Use a definition, postulate, or theorem to find the value of x in the figure described. Point E is between points D and F. If DE = x − 1, EF = 2x + 2, and DF = 4x − 6, find x.

Select each definition, postulate, or theorem you will use.

A Segment Addition Postulate
B definition of segment bisector
C Linear Pair Theorem
D definition of midpoint

The solution is x =

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?