Polygon abcd is plotted on a coordinate plane. if the polygon translates 3 units to the left and 1 unit down, the length of diagonal is units. if the polygon translates 3 units further to the left and four units down, the length of diagonal .

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?

For what values of x is x2 + 2x = 24 true?

Rena is building a 1: 180 scale model of a real castle. her model has a rectangular base that is 3 feet wide and 4 feet long what is the area of the base of the actual castle in square feet