VIEWS: 34 PAGES: 24 POSTED ON: 2/25/2012
Intermediate Algebra Chung 1 HOMEWORK 1.1 Consider a set of numbers 1 7 17 2, , 2, , 3 , 1.21212121 ...., , 0, 6.78, 6.723514 , 70 , 201, , 0.2312312312 31 .... 5 19 3 1. List all natural numbers 2. List all whole numbers 3. List all integers 4. List all rational numbers 5. List all irrational numbers 6. List all real numbers 7. List all natural numbers and integers 8. List all natural numbers and irrational numbers 9. List all whole numbers and rational numbers 10. List all integers and real numbers True or False. Explain or give a correct answer 11. Whole numbers are natural numbers 12. Natural numbers are whole numbers 13. Irrational numbers are real numbers 14. Rational numbers are integers Give an example for each scenario. 15. An integer which is a whole number. 16. An integer which is not a whole number. 17. A natural number which is a rational number. 18. A natural number which is not a rational number. 19. A real number which is a rational number. 20. A real number which is a whole number and a rational number. 21. A real number which is a rational number and an irrational number. Identify the property applied on each statement. 22. 3+2=2+3 23. 2a = a2 24. 3x(2) = 3(2)x 25. 2+0=2 26. a + (b + c) = (b + c) + a 27. 2(3 + 7) = 2(3) + 2(7) 28. 5 + (-5) = 0 2 3 29. 1 3 2 30. (x + y)1 = (x + y) True or False. Explain or give a correct answer. 31. 4a(5) = 20a 32. 4(5a) = 20(4a) 33. y5x = 5yx 34. A +B = B + A 35. A–B=B–A Intermediate Algebra Chung 2 1.2 Simplify each expression. Use the order of operations. 1. 15 5 2 2. 9 4 8 2 3. 12 24 3 2 4. 9(2) (3)( 2) 2 5. 4 3 5 6 2 6. 8( 64 ) (3)( 7) 3 5 7. 4 | 2 4 | 8 2 8. (6 3) | 2 3 | 9 9. 7 (8) 12 4 6 10. 3 12 (6 5 3) 11. 9 16 (3 2 ) 12. 3(4) (5)(8) 4 4 1 23 2 6 Evaluate each expression if a = –3, b = 64, and c = 6 3c a 2 13. a b 14. b ca 15. 3a 3c 4 16. 2b 6c 3 1 Evaluate each expression if w = 4, x , y , and z = 1.25 4 2 7 y 5x 18. xy x 2 17. wz – 12y 19. w – 6x + 5y – 3z 20. 2w Combine like terms 21. –5r – 9r + 8r – 5 22. –8x – 12 + 3x – 5x + 9 23. 5(r – 3) + 6r – 2r + 4 24. 6(a – 5) – (a + 6) 25. 0.4(10 – 5x) – 0.8(5 + 10x) 26. –(7m – 12) – 2(4m + 7) – 8m 27. –4 + 4(4k – 3) – 6(2k + 8) + 7 2.1 Solve each equation. State the number of solutions and tell whether the equation is conditional, an identity or a contradiction 1. 4(2d + 7) = 2d + 25 + 3(2d + 1) 2. 4[2t – (3 – t) + 5] = –(2 + 7t) 3. –[6x – (4x + 8)] = 9 + (6x + 3) 4. 4(k + 2) – 8k – 5 = –3k + 9 –2(k + 6) 5. 4[6 – (1 + 2x)] + 10x = 2(10 – 3x) + 8x 6. 2[–(x –1) + 4] = 5 + [–(6x – 7) + 9x] 2r 3 3 r 7. –6x + 2x – 11 = –2(2x – 3) + 4 8. 7 7 3 3x 2 x 4 2 x 5 3x 1 x 7 9. 2 10. 7 5 5 2 2 11. 0.09k + 0.13(k + 300) = 61 12. 0.2(14,000) + 0.14t = 0.18(14,000 + t) Solve for the specified variable 1 13. A bh for h 14. S 2rh 2r 2 for h 2 2t 4 15. 4s + 7p = tp – 7 for p 16. c for t t Intermediate Algebra Chung 3 2.2 Translate. 1. The product of 6 and a number, decreased by 12. 2. 12 more than one-half of a number. 3. The product of 9 more than a number and 6 less than the number. 4. The quotient of 6 and five times a number. 5. The sum of a number and –4 is 12. 6. If the quotient of a number and 6 is added to twice number, the result is 8 less than the number. 7. When 75% of a number is added to 6, the result is 3 more than the number. Translate and solve 8. Luke Corey works at an ice cream shop. At the end of his shift, he counted the bills in his cash drawer and found 119 bills with a total value of $347. If all the bills are $5 bills and $1 bills, how many of each denomination were in his cash drawer? 9. Dave Bowers collects U.S. gold coins. He has a collection of 41 coins. Some are $10 coins, and the rest are $20 coins. If the face value of the coins is $540, how many of each denomination does he have? 10. General admission to the Field Museum in Chicago costs $12 for adults and $7 for children and seniors. If $11,571 was collected from the sale of 1298 general admission tickets, how many adult tickets were sold? 11. For a high school production of West Side Story, student tickets cost $5 each while nonstudent tickets cost $8. If 480 tickets were sold for the Saturday night show and a total of $2895 was collected, how many tickets of each type were sold? Find the measure of each angle 12. 13. 14. 15. 16. 17. Intermediate Algebra Chung 4 2.3 Solve each inequality. Give the solution set in both interval and graph form. 2.4 Solve each equation or inequality. Write the solution set in interval notation when possible 1. |–3 + t| > 8 2. |2x – 1| < 7 3. |9 – 3p| = 3 4. |2s – 6| ≤ 6 5. |–2x – 6| ≤ 5 6. |–4 + k| ≤ 9 7. |x + 3| = 10 8. |x – 4| = 1 9. |x| + 3 = 10 10. |x + 5| – 2 = 12 11. |6x – 1| – 2 > 6 12. |r – 2| – 3 ≤ 4 2 1 13. |7x+12| = |x – 8| 14. r 2 r 3 15. |13x| = |2x+1| 3 3 16. |3x − 1| = |3x + 9| 17. |x| ≥ −15 18. |13w + 1| = –3 19. |6r − 2| = 0 20. |8n + 4| = −4 21. |x + 9| > −3 22. |4x − 1| ≤ 0 23. |4 + 7x| = 0 24. |k – 4| + 5 ≥ 4 2.5 Let A = {1, 2, 3, 4, 5, 6,}, B = {1, 3, 5}, C = {1, 6}, and D = {4}. Find the intersection or union as specified. 1. A B 2. B C 3. A U C 4. B U D 5. C D 6. C U D Solve each compound inequality, give the solution set in both interval notation and graph form. 7. x < −1 and x > −5 8. x > −1 and x < 7 9. x < 4 or x < −2 10. x < 5 or x < −3 11. −3x ≤ −6 or −3x ≥ 0 12. 2x − 6 ≤ −18 and 2x ≥ −18 13. x + 1 ≥ 5 and x − 2 ≤ 10 14. −8x ≤ − 24 or −5x ≥ 15 3.1 Determine if the line is given in standard form or in slope intercept form or neither 1. 2x + 5y = 11 2. −y = 6x + 9 3. y = −4x + 9 4. 7x = 9y − 2 5. 5x − 6y = 7 6. x = 2 − 6y Intermediate Algebra Chung 5 Graph each equation 7. 5x + 2y = 10 8. x – 2y = −4 9. y = −3 10. x = −3 11. x – 3y = 0 12. 4y = 3x 13. x + 3y = −6 14. 4x – y = 4 15. y = −3x 16. x + 2 = 0 17. y = −4 3.2 Find the slope of the line through each pair of points. 1. (−4, 3) and (−3, 4) 2. (−3, −3) and (5, 6) 3. (−6, 3) and (2, 3) 3 1 5 10 4 9 3 1 4. (3.4, 4.3) and (1.4, 10.3) 5. , and , 6. , and , 4 3 4 3 5 10 10 5 Decide if each pair of lines is parallel, perpendicular or neither. 7. 2x + 5y = −7 and 5x – 2y = 1 8. 2x + y = 6 and x – y = 4 9. 3x = y and 2y – 6x = 5 10. 2x + 5y = −8 and 6 + 2x = 5y 11. 4x – 3y = 8 and 4y + 3x = 12 12. 2x = y + 3 and 2y + x = 3 3.3 Find an equation of a line with the given conditions 5 1. Through (12, 10); slope = 1 2. Through (−1, 6); slope 6 1 3. Through (7, −2); slope 4. Through (−2, 0); slope −5 4 5. Through (6, −12); slope 0.8 6. Through (−4, −2); slope 0 5 2 7. Through (−2, 8); undefined slope 8. Through , ; vertical 8 9 9. Through (2, 7); horizontal 10. Through (5, −2) and (−3, 14) 3 8 2 2 11. Through (−2, 5) and (−8, 1) 12. Through , and , 4 3 5 3 13. (−2, 2) and (4, 2) 14. Through (13, 5) and (13, −1) 4 12 15. Through , 6 and , 6 16. Through (4, 1); parallel to 2x + 5y = 10 9 7 17. Through (−1, 3); parallel to −x + 3y = 12 18. Through (2, −7); perpendicular 5x + 2y = 18 19. Through (8, 4); perpendicular to x = −3 3.4 Graph each inequality 1. x + y ≤ −3 2. 3x – y < 3 3. x + 4y ≥ −3 4. x + 2y > 0 5. x – 5y ≤ 0 6. y ≤ 4x Graph each compound inequality 7. x – y ≥ 2 and x ≥ 3 8. 3x – y ≥ 3 and y < 3 9. 6x – 4y < 10 and y > 2 10. x + y ≤ 2 or y ≥ 3 11. x + 3 < y or x > 3 12. x – y ≥ 1 or x + y ≤ 4 3.5 Intermediate Algebra Chung 6 Determine if each relation is a function. Find the domain and the range 1. {(5, 1), (3, 2), (4, 9), (7, 6)} 2. {(8, 0), (5, 4), (9, 3), (3, 8)} 3. {(2, 4), (0, 2), (2, 5)} 4. {(9, −2), (−3, 5), (9, 2)} 5. {(−3, 1), (4, 1), (−2, 7)} 6. {(−12, 5), (−10, 3), (8, 3)} Use the vertical line test to determine if each graph is a function. 7. y 8. y 9. y x x x 10. 11. 12. y y y x x x 7 13. f(−3) 14. g(10) 15. f 16. g(1.5) 17. g(k) 18. g(−x) 3 19. f(x – 2) 20. g(e) 3.6 Intermediate Algebra Chung 7 4.1 Solve each system by graphing. Solve each system by substitution. If the system is inconsistent or has dependent equations say so. Intermediate Algebra Chung 8 Solve each system by elimination. If the system is inconsistent or has dependent equations say so. Solve each system by the elimination/addition method. If the system is inconsistent or has dependent equations say so. 4.2 1. A total of $3000 is invested in two saving accounts, which pay 2% and 4% simple interest. If the total annual return from the two investments is $100, how much is invested at each rate? 2. Kiki inherited $15,000 and invested in two municipal bonds, which pay 7% and 9% simple interest. The annual interest is $1230. Find the amount invested at each rate. 3. Kate’s two student loans totaled $12,000. One of her loans was a 6% simple interest and the other at 9%. After one year, Kate owed $885 in interest. What was the amount of each loan? 4. Adult tickets for a play cost $5.00 and children’s tickets cost $2.00. For one performance, 460 tickets were sold. Receipts for the performance were $1880. Find the number of adult tickets and children tickets sold. 5. The tickets for a local production of Gilbert and Sullivan’s H.M.S. Pinafore cost $6.00 for adults and $3.00 for children and seniors. There were 505 tickets sold with revenue of $1977. How many adult tickets were sold? 4.3 Use row operations to solve each system Intermediate Algebra Chung 9 5.1 Simplify. Write each answer with positive exponents. 5.2 Determine if each polynomial is a monomial, binomial, trinomial or none of these. Also state the degree of the polynomial. Intermediate Algebra Chung 10 Add or subtract as indicated. Write the result in descending powers. 5.3 Use the FOIL method to find each product Use one of the formulas learned in this section to find each product. Divide. Intermediate Algebra Chung 11 6.1 Factor out the Greatest Common Factor (GCF) Factor by grouping 6.2 Factor each trinomial. Note: In some problems you might need to factor out the GCF first Intermediate Algebra Chung 12 6.3 Factor. Note: In some problems you might need to factor out the GCF first. 6.4 Solve each equation. Intermediate Algebra Chung 13 7.1 Determine if the following is a sum or a product. List all factor(s) 1. x + y 2. 2(x + y) 3. 3 – 2(x + y) 4. (3x + 2y)(x + y) 5. 6. (6x + 9)(x + y) 7. 12 – (x + y)(x – 2) 8. (x + 1)(x + 2)(x + 3)(x + 4) 9. 9 – 2x True or False. Explain or give a correct answer 10. Terms are separated by a plus/minus sign 11. Factors are separated by the multiplication sign or the parenthesis symbols 12. We can always cancel terms 13. When an expression is a sum, the whole expression is a single term. The expression 2 6( x y ) 3 xy 9 x is an example of a sum 2 3 14. Multiply or divide as indicated Add or subtract as indicated. Write all answers in lowest terms. Intermediate Algebra Chung 14 7.2 Simplify each complex fraction. Simplify each expression. 2 1 Hint: Rewrite negative exponents to fractions, then simplify. Example: rewrite x as x2 7.3 Solve each equation. Intermediate Algebra Chung 15 Solve for the specified variable. 7.4 1. Butch and Peggy want to pick up the mess that their grandson, Grant, has made in his play room. Butch can do it in 15 minutes working alone, Peggy, working alone, can clean it in 12 minutes. How long will it take them if they work together? 2. Lou can groom Jay’s dogs in 8 hours, but it takes his business partner, Janet, only 5 hours to groom the same dogs. How long will it take them to groom Jay’s dogs if they work together? 3. If a vat of acid can be filled by an inlet pipe in 10 hours and emptied by an outlet pipe in 20 hours, how long will it take to fill the vat if both pipes are open? 4. A winery has a vat to hold Chardonnay. An inlet pipe can fill the vat in 9 hours, while an outlet pipe can empty it in 12 hours. How long will it take to fill the vat if both the outlet and the inlet pipes are open? 8.1 Find each root. If it’s not a real number say so. Use a calculator when necessary. 2. 18 7 9 24 4 1. 9 3. 4. 3 8 5. 3 6. 7. 5 243 Rewrite each expression as radicals. Convert to rational exponents, simplify when possible. Simplify. Write all answers with positive exponents. Intermediate Algebra Chung 16 Rewrite each expression with rational exponents, then apply the properties of exponents to simplify. 8.2 Multiply. If it’s not possible say so. Divide. If it’s not possible say so. Express each radical in simplified form. Intermediate Algebra Chung 17 Multiply. Simplify the product when possible. Rationalize the denominator. 8.3 Simplify, then add or subtract as indicated. Intermediate Algebra Chung 18 8.4 Solve each equation. 8.5 Add or subtract as indicated. Intermediate Algebra Chung 19 Multiply. Write each complex number in the form a +bi Find each power of i 9.1 Solve by the square root property. Leave the answers as complex numbers when possible. Solve by completing the square. Leave the answer as complex numbers possible. 9.2 Solve by applying the quadratic formula. Write the answers as complex numbers when possible. Intermediate Algebra Chung 20 Solve by applying one of these methods. Write the answers as complex numbers when possible. 1. Factoring 2. The square root property 3. Completing the square 4. The quadratic formula Solve for the indicated variable. 9.3 Solve each quadratic inequality. Write the solution set in interval notation. Solve each inequality. Intermediate Algebra Chung 21 9.4 Solve each rational inequality. Write the solution set in interval notation. 10.1 Find the inverse of each function 1. f(x) = 2x – 1 2. f(x) = 2x + 3 3. g(x) = −4x 4. g(x) = −2x 5. f(x) = 2x – 7 6. f(x) = −3x + 2 7. 8. f ( x) 3 x 2 10.2 Write in logarithmic form. 1. 2. 3. 4. Write in exponential form. 5. 6. 7. 8. True or False. Explain or give a correct answer. 9. f(x) = is an example of an exponential function. 10. f(x) = is an example of an exponential function. 11. f(x) = is an example of a logarithmic function. 12. =2 13. =1 14. =0 Intermediate Algebra Chung 22 10.3 Use a calculator to find the value of each logarithm. Round the answers to four decimal places. Use the change-of-base rule to find each logarithm. Round the answers to four decimal places. Write as a sum or difference of logarithms. Write as a single logarithm. True or False. Explain or give a correct answer. 31. Natural logarithm is a logarithm with the base equals to 10 32. The letter e which is the base of the natural logarithm is a variable. 33. Common logarithm and natural logarithm are equal. 34. log (a + b) = (loga)(logb) 35. Logarithms are undefined when their expression is 0 or negative. 36. When solving exponential equations, we must go back and check the solution. 10.4 Solve each exponential equation. Intermediate Algebra Chung 23 Hint: 0.1 = Hint: = Solve each exponential equation. Round the answers to 3 decimal places Solve each logarithmic equation. 11.1 Graph each function. Label the crucial point(s) and draw the horizontal/vertical asymptote(s) if there is any. x 1 1. y = |x + 1| 2. y x 1 3. y 2 2 1 4. y log 1 / 2 ( x 2) 3 5. y 6. y = −|x – 1| + 4 x x 3 7. y log 5 ( x 2) 1 8. y x 2 3 9. y (0.5) 4 1 1 1 10. y 11. y 2 12. y 2 x2 x x2 Intermediate Algebra Chung 24 2 13. y 2 14. y log 3 ( x 3) 4 15. y log 0.25 ( x 1) 2 x2 16. y x 2 3 17. y = −|x| + 1 True or False. Explain, provide an example or give a correct answer to support your choice. 18. Absolute value functions have a V-shaped graph. 19. The crucial point of the square root functions is (1, 0) 20. Exponential functions have a vertical asymptote. 21. Logarithmic functions don’t have any asymptotes. 22. Rational functions only have one asymptote. 23. Rational functions have 2 crucial points 24. The graph of the square root functions have a U shape. 25. The crucial point of the exponential functions and the logarithmic functions is the same point. 26. The domain of the exponential functions is all real numbers. 27. The range of the absolute value functions is all real numbers. 28. 11.2 Graph. Label the crucial point. Draw the asymptote(s) if there is any. 1. y 2. 3. 4. y = −(x – 5. 6. (x – =9 7. – 8. 3 9. 32 x2 y2 ( x 1) 2 ( y 2) 2 ( x 3) 2 ( y 1) 2 10. 1 11. 1 12. 1 4 9 9 4 16 25 x2 y2 x2 y2 y2 x2 13. 1 14. 1 15. 1 4 9 25 9 25 9 y2 x2 x2 y2 y2 x2 16. 1 17. 1 18. 1 4 49 25 36 25 36 True or False. Explain, provide an example or give a correct answer to support your choice. 19. Hyperbolas have a center at (0, 0). 20. Circles have a center at (0, 0). 21. Parabolas have a center. 22. 23. Parabolas have two asymptotes. x2 y2 24. The equation 1 is an example of an ellipse. 4 9 25. (0, 0). 26. form of a hyperbola.