The parabola y=x2y=x2 is changed to the form y=a(x−p)2+qy=a(x−p)2+q by translating the parabola 4 units down and 2 units right and expanding it vertically by a factor of 3. what are the values of aa, pp, and qq?

At the many chips cookie company they are serious about the number of chocolate chips in their cookies they claim that each cookie hasn't c chips. if their claim is true there will be 200 chips in 10 cookies

Adam drew two same size rectangles and divided them into the same number of equal parts. he shaded 1/3 of one rectangle and 1/4 of the other rectangle. what is the least number of parts into which both rectangles could be divided into?

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