating decimal.
its terms cannot be combined.

Which graph represents y=^3 sqrt x+8-3 ?

Hye ryung is the president of the local chapter of the american medical students association (amsa). she is organizing local outreach and informational meetings. at her first meeting there are five people present (including herself). every month after that her group grows by 5 people. a. how many members are in the group after 6 months? b. the logistics of hosting and feeding her group at meetings was more complicated than expected. the cost of feeding 5 people at her first meeting was $30, for 10 people it was $35, for 15 it was $45, and after 6 months all of the costs had added up to $100. write a function to model the cost with the number of people attending meetings. c. what connections can you make between the linear growth of the group’s membership and the increasing costs of running meetings?

You are cycling around europe with friends. a cycling festival is starting soon in barcelona. it will take 4.5 hours to cycle there. how many minutes in total is this?