Find all values z1 and z2 such that (2, −1, 3), (1, 2, 2), and (−4, z1, z2) do not span R3. I got z1 != 4.5 and z2 != -14.5, but how do I verify that it's correct?

Find a number such that if you add 8 and divide the result by 4 you will get the same answer as if you subtracted 3 from the original number and divided by 2

Which equations represents circles that have a diameter of 12 units and a center that lies on the y-axis? check all that apply

Afurniture manufacturer produces chairs and sofas. each chair requires 10 yards of fabric, and each sofa requires 20 yards of fabric. the manufacturer has 300 yards of fabric available. to fulfill orders, the number of sofas must be at least twice the number of chairs. let x be the number of chairs and y the number of sofas. which inequalities are described in the problem? check all of the boxes that apply