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All Textbook Solutions for College Algebra
Write each of thefollowing as a rational number. a.11b.3c.4Write each of the following rational numbers as either a terminating or repeating decimal. a.6817b.813c.1720Determine whether each of the following numbers is rational or irrational. If it is rational, determine whether it terminating or repeating decimal. a.777b.81c.4.27027002700027d.9113e.39Classify each number as either positive or negative and as either rational or irrational. Does the number lie to the left or the right of 0 on the number line? \n a.73b.11.411411411c.4719d.52e.6.210735Classify each number as being a natural number (N), whole number (W), Integer (I), rational number (Q), and/or irrational number (Q’). a.357b.0c.169d.24e.4.763763763...Use the order of operations to evaluate each of the following expressions. a.5242+7(54)2 b.1+7.58.496 c.|1.84.3|+0.415+10 d.12[5.3272]+1392 e.[(38)24](38)Use the properties of real numbers to rewrite and simplify each expression. State which properties apply. a.(235)[11(523)] b.5(6.2+0.4) c.18-(715) d.1718+[49+(1718)] e.6(3)+63List the constants and variables for each algebraic expression. a.2r(r+h)b.2(L+W)c.4y3+yEvaluate the expression 113y for each value of y. a.y=2b.y=0c.y=23d.y=5Evaluate each expression for the given values. a.y+3y3fory=5b.72tfort=2c.13r2for11 d.(p2q)3forp=2,q=3e.4(mn)5(nm)form=23,n=13A photograph with length L and width W is placed in a matteof width 8 centimeters (cm). The area of the matte (in square centimeters, or cm2) is found to be A=(L+16)(W+16)LW . See Figure 5. Find the area of a matte for a photograph with length 32 cm and width 24 cm.Simplify each algebraic expression. a.23y2(43y+z)b.5t23t+1c.4p(q1)+q(1p)d.9r(s+2r)+(6s)If the amount P is deposited into an account paying simple interest rfor time t,the total value of the deposit A is given by A=P+Prt.Simplify the expression. (This formula will be explored in more detail later in the course.)Is 2 an example of a rational terminating, rational repeating, or irrational number? Tell why it fits that category.What is the order of operations? What acronym is used to describe the order of operations, and what does it stand for?What do the Associative Properties allow us to do when following the order of operations? Explain your answer.For the following exercises, simplify the given expression. 4. 10+2(53)For the following exercises, simplify the given expression. 5.62(8132)For the following exercises, simplify the given expression. 6.18+(68)3For the following exercises, simplify the given expression. 7.2[16(84)2]2For the following exercises, simplify the given expression. 8.46+27For the following exercises, simplify the given expression. 9. 3(58)For the following exercises, simplify the given expression. 10.4+6102For the following exercises, simplify the given expression. 11.12(369)+6For the following exercises, simplify the given expression. 12. (4+5)23For the following exercises, simplify the given expression. 13. 3122+19For the following exercises, simplify the given expression. 2+874For the following exercises, simplify the given expression. 15.5+(6+4)11For the following exercises, simplify the given expression. 16.91832For the following exercises, simplify the given expression. 17.14376For the following exercises, simplify the given expression. 18.9(3+11)2For the following exercises, simplify the given expression. 19.6+221For the following exercises, simplify the given expression. 20. 64(8+42)For the following exercises, simplify the given expression. 21. 9+4(22)For the following exercises, simplify the given expression. 22. (1233)2For the following exercises, simplify the given expression. 23. 25527For the following exercises, simplify the given expression. 24. (157)(37)For the following exercises, simplify the given expression. 25. 249()For the following exercises, simplify the given expression. 26. 422515For the following exercises, simplify the given expression. 27. 12(31)6For the following exercises, solve for the variable. 28. 8(x+3)=64For the following exercises, solve for the variable. 29. 4y+8=2yFor the following exercises, solve for the variable. 30. (11a+3)18a=4For the following exercises, solve for the variable. 31.4z2z(1+4)=36For the following exercises, solve for the variable. 32. 4y(72)2=200For the following exercises, solve for the variable. 33. (2x)2+1=-3For the following exercises, solve for the variable. 34. 8(2+4)15b=bFor the following exercises, solve for the variable. 35. 2(11c4)=36For the following exercises, solve for the variable. 36. 4(31)x=4For the following exercises, solve for the variable. 37. 14(8w42)=0For the following exercises, solve for the variable. 38. 4x+x(137)For the following exercises, simplify the expression. 39. 2y(4)2y11For the following exercises, simplify the expression. 40. a23(64)12a6For the following exercises, simplify the expression. 41.8b-4b(3)+1For the following exercises, simplify the expression. 42. 5l3l(96)For the following exercises, simplify the expression. 43. 7z3+z62For the following exercises, simplify the expression. 44. 43+18x912For the following exercises, simplify the expression. 45. 9(y+8)27For the following exercises, simplify the expression. 46. (96t)2For the following exercises, simplify the expression. 47. 6+12b36bFor the following exercises, simplify the expression. 48. 18y2(1+7y)For the following exercises, simplify the expression. 49. (49)227xFor the following exercises, simplify the expression. 50. 8(3m)+1(8)For the following exercises, simplify the expression. 51.9x+4x(2+3)4(2x+3x)For the following exercises, simplify the expression. 52. 524(3x)REAL-WORLD APPLICATIONS For the following exercises, consider this scenario: Fred earns $40 mowing lawns. He spends $10 on mp3s, puts half of what is left in a savings account, and gets another $5 for washing his neighbor’s car. 53. Write the expression that represents the number of dollars Fred keeps (and does not put in his savings account). Remember the order of operations.REAL-WORLD APPLICATIONS For the following exercises, consider this scenario: Fred earns $40 mowing lawns. He spends $10 on mp3s, puts half of what is left in a savings account, and gets another $5 for washing his neighbor’s car. 54. How much money does Fred keep?For the following exercises, solve the given problem. 55. According to the U.S. Mint, the diameter of a quarter is 0.955 inches. The circumference of the quarter would be the diameter multiplied by . Is the circumference of a quarter a whole number, a rational number, or an irrational number?For the following exercises, solve the given problem. 56. Jessica and herroommate, Adriana, have decided to share a change jar for joint expenses. Jessica put her loose change in the jar first, and then Adriana put her change in the jar. We know that it does not matter in which order the change was added to the jar. What property of addition describes this fact?For the following exercises, consider this scenario: There is a mound of g pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel. 57. Write the equation that describes the situation.For the following exercises, consider this scenario: There is a mound of g pounds of gravel in a quarry. Throughout the day, 400 pounds of gravel is added to the mound. Two orders of 600 pounds are sold and the gravel is removed from the mound. At the end of the day, the mound has 1,200 pounds of gravel. 58. Solve for g.For the following exercise, solve the given problem. 59. Ramon runs the marketing department at his company. His department gets a budget every year, and every year, he must spend the entire budget without going over. If he spends less than the budget, then his department gets a smaller budget the following year. At the beginning of this year, Ramon got $2.5 million for the annual marketing budget. He must spend the budget such that 2,500,000x=0 . What propertyof addition tells us what the value of x must be?For the following exercises, use a graphing calculator to solve for x. Round the answers to the nearest hundredth. 60. 0.5(12.3)248x=35For the following exercises, use a graphing calculator to solve for x. Round the answers to the nearest hundredth. 61.(0.250.75)2x7.2=9.9If a whole number is not a natural number, what must the number be?Determine whether the statement is true or false: The multiplicative inverse of a rational number is also rational.Determine whether the statement is true or false: The product of a rational and irrational number is always irrational.Determine whether the simplified expression is rational or irrational: 184(5)(1).Determine whether the simplified expression is rational or irrational: 16+4(5)+5.The division of two whole numbers will always result in what type of number?What property of real numbers would, simplify the following expression: 4+7(x1) ?Write each of the following products with a single base. Do not simplify further. a.k6k9b.(2y)4(2y)c.t3t6t5Write each of the following products with a single base. Do not simplify further. a.s75s68b.(3)63c.(ef2)5(ef2)3Write each of the following products with a single base. Do not simplify further. a.((3y)8)3b.(t5)7c.((g)4)4Simplify each expression using the zero exponent rule of exponents. a.t7t7 b.(de2)112(de2)11 c.w4w2w6 d.t3t4t2t5Write each of the following quotients with a single base. Do not simplify further. Write answers with positive exponents. a.(3t)2(3t)8 b.f47f49f c.2k45k7Write each of the following quotients with a single base. Do not simplify farther. Write answers with positive exponents. a.t11t6 b.25122513Simplify each of the following quotients as much as possible using the power of a quotient rule. Write answers with positive exponents. a.(g2h3)5b.(5t)3c.(3y5)3d.1(a6b7)3e.(r3s2)4Simplify each of the following quotients as much as possible suing the power of a quotient rule. Write answers with positive exponents. a.(b5c)3 b.(5u8)4 c.(1w3)35 d.(p4q3)8 e.(c5d3)4Simplify each expression and write the answer with positive exponents only. a.(2uv2)3 b.x8x12x c.(e2f3f1)2 d.(9r5s3)(3r6s4) e.(49tw2)3(49tw2)3 f.(2h2k)4(7h1k2)2Write each number in scientific notation. U.S. national debt per taxpayer (April 2014): $152,000 World population (April 2014): 7,158,000,000 World gross national income (April 2014): $85,500,000,000,000 Time for light to travel 1 m: 0.00000000334 s Probability of winning lottery (match 6 of 49 possible numbers): 0.0000000715Convert each number in scientific notation to standard notation. a.7.03105b.8.161011c.3.91013d.8106Perform the operations and write the answer in scientific notation (7.5108)(1.13102) (1.241011)(1.551018) (3.72109)(8103) (9.9331023)(2.311017) (6.04109)(7.3102)(2.81102)An average human body contains around 30,000,000,000,000 red blood cells. Each cell measures approximately 0.000008 m long. Write each number in scientific notation and find the total length if the cells were laid end-to-end. Write the answer in both scientific and standard notations.Is 23 the same as 32 ? Explain.When can you add two exponents?What is the purpose of scientific notation?Explain what a negative exponent does.For the following exercises, simplify the given expression. Write answer with positive exponents. 5. 92For the following exercises, simplify the given expression. Write answers with positive exponents. 6. 152For the following exercises, simplify the given expression. Write answers with positive exponents. 7. 3233For the following exercises, simplify the given expression. Write answers with positive exponents. 8. 444For the following exercises, simplify the given expression. Write answers with positive exponents. 9. (22)2For the following exercises, simplify the given expression. Write answers with positive exponents. (58)0For the following exercises, simplify the given expression. Write answers with positive exponents. 11.113114For the following exercises, simplify the given expression. Write answers with positive exponents. 12. 6567For the following exercises, simplify each expression. Write answers with positive exponents. 13. (80)2For the following exercises, simplify the given expression. Write answers with positive exponents. 14. 5252For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. 15. 424344For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. 16. 61269For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. 17. (12312)10For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. 18. 106(1010)2For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. 19. 7673For the following exercises, write each expression with a single base. Do not simplify further. Write answers with positive exponents. 20. (3334)5For the following exercises, express the decimal in scientific notation. 21. 0.0000314For the following exercises, express the decimal in scientific notation. 22. 148,000,000For the following exercises, convert each number in scientific notation to standard notation. 23. 1.61010For the following exercises, convert each number in scientific notation to standard notation. 29. 9.8109For the following exercises, simplify the given expression. Write answers with positive exponents. 25. a3a2aFor the following exercises, simplify the given expression. Write answers with positive exponents. 26. mn2m2For the following exercises, simplify the given expression. Write answers with positive exponents. 27. (b3c4)2For the following exercises, simplify the given expression. Write answers with positive exponents. 28. (x3y2)5For the following exercises, simplify the given expression. Write answers with positive exponents. 29. ab2d3For the following exercises, simplify the given expression. Write answers with positive exponents. 30. (w0x5)1For the following exercises, simplify the given expression. Write answers with positive exponents. 31. m4n0For the following exercises, simplify the given expression. Write answers with positive exponents. 32. y4(y2)2For the following exercises, simplify the given expression. Write answers with positive exponents. 33. p4q2p2q3For the following exercises, simplify the given expression. Write answers with positive exponents. 34. (lw)2For the following exercises, simplify the given expression. Write answers with positive exponents. 35. (y7)3x14For the following exercises, simplify the given expression. Write answers with positive exponents. 36. (a23)2For the following exercises, simplify the given expression. Write answers with positive exponents. 37. 52m5mFor the following exercises, simplify the given expression. Write answers with positive exponents. 38. (16x)2y1For the following exercises, simplify the given expression. Write answers with positive exponents. 39. 23(3a)2For the following exercises, simplify the given expression. Write answers with positive exponents. 40. (ma6)21m3a2For the following exercises, simplify the given expression. Write answers with positive exponents. 41. (b3c)3For the following exercises, simplify the given expression. Write answers with positive exponents. 42. (x2y13y0)2For the following exercises, simplify the given expression. Write answers with positive exponents. 43 . (9z3)2yTo reach escape velocity, a rocket must travel at the rate of 2.2106ft/min . Rewrite the rate in standard notation.A dime is the thinnest coin in U.S. currency. A dime’s thickness measures 135103m . Rewrite the number in standard notation.The average distance between Earth and the Sun is 92,960,000 mi. Rewrite the distance using scientific notation.A terabyte is made of approximately 1,099,500,000,000 bytes. Rewrite in scientific notation.The Gross Domestic Product (GDP) for the United States in the first quarter of 2014 was 1.714961013 . Rewrite the GDP in standard notation.One picometer is approximately 3.3971011in. Rewrite this length using standard notation.The value of the services sector of the U.S. economy in the first quarter of 2012 was $10,633.6 billion. Rewrite this amount in scientific notation.For the following exercises, use a graphing calculator to simplify. Round the answers to the nearest hundredth. 51. (123m3343)2For the following exercises, use a graphing calculator to simplify. Round the answers to the nearest hundredth. 52. 173152x3For the following exercises, simplify the given expression. Write answers with positive exponents. 53. (32a3)2(a422)2For the following exercises, simplify the given expression. Write answers with positive exponents. 54. (6224)2(xy)5For the following exercises, simplify the given expression. Write answers with positive exponents. 55. m2n3a2c3a7n2m2c4For the following exercises, simplify the given expression. Write answers with positive exponents. 56. (x6y3x3y3y7x3)10For the following exercises, simplify the given expression. Write answers with positive exponents. 57. ((ab2c)3b3)2For the following exercises, simplify the given expression. Write answers with positive exponents. 58. Avogadro’s constant is used to calculate the number of particles in a mole. A mole is a basic unit in chemistry to measure the amount of a substance. The constant is 6.02214131023 . Write Avogadro’s constant in standard notation.For the following exercises, simplify the given expression. Write answers with positive exponents. 59. Planck's constant is an important unit of measure in quantum physics. It describes the relationship between energy and frequency. The constant is written as 6.626069571034 . Write Planck’s constant in standard notation.225 b. 81 c. 259 d. 36+121Simplify 50x2y3z .Simplify 50x2x assuming x0 .Simplify 2x29y4 .Simplify 9a5b143a4b5 .Add 5+620 .Subtract: 380x445x .Write 1232 in simplest form.Write 72+3 in simplest form.Simplify. 2163 380454 69,0003+75763Write 952 as a radical. Simplify.Write x(5y)9 using a rational exponent.Simplify 8x13(14x65) .What does it mean when a radical does not have an index? Is the expression equal to the radicand? Explain.Where would radicals come in the order of operations? Explain why.Every number will have two square root? What is the principal square root?Can a radical with a negative radicand have a real square root? Why or why not?For the following exercises, simplify the given expression. 5. 256For the following exercises, simplify each expression. 6. 256For the following exercises, simplify each expression. 7. 4(9+16)For the following exercises, simplify each expression. 8.For the following exercises, simplify each expression. 9. 196For the following exercises, simplify each expression. 10. 1For the following exercises, simplify each expression. 11. 98For the following exercises, simplify each expression. 12. 2764For the following exercises, simplify the given expression. 13. 815For the following exercises, simplify each expression. 14. 800For the following exercises, simplify each expression. 15. 169+144For the following exercises, simplify each expression. 16. 850For the following exercises, simplify each expression. 17. 18162For the following exercises, simplify each expression. 18. 192For the following exercises, simplify each expression. 19. 146624For the following exercises, simplify each expression. 20. 155+745For the following exercises, simplify each expression. 21. 150For the following exercises, simplify each expression. 22. 96100For the following exercises, simplify each expression. 23. (42)(30)For the following exercises, simplify each expression. 24. 123475For the following exercises, simplify each expression. 25. 4225For the following exercises, simplify each expression. 26. 405324For the following exercises, simplify each expression. 27. 360361For the following exercises, simplify each expression. 28. 51+3For the following exercises, simplify each expression. 29. 8117For the following exercises, simplify each expression. 30. 164For the following exercises, simplify each expression. 31. 1283+323For the following exercises, simplify each expression. 32. 322435For the following exercises, simplify each expression. 33. 15125454For the following exercises, simplify each expression. 34. 34323+163For the following exercises, simplify each expression. 35. 400x4For the following exercises, simplify each expression. 36. 4y2For the following exercises, simplify each expression. 37. 49pFor the following exercises, simplify each expression. 38. (144p2q6)12For the following exercises, simplify each expression. 39. m52289For the following exercises, simplify each expression. 40. 93m2+27For the following exercises, simplify each expression. 41. 3ab2baFor the following exercises, simplify each expression. 42. 42n16n4For the following exercises, simplify each expression. 48. 225x349xFor the following exercises, simplify each expression. 44. 344z+99zFor the following exercises, simplify each expression. 45. 50y8For the following exercises, simplify each expression. 46. 490bc2For the following exercises, simplify each expression. 47. 3214dFor the following exercises, simplify each expression. 48. q3263pFor the following exercises, simplify each expression. 49. 813xFor the following exercises, simplify each expression. 50. 20121d4For the following exercises, simplify each expression. 51. w3232w3250For the following exercises, simplify each expression. 52. 108x4+27x4For the following exercises, simplify each expression. 53. 12x2+23For the following exercises, simplify each expression. 54. 147k3For the following exercises, simplify each expression. 55. 125n10For the following exercises, simplify each expression. 56. 42q36q3For the following exercises, simplify each expression. 57. 81m361m2For the following exercises, simplify each expression. 58. 72c22cFor the following exercises, simplify each expression. 59. 144324d2For the following exercises, simplify each expression. 60. 24x63+81x63For the following exercises, simplify each expression. 61. 162x616x44For the following exercises, simplify each expression. 62. 64y3For the following exercises, simplify each expression. 63. 128z3316z33For the following exercises, simplify each expression. 64. 1,024c105A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So the length of the guy wire can be found by evaluating 90,000+160,000 . What is the length of the guy wire?A car accelerates at a rate of 64tm/s2 where tis the time in seconds after the car moves from rest.Simplify the expression.For the following exercises, simplify each expression. 67. 81642212For the following exercises, simplify each expression. 68. 4321632813For the following exercises, simplify each expression. 69. mn3a2c3a7n2m2c4For the following exercises, simplify each expression. 70. aacFor the following exercises, simplify each expression. 71. x64y+4y128yFor the following exercises, simplify each expression. 72. ( 250 x 2 100 b 3 )(7b 125x)For the following exercises, simplify each expression. 73. 643+ 2564 64+ 256Identify the degree, leading term, and leading coefficient of the polynomial 4x2x6+2x6 .Find the sum. (2x3+5x2x+1)+(2x23x4)Find the difference. (7x37x2+6x2)(4x36x2x+7)Find the product. (3x+2)(x34x2+7)Use FOIL to find the product. (x+7)(3x5)Expand (4x1)2.Multiply (2x+7)(2x7) .Multiply (3x1)(2x+7y9) .Evaluate the following statement: The degree of a polynomial in standard form is the exponent of the leading term. Explain why the statement is true or false.Many times, multiplying two binomials with two variables results in a trinomial. This is not the case when there is a difference of two squares. Explain why the product in this case is also a binomial.You can multiply polynomials with any number of terms and any number of variables using four basic steps over and over until you reach the expanded polynomial. What are the four steps?State whether the following statement is true and explain why or why not: A trinomial is always a higher degree than a monomial.For the following exercises, identify the degree of the polynomial. 5. 7x2x2+13For the following exercises, identify the degree of the polynomial. 6. 14m3+m216m+8For the following exercises, identify the degree of the polynomial. 7. 625a8+16b4For the following exercises, identify the degree of the polynomial. 8. 200p30p2m+40m3For the following exercises, identify the degree of the polynomial. 9. x2+4x+4For the following exercises, identify the degree of the polynomial. 10. 6y4y5+3y4For the following exercises, find the sum or difference. 11. (12x2+3x)(8x219)For the following exercises, find the sum or difference. 12. (4z3+8z2z)+(2z2+z+6)For the following exercises, find the sum or difference. 13. (6w2+24w+24)(3w6w+3)For the following exercises, find the sum or difference. 14. (7a3+6a24a13)+(3a34a2+6a+17)For the following exercises, find the sum or difference. 15. (11b46b3+18b24b+8)(3b3+6b2+3b)For the following exercises, find the sum or difference. 16. (49p225)+(16p432p2+16)For the following exercises, find the sum or difference. 17. (4x+2)(6x4)For the following exercises, find the product. 18. (14c2+4c)(2c23c)For the following exercises, find the product. 19. (6b26)(4b24)For the following exercises, find the product. 20. (3d5)(2d+9)For the following exercises, find the product. 21. (9v11)(11v9)For the following exercises, find the product. 22. (4t2+7t)(3t2+4)For the following exercises, find the product. 23. (8n4)(n2+9)For the following exercises, expand the binomial. 24. (4x+5)2For the following exercises, expand the binomial. 25. (3y7)2For the following exercises, expand the binomial. 26. (124x)2For the following exercises, expand the binomial. 27. (4p+9)2For the following exercises, expand the binomial. 28. (2m3)2For the following exercises, expand the binomial 29. (3y6)2For the following exercises, expand the binomial. 30. (9b+1)2For the following exercises, multiply the binomials. 31. (4c+1)(4c1)For the following exercises, multiply the binomials. (9a4)(9a+4)For the following exercises, multiply the binomials. 33. (15n6)(15n+6)For the following exercises, multiply the binomials 34. (25b+2)(25b2)For the following exercises, multiply the binomials. 35. (4+4m)(44m)For the following exercises, multiply the binomials. 36. (14p+7)(14p7)For the following exercises, multiply the binomials. 37. (11q10)(11q+10)For the following exercises, multiply the polynomials 38. (2x2+2x+1)(4x1)For the following exercises, multiply the polynomials 39. (4t2+t7)(4t21)For the following exercises, multiply the polynomials. 40. (x1)(x22x+1)For the following exercises, multiply the polynomials. 41. (y2)(y24y9)For the following exercises, multiply the polynomials. 42. (6k5)(6k2+5k1)For the following exercises, multiply the polynomials. 43. (3p2+2p10)(p1)For the following exercises, multiply the polynomials. 44. (4m13)(2m27m+9)For the following exercises, multiply the polynomials. 45. (a+b)(ab)For the following exercises, multiply the polynomials. 46. (4x6y)(6x4y)For the following exercises, multiply the polynomials. 47. (4t5u)2For the following exercises, multiply the polynomials. 48. (9m+4n1)(2m+8)For the following exercises, multiply the polynomials. 49. (4tx)(tx+1)For the following exercises, multiply the polynomials. 50. (b21)(a2+2ab+b2)For the following exercises, multiply the polynomials. 51. (4rd)(6r+7d)For the following exercises, multiply the polynomials. 52. (x+y)(x2xy+y2)A developer wants to purchase a plot of land to build a house. The area of the plot can be described by the following expression: (4x+1)(8x3) where x is measured in meters. Multiply the binomials to find the area of the plot in standard form.