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The units digit of 7 is v. and the units digit of What is the value of the product xy

She constantly_________herself for not living up to her own ideals—for not working hard enough, or not having motives that were pure enough.

Instances of "galactic cannibalism"—mergers in which large galaxies completely consume smaller ones—may be fairly common. Tidal forces produced by the Milky Way's powerful gravity, for example, appear to be dismantling and engulfing a dwarf galaxy in the constellation Sagittarius, producing large clumps and streamers of stars connecting the two galaxies. Astronomers have also observed two dense clusters of stars and gas at the heart of the Andromeda galaxy, an apparent "double nucleus" that may contain the remnant of a cannibalized dwarf galaxy. But this twin-lobed appearance could also be created by two parts of a single nucleus bisected by a lane of dust. Scientists believe that only about 25 percent of such apparent double nuclei actually represent galactic cannibalism. Many of the rest result from the illusion of proximity that occurs when objects at different distances appear along the same line of sight: others consist of debris from galactic "collisions." in which one galaxy has passed through another without merging, causing waves of new star formation.

The primary purpose of the passage is to