In the cube shown below, the distance between vertices 2 and 6 is 18 cm. If the cube is divided into two equal parts by a plane parallel to the face defined by vertices 2, 3, 6, and 7, what will be the area of the cross-section?
A.
18 sq cm
B.
324 sq cm
C.
54 sq cm
D.
72 sq cm

Find the value of p for which the polynomial 3x^3 -x^2 + px +1 is exactly divisible by x-1, hence factorise the polynomial

Quick! a survey of 57 customers was taken at a bookstore regarding the types of books purchased. the survey found that 33 customers purchased mysteries, 25 purchased science fiction, 18 purchased romance novels, 12 purchased mysteries and science fiction, 9 purchased mysteries and romance novels, 6 purchased science fiction and romance novels, and 2 purchased all three types of books. a) how many of the customers surveyed purchased only mysteries? b) how many purchased mysteries and science fiction, but not romance novels? c) how many purchased mysteries or science fiction? d) how many purchased mysteries or science fiction, but not romance novels? e) how many purchased exactly two types of books?

Arectangle has a width of 5 cm and a length of 10 cm. if the width is increased by 3, how does the perimeter change?