Solutions To Review Questions

 

 

  1. We first raise both the numerator and the denominator to the -3 power.
  2. Now a negative exponents mean that we move the to the denominator and the to the numerator and make the exponents positive. Thus

    and so the correct answer is (c): .

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  3. Since the base (-2) is the same in both terms, we just add the exponents. Thus:
  4. hence (b) is the correct answer.

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  5. This expression is the difference of two squares and hence it factors. Since and 9 = 32 we have that
  6. giving (a) as the correct answer.

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  7. To determine if factors, we look at the factorizations of and -3. These are and , and and respectively. (Notice that the 1 and the 3 will have opposite signs since theconstant term is -3.) Thus we get
  8. or

    .

    To determine which one is correct, we notice that the middle term in the trinomial is negative, hence when we multiply the inner terms and then the outer terms, the negative term should have the larger coefficient. Looking at the possibilities we see that the correct factorization is since multiplying the outer terms give us and multiplying the inner terms gives us , which add up to the as desired. Thus (b) is the correct answer.

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  9. To solve this equation, we first combine like terms:
  10. 12x - 7x - 4x + 9 = 19

    x + 9 = 19

    Then subtract 9 from both sides to get

    x = 10,

    making (b) the correct answer.

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  11. To solve this equation, we first distribute the 4:
  12. -7b + 4(2b - 3) = 16

    -7b+8b - 12 = 16

    Now combine like terms:

    b - 12 = 16

    and add 12 to both sides to get b = 28 which is answer (a).

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  13. To solve this equation, we first subtract 6 from both sides:
  14. We now multiply both sides by 10 and then divide both sides by 3:

    Hence (c) is the correct answer.

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  15. To solve the inequality, we first add 3 to both sides:
  16. 5k - 3 > 2k + 9

    5k > 2k + 12

    we then subtract 2k from both sides to get

    3k > 12

    Dividing by 3 gives us:

    k > 4

    Thus, (a) is the correct answer.

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  17. To solve this inequality we divide both sides by 0.2
  18. To move the decimal point in both the numerator and the denominator one spotto the right, multiply the top and the bottom by 10 to get

    Thus , which is (c).

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  19. To solve this equation we first subtract from both sides giving us:
  20. We then take reciprocals of both sides to find the value of :

    which is answer (c).

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  21. To solve this equation we cross multiply:
  22. We now add 35 to both sides and then subtract 2b from both sides:

    and finally we divide by 3 to get as our answer, which is answer (c).

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  23. Simplifying:
  24. which is answer (a).

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  25. Simplifying:
  26. which is answer (c).

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  27. Simplifying:
  28. which is answer (d).

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  29. Since the -coordinate is negative and the -coordinate is positive the point (-3,4) is in quadrant II, which is answer (b).
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  31. The slope-intercept equation of a line is where is the slope and is the -intercept. Since we are told that , all we need to do is find the value of . Since the line passes through the point (-1,5), we know that when . Substituting we get:
  32. Thus the equation of the line is: . Which is answer (c).

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  33. To solve this equation we first need to factor . Since the constant term (9) is positive, it means that both factors of 9 have the same sign and since the middle term is negative they both must be negative. Thus the factors of 9 are -1 and -9 or -3 and -3. Hence
  34. or

    However only the first factorization gives the correct middle term of . Thus

    .

    The solutions to are foundby solving . However, the only way a product of two numbers can be 0 is if one of the numbers is 0. Thus,

    or

    .

    Thus or , giving (b) as the correct answer.

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  35. Since the dieter will be losing 2 pounds every 3 weeks, and , we have that the dieter will need weeks to lose the pounds. Hence (d) is the correct answer.
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  37. First we convert the Mixed Fraction to:

    Second You Get a comon denomiantor of 15 and convert the 2 fractions to
    and . Last you get Which Yields the answer .

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  38. First Convert the Mixed Fractions to and Then get a common denomiator of 24 and subtract them to get . This will get you None of the answers.
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  39. Divide: and you get .11
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  40. Divide: and Multipy by 100. You will get the percent listed as answer 18.75%
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  41. .07 X $1,400 is $98.
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  42. There was a 400 Student increase from 6000 Students. So you take 400 and divide by 6000 and you will get .067, which corresponds to 6.7%.
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  43. The car was $11,000 and 12% was taken off. $11,000 X .12 = 1320 Which is the discount price. Now subtract and you get the answer $9,680.
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  44. .05% of a dollar is .05 cents. 30/.05 = $600.
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  45. 4(y-3)=42-2y
    4y-12=42-2y
    6y=54
    y=9
    which is none of the Answers listed.

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  46. If one side is 8 cm longer than the other we can say that h=x and l=x+8 then we use the formula for parameter of a rectangle. 2*L+2*W=P
    So, 2(x)+2(x+8)=48
    2x+2x+16=48
    4X=32
    x=8

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  47. By Factoring we can Find the Answer:
    (x-6)(x+4)=0
    x=6,-4

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  48. Graph Needed.
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  49. First Multiply and simplify all fractions to get this:
    Then simplify into decimals because the answers are in that form.
    x+.4x-.12x=19.2
    1.28x=19.2
    x=15

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  50. 13X89=1157 so 1000 would be the best guess.
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  51. Multipy 1157 college by 600 students and you get 694,200. Therefore the best guess would be 600,000
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  52. Much higher is the correct answer because the number of people in question 33 is the MINIMUM amount of students.
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  53. 4x-2y=-2
    4x+2=2y
    2x+1=y which is the same as the other line, Therefore The lines are the same.

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  54. Use the Formula a^2 + b^2 = c^2
    4+49=c^2
    53=c^2
    Take the square root of 53 and you get 7.28.

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  55. The basic fee would give you a +10 which eliminates (d). You would need to divide the total feet of mowed area by 250 to get a dollar amount and .004m+10 expresses that.
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  56. Factor Expression:
    10(x^2 -1)
    10(x-1)(x+1)

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  57. Solving for X:
    -2x=-4y-5
    2x=4y+5
    x=2y+2.5 which is none of the answers.

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  58. Solve as a system of 2 equations:
    2x-3y=17
    3x+2y=19
    --------
    2(2x-3y=17)
    3(3x+2y=19)
    ------------
    4x-6y=34
    9x+6y=57
    --------
    13x=91
    x=7

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  59. Express as an equation:
    2/3 X = 9
    Solve:
    2x=27
    x=13.5

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  60. The equation is setup as follows: (92+90+89+X)/4 = 90
    Now Solve for X:
    92+90+89+x=360
    271+x=360
    x=89

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  61. Graph?
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  62. By Putting in the numbers you get:
    After calculating you get 7.81.

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  63. Create an Equation:
    If the population in 1981 was x, then x + 0.2 x = 5.88 billion, the population in 1991. So the population in 1981 is x = 5.88/1.2 billion = 4.9 billion.

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  64. Solve by Elimination:
    In order to get a completely parallel line you need to have the "b" in the y=mX+b moved. None of the lines listed do that.

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  65. Solve By Plugging in the data, assuming that the dot represents multiplication:

    Simplifying this yields answer -12.5.

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  66. Combine the first 2 fractions into the following:

    Now that they have the same Denominator, you can subtract them.
    After simplification you get:


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