An open rectangular box having a volume of 108 in.3 is to be constructed from a tin sheet. Find the dimensions of such a box if the amount of material used in its construction is to be minimal. Hint: Let the dimensions of the box be x in. by y in. by z in. Then, xyz = 108 and the amount of material used is given by S = xy + 2yz + 2xz. Show that the following is true and minimize f(x, y). a) s = f(x, y) = xy + 216/x + 216/y
b) x= ? in.
c) y= ? in.
d) z= ? in.

Asequence of numbers begins with 12 and progresses geometrically. each number is the previous number divided by 2. which value can be used as the common ratio in an explicit formula that represents the sequence? 1/2 2 6 12

Two parallel lines are crossed by a transversal. what is the value of x? x = 40 x = 70 x = 110 x = 130

Jessica and martha each have a bag of cookies with unequal quantities. they have 30 cookies total between the two of them. each of them ate 6 cookies from their bag. the product of the number of cookies left in each bag is not more than 80. how many more cookies will jessica have martha? if x represents the number of cookies jessica started with, complete the statements below.the inequality that describes the relationship between the number of cookies each one of them has is x^2 - x +224 > = 0.jessica has at least cookies more than martha.