In Relation to Each of the Following Statements, Identify the Way

In relation to each of the following statements, identify the way in which the agency relationship has been established.
a. X consigned his automobile to Z with instructions to sell same immediately. Z was a mercantile agent. Z used the vehicle as security for a loan from Y who knew nothing about X or his instructions to Z.
b. Z, a common carrier, transported perishable goods for X. The goods started to spoil and Z was unable to contact X who had left the country on an extended vacation. Z sold the goods to Y and received a reasonable price with regard to the condition of the goods.
c. X executes a power of attorney in favour of Z authorising Z to sell specific land described in the power of attorney.
d. X, without the authority of Z, sells certain of Z's furniture at a garage sale. Shortly after the sale Z learns of it and approves of X's actions.