Homework 1 - Garcia, Ilse Homework 1 Due: Sep 7 2007, 3:00...

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Unformatted text preview: Garcia, Ilse Homework 1 Due: Sep 7 2007, 3:00 am Inst: Fonken 1 This print-out should have 21 questions. Multiple-choice 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) 2. 5 x x + 4- x- 1 3. 3 x x + 4 + x- 1 4. 3 x ( x + 4 + x- 1) 5. 5 x ( x + 4 + x- 1) correct 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 ) = 5 + 15 x- 2 2- 6 x x 2- 4 as much as possible. 1. f ( x ) = x + 2 x + 4 2. f ( x ) = 5 2 x- 2 x- 4 3. f ( x ) = 5 2 x + 2 x- 4 correct 4. f ( x ) = 5 2 x + 2 2 x- 4 5. f ( x ) = x- 2 x + 4 6. f ( x ) = x- 2 2 x + 4 Explanation: After bringing the numerator to a common denominator it becomes 5 x- 10 + 15 x- 2 = 5 x + 5 x- 2 . Similarly, after bringing the denominator to a common denominator and factoring it be- comes 2 x 2- 8- 6 x x 2- 4 = 2( x + 1)( x- 4) x 2- 4 . Consequently, f ( x ) = 5 + 15 x- 2 2- 6 x x 2- 4 = 5 x + 5 2( x + 1)( x- 4) x 2- 4 x- 2 . On the other hand, x 2- 4 = ( x + 2)( x- 2) . Thus, finally, we see that f ( x ) = 5 2 x + 2 x- 4 . Garcia, Ilse Homework 1 Due: Sep 7 2007, 3:00 am Inst: Fonken 2 keywords: 003 (part 1 of 1) 10 points Find the solution set of the inequality x- 3 x- 5 < x + 6 x + 5 . 1. - ,- 15 i [ - 5 , 5 2. - 15 ,- 5 [ 5 , 3. - ,- 15 [ h- 5 , 5 4. h- 15 ,- 5 [ 5 , 5. - ,- 15 [ - 5 , 5 correct 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 + 6 x + 5 < , which in turn becomes ( ) x + 15 ( x + 5)( 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 =- 15 , 5 ,- 5, and the sign chart- 15- 5 5- +- + determines which sign it takes in a given in- terval. Thus the solution set of ( ) is the union - ,- 15 [ - 5 , 5 . keywords: 004 (part 1 of 1) 10 points The straight line is parallel to y + 5 x = 3 and passes through the point P (5 , 4). Find its x-intercept. 1. x-intercept = 29 5 correct 2. x-intercept =- 21 5 3. x-intercept = 29 6 4. x-intercept =- 29 5 5. x-intercept = 6 Explanation: Since is parallel to the line y + 5 x = 3, these lines have the same slope- 5, Thus by the point-slope formula the equation of is given by y- 4 =- 5( x- 5) ....
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Homework 1 - Garcia, Ilse Homework 1 Due: Sep 7 2007, 3:00...

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