In algebra, we use systems to organize information about a situation in an efficient way. Relationships between variables can be described using the
language and notation of mathematics. You have studied different types of
systems - systems of the same function type (linear), of mixed function type
(linear-quadratic), systems that represent constraints (inequalities), and others
that are representing a relationship between three variables.
Though these systems have differences and unique properties, they share a common trait:
we can show the relationship graphically. Other than systems in algebra, what other systems
are in place in our world that are unique but share a common trait or purpose?

Which of the following equations is equivalent to x/3-6/x=1

Sophia wrote an equation to represent the revenue of a movie theater for one day. she let x represent the number of child tickets sold and y represents the nunver of adult tickets sold. if a child ticket cost $4, an adult ticket cost $6, and the total revenue for the daybwas $420, which equation could sophia use to represent the number of chikd and adult tickets that were sold?

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.