X2+y2+z2=9, z≥0 and 3z2=x2+y2, z≥0

What properties allow transformation to be used as a problem solving tool

Larry wants to buy some carpeting for his living room. the length of the room is 4 times the width and the total area of the room is 16 square meters. what is the length of the living room

Afactory buys 10% of its components from suppliers b and the rest from supplier c. it is known that 6% of the components it buys are faulty. of the components brought from suppliers a,9% are faulty and of the components bought from suppliers b, 3% are faulty. find the percentage of components bought from supplier c that are faulty.