Which characteristic does a translation not preserve?

a. distance from the origin
b. size of the figure
c. rotational symmetry
d. shape

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?

When 142 is added to a number the result is 64 more times the number my options are 35 37 39 41

Find the volume of the solid obtained by rotating the region enclosed by the curves y=1x and y=7^-x about the x-axis. (use symbolic notation and fractions where needed.) volume =