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Quest HW 1-solutions

# Quest HW 1-solutions - syed(sms3768 Quest HW 1 seckin(56425...

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syed (sms3768) – Quest HW 1 – seckin – (56425) 1 This print-out should have 20 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the x -intercept of the straight line passing through the points P (1 , 5) and Q (9 , 2). 1. x -intercept = 43 3 correct 2. x -intercept = 47 3 3. x -intercept = 15 4. x -intercept = 44 3 5. x -intercept = 46 3 Explanation: The slope of the straight line passing through the points P (1 , 5) and Q (9 , 2) is given by slope = rise run = 3 8 . By the point slope formula, therefore, this line has equation y 2 = 3 8 ( x 9) . Now the x -intercept of the line is the solution of y = 0, i.e. , the solution of 3 x = 43. Consequently, x -intercept = 43 3 . 002 10.0 points Rationalize the denominator of 6 14 + 7 . 1. 6 7 parenleftBig 14 7 parenrightBig correct 2. 6 14 7 3. 6 7 parenleftBig 14 + 7 parenrightBig 4. 6 parenleftBig 14 7 parenrightBig 5. 14 + 7 7 Explanation: Multiplying the numerator and denomina- tor by the conjugate of the denominator, we see that 6 14 + 7 = 6( 14 7) ( 14 + 7)( 14 7) = 6( 14 7) 14 7 . Consequently, 6 14 + 7 = 6 7 parenleftBig 14 7 parenrightBig . 003 10.0 points Rationalize the denominator of 3 x + 4 x 3 . 1. 3 parenleftBig x + 4 x 3 parenrightBig 2. 3 7 parenleftBig x 4 + x + 3 parenrightBig 3. 3 parenleftBig x + 4 + x 3 parenrightBig 4. 3 7 parenleftBig x + 4 + x 3 parenrightBig correct 5. 3 7 parenleftBig x 4 x + 3 parenrightBig

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syed (sms3768) – Quest HW 1 – seckin – (56425) 2 Explanation: By the difference of squares, ( x + 4 x 3)( x + 4 + x 3) = ( x + 4) 2 ( x 3) 2 = 7 . Thus, after multiplying both the numerator and the denominator in the given expression by x + 4 + x 3 , we obtain 3 7 parenleftBig x + 4 + x 3 parenrightBig . 004 10.0 points Simplify the expression ( 9 b 2 ) parenleftbigg 1 6 b 3 parenrightbigg ( 4 b 4 ) as much as possible. 1. 3 b 9 2. b 9 3. 6 b 2 4. 6 b 5 5. 6 b 9 correct Explanation: By the Laws of Exponents, ( 9 b 2 ) parenleftbigg 1 6 b 3 parenrightbigg ( 4 b 4 ) = 9 · 4 6 b 2+3+4 = 6 b 9 . 005 10.0 points Express the number x = parenleftbigg 4 3 parenrightbigg 4 3 - 4 in the form a b , where a and b are integers. 1. x = 56 27 2. x = 85 27 correct 3. x = 139 27 4. x = 112 27 5. x = 85 54 Explanation: Notice first that parenleftbigg 4 3 parenrightbigg 4 = parenleftbigg 4 3 parenrightbigg 4 . On the other hand, using the difference of squares formula we obtain parenleftbigg 4 3 parenrightbigg 4 3 - 4 = parenleftBigg parenleftbigg 4 3 parenrightbigg 2 parenleftbigg 1 3 parenrightbigg 2 parenrightBigg × × parenleftBigg parenleftbigg 4 3 parenrightbigg 2 + parenleftbigg 1 3 parenrightbigg 2 parenrightBigg = 5 3 · 17
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