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Unformatted text preview: Jolley, Garrett Homework 1 Due: Sep 7 2007, 3:00 am Inst: R Heitmann 1 This printout should have 21 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. The due time is Central time. Yes, Homework 1 is due AFTER Homework 2. 001 (part 1 of 1) 10 points Rationalize the numerator of x + 4 x 1 x . 1. 5 x ( x + 4 + x 1) correct 2. 3 x ( x + 4 + x 1) 3. 5 x ( x + 4 x 1) 4. 3 x x + 4 + x 1 5. 5 x x + 4 x 1 Explanation: By the difference of squares, ( x + 4 x 1)( x + 4 + x 1) = ( x + 4) 2 ( x 1) 2 = 5 . Thus, after multiplying both the numerator and the denominator in the given expression by x + 4 + x 1 , we obtain 5 x ( x + 4 + x 1) . keywords: rationalization numerator, 002 (part 1 of 1) 10 points Simplify the expression f ( x ) = 4 + 24 x 5 1 24 x x 2 25 as much as possible. 1. f ( x ) = 4 x + 5 2 x 25 2. f ( x ) = x + 5 x + 25 3. f ( x ) = x 5 x + 25 4. f ( x ) = 4 x + 5 x 25 correct 5. f ( x ) = 4 x 5 x 25 6. f ( x ) = x 5 2 x + 25 Explanation: After bringing the numerator to a common denominator it becomes 4 x 20 + 24 x 5 = 4 x + 4 x 5 . Similarly, after bringing the denominator to a common denominator and factoring it be comes x 2 25 24 x x 2 25 = ( x + 1)( x 25) x 2 25 . Consequently, f ( x ) = 4 + 24 x 5 1 24 x x 2 25 = 4 x + 4 ( x + 1)( x 25) x 2 25 x 5 . On the other hand, x 2 25 = ( x + 5)( x 5) . Thus, finally, we see that f ( x ) = 4 x + 5 x 25 . Jolley, Garrett Homework 1 Due: Sep 7 2007, 3:00 am Inst: R Heitmann 2 keywords: 003 (part 1 of 1) 10 points Find the solution set of the inequality x 3 x 5 < x + 5 x + 4 . 1.  , 13 [ h 4 , 5 2.  , 13 i [  4 , 5 3. h 13 , 4 [ 5 , 4.  , 13 [  4 , 5 correct 5.  13 , 4 [ 5 , Explanation: To begin we need to arrange that all the terms are on one side of the inequality. Thus the inequality becomes x 3 x 5 x + 5 x + 4 < , which in turn becomes ( ) x + 13 ( x + 4)( x 5) < after the right hand side is brought to a com mon denominator. Now the right hand side changes sign at the zeros of its numerator and denominator, i.e. , at x = 13 , 5 , 4, and the sign chart 13 4 5 + + determines which sign it takes in a given in terval. Thus the solution set of ( ) is the union  , 13 [  4 , 5 . keywords: 004 (part 1 of 1) 10 points The straight line is parallel to y + 4 x = 1 and passes through the point P (5 , 2). Find its xintercept. 1. xintercept = 11 2 correct 2. xintercept = 22 5 3. xintercept = 11 2 4. xintercept = 9 2 5. xintercept = 23 4 Explanation: Since is parallel to the line y + 4 x = 1, these lines have the same slope 4, Thus by the pointslope formula the equation of is given by y 2 = 4( x 5) ....
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 Spring '08
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