Math 012 Quiz 4 Fall 2016 Professor: Jean Alexander Name________________________________ Instructions: The quiz is worth 50 points. There are 10 problems, each worth 5 points. Your score on the quiz will be converted to a percentage and posted in your assignment folder with comments. This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module. If you have any questions, please contact me by e-mail (jean.alexander@umuc.edu). At the end of your quiz you must include the following dated statement with your name typed in lieu of a signature. Without this signed statement you will receive a zero. I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Name: Date: Please remember to show all of your work. 1) Find the excluded value for the algebraic fraction: 2 x5 4 x9 Math 012 Quiz 4 Page 2 2) Find the excluded values for the algebraic fraction: x +3 x 2 x24 2 3) Perform the indicated operation and simplify your answer: 3 12 x 4 x8 3 2 10 x Math 012 Quiz 4 Page 3 4) Perform the indicated operation and simplify your answer: 2 2 x 9 x +14 4 x 28 x x2 x +3 5) Perform the indicated operation and simplify your answer: 4 5 + 3 x +2 x +1 6) Perform the indicated operation and simplify your answer: 4 3 x5 x +2 Math 012 Quiz 4 Page 4 7) Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state than on your paper. Use the method discussed in Section 7.7 of our text, clearing fractions from the equation first. x6 x 2+ 9 x+24 2 + = 2 x2 3 x2 x 8) Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state that your paper. Use the method discussed in Section 7.7 of our text, clearing fractions from the equation first. x 5 4x 2 = 2 x +5 x +5 x x +5 x Math 012 Quiz 4 Page 5 9) To determine the number of deer in a forest, a forest ranger tags 280 and releases them back into the forest. Later, 405 deer are caught, out of which 45 of them are tagged. Estimate how many deer are in the forest. Use a proportion to set up and solve an equation. Round your answer to the nearest whole number if necessary. 10) In a basketball game, the home team was down by three points at the end of the game. They only scored 9 points for every 10 points the visiting team scored. What was the final score of the game? End of quiz: please remember to sign and date the statement in the box on the first page of the quiz. Math 012 Quiz 4 Fall 2016 Professor: Jean Alexander Name________________________________ Instructions: The quiz is worth 50 points. There are 10 problems, each worth 5 points. Your score on the quiz will be converted to a percentage and posted in your assignment folder with comments. This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module. If you have any questions, please contact me by e-mail (jean.alexander@umuc.edu). At the end of your quiz you must include the following dated statement with your name typed in lieu of a signature. Without this signed statement you will receive a zero. I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Name: Date: Please remember to show all of your work. 1) Find the excluded value for the algebraic fraction: 2 x5 4 x9 Ans : The excluded value of the algebraic fraction when 4 x9=0 9 > x= is excluded value. 4 Math 012 Quiz 4 Page 2 2) Find the excluded values for the algebraic fraction: x +3 x 2 x24 2 Ans : The excluded value of the algebraic fraction is 2 when x 2 x24=0 2 > x 6 x +4 x 24=0 > x ( x 6 ) +4 ( x6 )=0 > ( x6 )( x +4 )=0 > x=6 ,4 are excluded values . 3) Perform the indicated operation and simplify your answer: 12 x 3 4 x8 2 10 x 3 Ans : 3 12 x 4 x8 6 2 ( 2 x 4 ) 6 ( = = 2 x 4 ) . 3 2 5 2 5 10 x Math 012 Quiz 4 Page 3 4) Perform the indicated operation and simplify your answer: 2 2 x 9 x +14 4 x 28 x x2 x +3 Ans : 2 2 2 x 9 x +14 4 x 28 x x 9 x +14 x +3 = 2 x2 x +3 x 2 4 x 28 x 2 x 7 x2 x +14 x +3 x2 4 x ( x7 ) x ( x7 )2 ( x7 ) x +3 x2 4 x ( x7 ) ( x7 )( x2 ) x +3 x2 4 x ( x7 ) x +3 4x Here excluded value is x=0 . 5) Perform the indicated operation and simplify your answer: 4 5 + 3 x +2 x +1 Ans : Math 012 Quiz 4 4 ( x +1 )+ 5 (3 x +2 ) 4 x +4 +15 x+10 4 5 + = = 3 x +2 x +1 ( 3 x +2 ) ( x +1 ) ( 3 x +2 )( x +1 ) 19 x +14 ( 3 x +2 ) ( x +1 ) Here the excluded value when ( 3 x +2 )( x +1 )=0 2 > x= ,1 are excluded values . 3 6) Perform the indicated operation and simplify your answer: 4 3 x5 x +2 Ans : 4 ( x +2 )3 ( x5 ) 4 x+ 83 x +15 4 3 x +23 = = = x5 x +2 ( x5 ) ( x+2 ) ( x5 )( x +2 ) ( x 5 )( x +2 ) Here the excluded value when ( x5 )( x +1 )=0 > x=5 ,1 are excluded values . Page 4 Math 012 Quiz 4 Page 5 7) Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state than on your paper. Use the method discussed in Section 7.7 of our text, clearing fractions from the equation first. x6 x 2+ 9 x+24 2 + = 2 x2 3 x2 x Ans : x6 x 2+ 9 x+24 2 + = 2 x2 3 x2 x 2 3 ( x 6 ) + x + 9 x+24 2 > = 2. 3 x2 x Docross multiplication. >3 x 2 ( x6 )+ x2 ( x 2+ 9 x+24 )=6 x 2 >3 x 2 ( x6 )+ x2 ( x 2+ 9 x+24 )6 x 2=0 . > x 2 {3 x 18+ x 2+ 9 x +246 }=0 2 2 > x ( x +12 x)=0 > x 3 ( x +12 )=0 > x=0 ,12 : When x=12 . 2 126 (12 ) + 9 (12 ) +24 2 + = 2 2 2 (12 ) 3 (12 ) (12 ) > 18 144108+24 2 + = 144 3 144 144 > 18 60 2 + = 144 3 144 144 > 18 2 0 2 + = 144 144 144 > 18+ 20 2 = 144 144 Math 012 Quiz 4 > Page 6 2 2 = Satisfied 144 144 When x=0 this is excluded value because when x=0 the denominator becomes zero . 8) Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state that your paper. Use the method discussed in Section 7.7 of our text, clearing fractions from the equation first. x 5 4x 2 = 2 x +5 x +5 x x +5 x Ans : x 5 4x 2 = 2 x +5 x +5 x x +5 x > x 5 4x = x+5 x ( x +5 ) x ( x +5 ) > x 25 4x = x ( x +5 ) x ( x+5 ) > x ( x +5 ) ( x 25 ) =4 x 2 ( x+5 ) Math 012 Quiz 4 Page 7 > x ( x +5 ) ( x 25 ) 4 x 2 ( x+5 )=0 > x ( x +5 ) ( x 254 x ) =0 > x ( x +5 ) ( x5 ) ( x+1 )=0 > x=0,5,5,1 : When x=0 ,5 Both x=0,5 are excluded values because denominator becomes zero when x=1 4 (1 ) 1 5 = 1+5 1 (1+ 5 ) 1 (1+5 ) 1 5 4 > + = 4 4 4 4 4 > = Satisfied 4 4 When x=1then 4 (5) 5 5 = 5+ 5 5 ( 5+5 ) 5 ( 5+5 ) > 5 1 4 = 10 10 10 > 4 4 = satisfied . 10 10 . 9) To determine the number of deer in a forest, a forest ranger tags 280 and releases them back into the forest. Later, 405 deer are caught, out of which 45 of them are tagged. Estimate how many deer are in the forest. Use a proportion to set up and solve an equation. Round your answer to the nearest whole number if necessary. Math 012 Quiz 4 Page 8 Ans : The forest ranger tags 280 deerrelease back forest Let total number of deer the fores is x then 45 280 = 405 x > x=280 405 45 81 9 280 9 280 x=2520 deer . . 10) In a basketball game, the home team was down by three points at the end of the game. They only scored 9 points for every 10 points the visiting team scored. What was the final score of the game? Ans : Let final score of the game is x then Math 012 Quiz 4 Page 9 x3 9 = x 10 >9 x=10 x30 >10 x9 x=30 > x=30 point . End of quiz: please remember to sign and date the statement in the box on the first page of the quiz. Math 012 Quiz 4 Fall 2016 Professor: Jean Alexander Name________________________________ Instructions: The quiz is worth 50 points. There are 10 problems, each worth 5 points. Your score on the quiz will be converted to a percentage and posted in your assignment folder with comments. This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module. If you have any questions, please contact me by e-mail (jean.alexander@umuc.edu). At the end of your quiz you must include the following dated statement with your name typed in lieu of a signature. Without this signed statement you will receive a zero. I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Name: Date: Please remember to show all of your work. 1) Find the excluded value for the algebraic fraction: 2 x5 4 x9 Ans : The excluded value of the algebraic fraction when 4 x9=0 9 > x= is excluded value. 4 Math 012 Quiz 4 Page 2 2) Find the excluded values for the algebraic fraction: x +3 x 2 x24 2 Ans : The excluded value of the algebraic fraction is 2 when x 2 x24=0 2 > x 6 x +4 x 24=0 > x ( x 6 ) +4 ( x6 )=0 > ( x6 )( x +4 )=0 > x=6 ,4 are excluded values . 3) Perform the indicated operation and simplify your answer: 12 x 3 4 x8 2 10 x 3 Ans : 3 12 x 4 x8 6 2 ( 2 x 4 ) 6 ( = = 2 x 4 ) . 3 2 5 2 5 10 x Math 012 Quiz 4 Page 3 4) Perform the indicated operation and simplify your answer: 2 2 x 9 x +14 4 x 28 x x2 x +3 Ans : 2 2 2 x 9 x +14 4 x 28 x x 9 x +14 x +3 = 2 x2 x +3 x 2 4 x 28 x 2 x 7 x2 x +14 x +3 x2 4 x ( x7 ) x ( x7 )2 ( x7 ) x +3 x2 4 x ( x7 ) ( x7 )( x2 ) x +3 x2 4 x ( x7 ) x +3 4x Here excluded value is x=0 . 5) Perform the indicated operation and simplify your answer: 4 5 + 3 x +2 x +1 Ans : Math 012 Quiz 4 4 ( x +1 )+ 5 (3 x +2 ) 4 x +4 +15 x+10 4 5 + = = 3 x +2 x +1 ( 3 x +2 ) ( x +1 ) ( 3 x +2 )( x +1 ) 19 x +14 ( 3 x +2 ) ( x +1 ) Here the excluded value when ( 3 x +2 )( x +1 )=0 2 > x= ,1 are excluded values . 3 6) Perform the indicated operation and simplify your answer: 4 3 x5 x +2 Ans : 4 ( x +2 )3 ( x5 ) 4 x+ 83 x +15 4 3 x +23 = = = x5 x +2 ( x5 ) ( x+2 ) ( x5 )( x +2 ) ( x 5 )( x +2 ) Here the excluded value when ( x5 )( x +1 )=0 > x=5 ,1 are excluded values . Page 4 Math 012 Quiz 4 Page 5 7) Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state than on your paper. Use the method discussed in Section 7.7 of our text, clearing fractions from the equation first. x6 x 2+ 9 x+24 2 + = 2 x2 3 x2 x Ans : x6 x 2+ 9 x+24 2 + = 2 x2 3 x2 x 2 3 ( x 6 ) + x + 9 x+24 2 > = 2. 3 x2 x Docross multiplication. >3 x 2 ( x6 )+ x2 ( x 2+ 9 x+24 )=6 x 2 >3 x 2 ( x6 )+ x2 ( x 2+ 9 x+24 )6 x 2=0 . > x 2 {3 x 18+ x 2+ 9 x +246 }=0 2 2 > x ( x +12 x)=0 > x 3 ( x +12 )=0 > x=0 ,12 : When x=12 . 2 126 (12 ) + 9 (12 ) +24 2 + = 2 2 2 (12 ) 3 (12 ) (12 ) > 18 144108+24 2 + = 144 3 144 144 > 18 60 2 + = 144 3 144 144 > 18 2 0 2 + = 144 144 144 > 18+ 20 2 = 144 144 Math 012 Quiz 4 > Page 6 2 2 = Satisfied 144 144 When x=0 this is excluded value because when x=0 the denominator becomes zero . 8) Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state that your paper. Use the method discussed in Section 7.7 of our text, clearing fractions from the equation first. x 5 4x 2 = 2 x +5 x +5 x x +5 x Ans : x 5 4x 2 = 2 x +5 x +5 x x +5 x > x 5 4x = x+5 x ( x +5 ) x ( x +5 ) > x 25 4x = x ( x +5 ) x ( x+5 ) > x ( x +5 ) ( x 25 ) =4 x 2 ( x+5 ) Math 012 Quiz 4 Page 7 > x ( x +5 ) ( x 25 ) 4 x 2 ( x+5 )=0 > x ( x +5 ) ( x 254 x ) =0 > x ( x +5 ) ( x5 ) ( x+1 )=0 > x=0,5,5,1 : When x=0 ,5 Both x=0,5 are excluded values because denominator becomes zero when x=1 4 (1 ) 1 5 = 1+5 1 (1+ 5 ) 1 (1+5 ) 1 5 4 > + = 4 4 4 4 4 > = Satisfied 4 4 When x=1then 4 (5) 5 5 = 5+ 5 5 ( 5+5 ) 5 ( 5+5 ) > 5 1 4 = 10 10 10 > 4 4 = satisfied . 10 10 . 9) To determine the number of deer in a forest, a forest ranger tags 280 and releases them back into the forest. Later, 405 deer are caught, out of which 45 of them are tagged. Estimate how many deer are in the forest. Use a proportion to set up and solve an equation. Round your answer to the nearest whole number if necessary. Math 012 Quiz 4 Page 8 Ans : The forest ranger tags 280 deerrelease back forest Let total number of deer the fores is x then 45 280 = 405 x > x=280 405 45 81 9 280 9 280 x=2520 deer . . 10) In a basketball game, the home team was down by three points at the end of the game. They only scored 9 points for every 10 points the visiting team scored. What was the final score of the game? Ans : Let final score of the game is x then Math 012 Quiz 4 Page 9 x3 9 = x 10 >9 x=10 x30 >10 x9 x=30 > x=30 point . End of quiz: please remember to sign and date the statement in the box on the first page of the quiz. Math 012 Quiz 4 Fall 2016 Professor: Jean Alexander Name________________________________ Instructions: The quiz is worth 50 points. There are 10 problems, each worth 5 points. Your score on the quiz will be converted to a percentage and posted in your assignment folder with comments. This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You must show all of your work to receive full credit. If a problem does not seem to require work, write a sentence or two to justify your answer. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your quiz in the Unit Quizzes Module. If you have any questions, please contact me by e-mail (jean.alexander@umuc.edu). At the end of your quiz you must include the following dated statement with your name typed in lieu of a signature. Without this signed statement you will receive a zero. I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Name: Date: Please remember to show all of your work. 1) Find the excluded value for the algebraic fraction: 2 x5 4 x9 Ans : The excluded value of the algebraic fraction when 4 x9=0 9 > x= is excluded value. 4 Math 012 Quiz 4 Page 2 2) Find the excluded values for the algebraic fraction: x +3 x 2 x24 2 Ans : The excluded value of the algebraic fraction is 2 when x 2 x24=0 2 > x 6 x +4 x 24=0 > x ( x 6 ) +4 ( x6 )=0 > ( x6 )( x +4 )=0 > x=6 ,4 are excluded values . 3) Perform the indicated operation and simplify your answer: 12 x 3 4 x8 2 10 x 3 Ans : 3 12 x 4 x8 6 2 ( 2 x 4 ) 6 ( = = 2 x 4 ) . 3 2 5 2 5 10 x Math 012 Quiz 4 Page 3 4) Perform the indicated operation and simplify your answer: 2 2 x 9 x +14 4 x 28 x x2 x +3 Ans : 2 2 2 x 9 x +14 4 x 28 x x 9 x +14 x +3 = 2 x2 x +3 x 2 4 x 28 x 2 x 7 x2 x +14 x +3 x2 4 x ( x7 ) x ( x7 )2 ( x7 ) x +3 x2 4 x ( x7 ) ( x7 )( x2 ) x +3 x2 4 x ( x7 ) x +3 4x Here excluded value is x=0 . 5) Perform the indicated operation and simplify your answer: 4 5 + 3 x +2 x +1 Ans : Math 012 Quiz 4 4 ( x +1 )+ 5 (3 x +2 ) 4 x +4 +15 x+10 4 5 + = = 3 x +2 x +1 ( 3 x +2 ) ( x +1 ) ( 3 x +2 )( x +1 ) 19 x +14 ( 3 x +2 ) ( x +1 ) Here the excluded value when ( 3 x +2 )( x +1 )=0 2 > x= ,1 are excluded values . 3 6) Perform the indicated operation and simplify your answer: 4 3 x5 x +2 Ans : 4 ( x +2 )3 ( x5 ) 4 x+ 83 x +15 4 3 x +23 = = = x5 x +2 ( x5 ) ( x+2 ) ( x5 )( x +2 ) ( x 5 )( x +2 ) Here the excluded value when ( x5 )( x +1 )=0 > x=5 ,1 are excluded values . Page 4 Math 012 Quiz 4 Page 5 7) Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state than on your paper. Use the method discussed in Section 7.7 of our text, clearing fractions from the equation first. x6 x 2+ 9 x+24 2 + = 2 x2 3 x2 x Ans : x6 x 2+ 9 x+24 2 + = 2 x2 3 x2 x 2 3 ( x 6 ) + x + 9 x+24 2 > = 2. 3 x2 x Docross multiplication. >3 x 2 ( x6 )+ x2 ( x 2+ 9 x+24 )=6 x 2 >3 x 2 ( x6 )+ x2 ( x 2+ 9 x+24 )6 x 2=0 . > x 2 {3 x 18+ x 2+ 9 x +246 }=0 2 2 > x ( x +12 x)=0 > x 3 ( x +12 )=0 > x=0 ,12 : When x=12 . 2 126 (12 ) + 9 (12 ) +24 2 + = 2 2 2 (12 ) 3 (12 ) (12 ) > 18 144108+24 2 + = 144 3 144 144 > 18 60 2 + = 144 3 144 144 > 18 2 0 2 + = 144 144 144 > 18+ 20 2 = 144 144 Math 012 Quiz 4 > Page 6 2 2 = Satisfied 144 144 When x=0 this is excluded value because when x=0 the denominator becomes zero . 8) Solve the equation and show the check of your solution(s). If an answer is an excluded value, please state that your paper. Use the method discussed in Section 7.7 of our text, clearing fractions from the equation first. x 5 4x 2 = 2 x +5 x +5 x x +5 x Ans : x 5 4x 2 = 2 x +5 x +5 x x +5 x > x 5 4x = x+5 x ( x +5 ) x ( x +5 ) > x 25 4x = x ( x +5 ) x ( x+5 ) > x ( x +5 ) ( x 25 ) =4 x 2 ( x+5 ) Math 012 Quiz 4 Page 7 > x ( x +5 ) ( x 25 ) 4 x 2 ( x+5 )=0 > x ( x +5 ) ( x 254 x ) =0 > x ( x +5 ) ( x5 ) ( x+1 )=0 > x=0,5,5,1 : When x=0 ,5 Both x=0,5 are excluded values because denominator becomes zero when x=1 4 (1 ) 1 5 = 1+5 1 (1+ 5 ) 1 (1+5 ) 1 5 4 > + = 4 4 4 4 4 > = Satisfied 4 4 When x=1then 4 (5) 5 5 = 5+ 5 5 ( 5+5 ) 5 ( 5+5 ) > 5 1 4 = 10 10 10 > 4 4 = satisfied . 10 10 . 9) To determine the number of deer in a forest, a forest ranger tags 280 and releases them back into the forest. Later, 405 deer are caught, out of which 45 of them are tagged. Estimate how many deer are in the forest. Use a proportion to set up and solve an equation. Round your answer to the nearest whole number if necessary. Math 012 Quiz 4 Page 8 Ans : The forest ranger tags 280 deerrelease back forest Let total number of deer the fores is x then 45 280 = 405 x > x=280 405 45 81 9 280 9 280 x=2520 deer . . 10) In a basketball game, the home team was down by three points at the end of the game. They only scored 9 points for every 10 points the visiting team scored. What was the final score of the game? Ans : Let final score of the game is x then Math 012 Quiz 4 Page 9 x3 9 = x 10 >9 x=10 x30 >10 x9 x=30 > x=30 point . End of quiz: please remember to sign and date the statement in the box on the first page of the quiz