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Unformatted text preview: syed (sms3768) – Quest HW 1 – seckin – (56425) 1 This printout should have 20 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the xintercept of the straight line passing through the points P (1 , 5) and Q (9 , 2). 1. xintercept = 43 3 correct 2. xintercept = 47 3 3. xintercept = 15 4. xintercept = 44 3 5. xintercept = 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 xintercept of the line is the solution of y = 0, i.e. , the solution of 3 x = 43. Consequently, xintercept = 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 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 ....
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This note was uploaded on 04/29/2010 for the course MATH 408K taught by Professor Seckin during the Spring '10 term at University of TexasTyler.
 Spring '10
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