Given f ( x ) = sin x and g ( x ) = cos x , show that f ( g ( x ) ) = 0 . Show all your steps.

Ateacher has $80 to buy workbooks. each work book cost $3. if she buys as many workbooks as possible, how much money does she have leftover? a) $2 b) $4 c) $6 d) $8

Kayla wants to find the width, ab, of a river. she walks along the edge of the river 65 ft and marks point c. then she walks 25 ft further and marks point d. she turns 90° and walks until her location, point a, and point c are collinear. she marks point e at this location, as shown. (a) can kayla conclude that δ and δ are similar? why or why not? (b) suppose de = 15 ft. what can kayla conclude about the width of the river?

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.