Proving the parallelogram side theorem

Asequence is a function whose is the set of natural numbers

X=4 / y=100 if x=10 then what is y=?

1.what’s the least common multiple (lcm) for each group of numbers? a. 6 and 15 b. 4 and 11 c. 6, 9, and 12 d. 8, 10, and 20 2.what’s the least common denominator (lcd) for each group of fractions? a. 1⁄6 and 7⁄8 b. 3⁄4 and 7⁄10 c. 7⁄12, 3⁄8 and 11⁄36 d. 8⁄15, 11⁄30 and 3⁄5 3.insert the “equal” sign or the “not equal” sign ( = or ≠) to make each statement true. a. 18/36 1/2 b. 13/15 7/10 c. 3/5 5/9 d. 3/8 10/16 4.on a hot summer day, john drank 5⁄11 of a quart of iced tea; gary drank 7⁄10 of a quart; and carter drank 3⁄5 of a quart. which man was the most thirsty? 5.what’s the largest fraction in each group? a. 5⁄6 and 29⁄36 b. 5⁄12 and 3⁄8 c. 2⁄5 and 19⁄45 d. 5⁄7, 13⁄14, and 19⁄21 e. 7⁄11 and 9⁄121 f. 1⁄2, 3⁄18, and 4⁄9 6.reduce each of the following fractions to its simplest form. a. 12⁄18 b. 48⁄54 c. 27⁄90 d. 63⁄77 e. 24⁄32 f. 73⁄365 7.what is the next fraction in each of the following patterns? a. 1⁄40, 4⁄40, 9⁄40, 16⁄40, 25⁄40 . .? b. 3⁄101, 4⁄101, 7⁄101, 11⁄101, 18⁄101, 29⁄101. .? c. 5⁄1, 10⁄2, 9⁄2, 18⁄4, 17⁄8, 34⁄32, 33⁄256. .? 8.in each pair, tell if the fractions are equal by using cross multiplication. a. 5⁄30 and 1⁄6 b. 4⁄12 and 21⁄60 c. 17⁄34 and 41⁄82 d. 6⁄9 and 25⁄36 9.this year, a baseball player made 92 hits out of 564 times at bat. another player made 84 hits out of 634 times at bat. did the two players have the same batting average? 10.on a test with 80 questions, bob got 60 correct. on another test with 100 questions, he got 75 correct. did bob get the same score on both tests? 11.find the missing numerators in each of the following problems. a. 10⁄15 = ⁄60 b. ⁄108 = 4⁄9 c. 7⁄11 = ⁄121 d. ⁄144 = 2⁄6 12.this handy application of lcms is used by astronomers. all the planets in our solar system revolve around the sun. the planets occasionally line up together in their journeys, as shown in the illustration. the chart shows the time it takes each planet to make one trip around the sun. now, imagine that the planets earth, mars, jupiter, saturn, uranus, and neptune aligned last night. how many years will pass before this happens again? (hint—find the lcm of the planets’ revolution times.) solar system planet revolution time earth 1 year mars 2 years jupiter 12 years saturn 30 years uranus 84 years neptune 165 years