For christmas, each member of a class
sends the other classmates a card. if
992 cards are exchanged, find the
number of pupils in the class.

number of pupils in the class = 32

Step-by-step explanation:

Let n be the number of students. So n-1 cards will be sent by each student.

n(n-1) =192

n² - n =192

n² - n - 192 = 0

n² - 32n + 31n - (31*32) = 0

n(n - 32) + 31 (n-32) = 0

(n-32)(n+31) = 0

n - 32 = 0    or n + 31 = 0

n = 32  or n = -31 is not possible because no. of students cannot be negative

n= 32

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.