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Solutions - Exam 1

# Solutions - Exam 1 - MATHEMATICS 111 EXAM 1 GREG RAINWATER...

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MATHEMATICS 111 - EXAM 1 GREG RAINWATER WINTER 2010 Name: SOLUTIONS Date: Question Pts. Worth Score #1 10 #2 10 #3 15 #4 15 #5 15 #6 10 #7 15 Total 90 1

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2 EXAM 1 - MATH 111 Problem #1. (a) Find the distance between the points (7 , - 4) and (9 , 1) . d = p (9 - 7) 2 + (1 - ( - 4)) 2 = 4 + 25 = 29 (b) Find the midpoint of the line segment containing the points (7 , - 4) and (9 , 1) . m = 7 + 9 2 , - 4 + 1 2 = 8 , - 3 2 Problem #2. Solve the equation. (a) 7 - 9 x = 2(3 - 4 x ) + x 7 - 9 x = 2(3 - 4 x ) + x 7 - 9 x = 6 - 8 x + x 7 - 9 x = 6 - 7 x - 2 x = - 1 x = 1 2 (b) 7 3 (2 x - 1) - 2 5 (4 - 3 x ) = 1 5 x 7 3 (2 x - 1) - 2 5 (4 - 3 x ) = 1 5 x 15( 7 3 (2 x - 1) - 2 5 (4 - 3 x )) = 15( 1 5 x ) 5 · 7(2 x - 1) - 3 · 2(4 - 3 x ) = 3 x 35(2 x - 1) - 6(4 - 3 x ) = 3 x 70 x - 35 - 24 + 18 x = 3 x 85 x = 59 x = 59 85
EXAM 1 - MATH 111 3 Problem #3. Given the equation (1) - 2 y - x = 4 (a) What is the y-intercept of Equation 1 (in other words, where does the equation cross the y-axis?) y-int: - 2 y - 0 = 4 ⇐⇒ y = 4 - 2 = - 2 This corresponds to the point (0 , - 2). (b) What is the x-intercept of Equation 1 (in other words, where does the equation cross the x-axis?) x-int: - 2(0) - x = 4 ⇐⇒ x = - 4 This corresponds to the point ( - 4 , 0) (c) What is the slope of Equation 1

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