Starting from the point (0,0), a grasshopper makes a series of moves on the coordinate plane. the grasshopper's first move takes her to (3,4). she then proceeds via this rule: move rule: after a move which adds (x, y) to the grasshopper's coordinates, her next move adds either (x, y-1) or (x-1,y) to her coordinates. thus, her second move adds either (3,3) or (2,4) to her position, landing her at (6,7) or (5,8) accordingly. if the grasshopper's x and y coordinates never decrease, and if she ends at the point (a, a) where a is as large as possible, then what is the value of a?

Cindy uses 1-inch cubes to find the volume of a jewelry box shaped like a rectangular prism. she uses 780 cubes to completely fill the jewelry box with no gaps or overlaps. if the jewelry box is 13 inches long and 5 inches wide, how tall is cindy’s jewelry box?

The table shows the relationship between the number of cups of cereal and the number of cups of raisins in a cereal bar recipe: number of cups of cereal number of cups of raisins 8 2 12 3 16 4 molly plotted an equivalent ratio as shown on the grid below: a graph is shown. the title of the graph is cereal bars. the horizontal axis label is cereal in cups. the x-axis values are 0, 20, 40, 60, 80,100. the vertical axis label is raisins in cups. the y-axis values are 0, 10, 20, 30, 40, 50. a point is plotted on the ordered pair 40,20. which of these explains why the point molly plotted is incorrect? (a) if the number of cups of cereal is 40, then the number of cups of raisins will be10. (b)if the number of cups of raisins is 40, then the number of cups of cereal will be10. (c) if the number of cups of cereal is 40, then the number of cups of raisins will be 80. (d) if the number of cups of raisins is 40, then the number of cups of cereal will be 80.

If you double the input of a function and it results in half the output, and if you triple the input and it results in a third of the output, what can be guessed about the function? check all that apply.