Find the width of a rectangular floor where the length is 5 feet less than twice the width, and the area is 150 square feet. Solution: Let the width be x feet. Then the length is 2x−5 feet. The area is x(2x−5)=150. Solving this quadratic equation, we get the width is x=10 feet.
Determine if the relation defined by the set of ordered pairs {(−1,20),(23,21),(−6,−19),(−16,14),(−20,10),(−14,−4)} is a function. State the domain and range.
Divide €2100 among 3 people such that the second gets 2x the first, and the third gets 2x the second. Find the amount each person receives. x+3x+2.4x=320000⇒6.4x=320000⇒x=50000 The first heir receives €50000, the second €150000 (= 3 * €50000), and the third €120000 (= 2.4 * €50000).
Rewrite the equation 0=−41(x+7)2+18 in standard form. Simplified problem statement (128 characters): Rewrite 0=−41(x+7)2+18 in standard form ax2+bx+c=0.
Find the composition f∘g for f(x)=x−3x and g(x)=x11. Simplify the result and write the domain using interval notation.
(f∘g)(x)=11−311
Domain of f∘g:x=0,3
Find the domain of the function f(x)=1.25x that models the amount of water, in quarts, in a bucket after x seconds, where the bucket needs to be filled with 70 quarts.