Triangle XYZ has vertices at X(-4, 2), Y(2, 2), and Z(2,4). After a dilation is applied, the image triangle X'Y'Z' has vertices X'(-12, 6), Y'(6, 6), and Z'(-6, 12). What is the scale factor for the dilation?

The party planning committee has to determine the number of tables needed for an upcoming event. if a square table can fit 8 people and a round table can fit 6 people, the equation 150 = 8x + 6y represents the number of each type of table needed for 150 people.