Two players X and Y take alternate turns in a game, starting with the diagram alongside. At each turn, one player writes one of 1, 2 or 3 in an empty circle, so that no two circles connected by an edge contain the same number.

A player loses when they cannot go. In each of the five diagrams below it is Y’s turn.

In which of the diagrams can Y’s move ensure that X loses the game?

Koji is installing a rectangular window in an office building. the window is 823 feet wide and 534 feet high. the formula for the area of a rectangle is a=bh. what is the area of the window? enter your answer as a mixed number in simplest form in the box. $$ ft2

Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.

Suppose you want to transform the graph of the function y=tan(x+pi/4)-1 into the graph of the function y=-tan(x+pi/2)+1 which transformations should you perform. a) reflect the graph of the first function across the x-axis, translate it pi/4 units to the left, and translate it 2 units up. b) reflect the graph of the first function across the x-axis, translate it pi/4 units to the right, and translate it 2 units up. c) reflect the graph of the first function across the line y = -1, translate it pi/4 units to the left, and translate it 2 units up. d) reflect the graph of the first function across the line y = -1, translate it pi/4 units to the right, and translate it 2 units up.