A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

pooja195

  • one year ago

@mathmate

  • This Question is Closed
  1. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @mathmate

  2. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Finally, got here!

  3. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Start with quadratic equations, ok?

  4. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok :)

  5. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Solve \(x^2 -6x +9=0\)

  6. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    a=1 b=-6 c=9

  7. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok.

  8. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~x=\frac{ -(-6)\pm \sqrt{(-6)^2-4(1)(9)} }{ 2(1) } \]

  9. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Great, now can you simplify that, because it will be greatly simplified when you put the numbers in there.

  10. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~x=\frac{ 6\pm \sqrt{0} }{ 2}\]

  11. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~\frac{ 6 }{ 2 }=3~~~~~x=3\]

  12. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, that is the same as {3,3}, or 3 (twice)

  13. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It's called a double root, andthe graph looks like this:|dw:1433211976391:dw| the vertex just touches the x-axis.

  14. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok so far?

  15. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ye

  16. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If you factored, you would have got (x-3)^2=0, which is the same as saying (x-3)=0, or x=3 (twice), or x={3,3}

  17. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Was wondering you still have the online textbook?

  18. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you dig some questions out of there, which will be more like what you have learned.

  19. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    T_T but there are answers ,_,

  20. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You don't have to look at them, in any case, we are looking at the work, can check the answers at the end.

  21. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    There may be word problems, which take more time to make. Using ready-made problems can help us do more.

  22. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

  23. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Have you done anything like this? "A picture has a height that is 4/3 its width. It is to be enlarged to have an area of 192 square inches. What will be the dimensions of the enlargement?"

  24. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :/

  25. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no O_O

  26. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Always the numerical equations, and nothing like word problems?

  27. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no ._.

  28. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, so we can skip that.

  29. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

  30. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Whenever you solve quadratics, there are three ways to do it. If the teacher does not specify, you can use any method you want. If he/she specifies completing the square, you have no choice. the three are:

  31. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    quad formula (just did) factoring (did over the weekend) completing the square Do youknow how to do the last one?

  32. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no :/ we havent learned it

  33. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, so we skip that too. Anything else you'd like to do on quadratic equations/

  34. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Nope.

  35. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So we will move onto system of linear equations. Have you done word problems?

  36. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes but dont like those :/

  37. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    How many ways do you know to solve system of linear equations?

  38. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Elmination Substituion :/

  39. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    comparison?

  40. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    eh?

  41. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    When you have y=2x+3 y=4x-2 then you equate the right-hand sides (since they both equal y) to give 4x-2=2x+3 and solve for x. It is a form of elimination, but makes life easier. (called method of comparison)

  42. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i know that :P

  43. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Ok, so let go: Solve y = 36 – 9x 3x + y/3 = 12

  44. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    *let's

  45. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    3x+(36-9x)/3=12 6x+36/3=12 6x+12=12 x=0

  46. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ...not finished! need y, and the final answer!

  47. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y=36-9(0) y=36-0 y=36? (0,36)

  48. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent!

  49. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Solve the following system by substitution. 2x – 3y = –2 4x + y = 24 When you see a singleton y, or singleton x, then you can try substitution, as in the above case.

  50. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y=-4x+24 2x-3y=-2 2x-3(-4x+24)=-2 2x+12x-72=-2 14x-72=-2 14x=70 x=5 y=-4(5)+24 y=20+24 y=44 Final answer (5,44)

  51. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Something wrong here, otherwise all correct. y=-4(5)+24 y=20+24 y=44

  52. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y=4

  53. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yep! Solve the following system using addition (a kind of elimination) 2x + y = 9 3x – y = 16

  54. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x=5 2(5)+y=9 10+y=9 y=-1 (5,-1)

  55. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That was fast! You solved for x by inspection! But show work in exams!

  56. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

  57. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    O_O

  58. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Nooooooooooooooooo

  59. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    With word problems, always define variables first, so you don't get confused at the end.

  60. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'll do this one, ok?

  61. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Define variables: Number of children = c Number of adults = a (we'll could get confused using x,y, but never this way)

  62. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Admission for children = $1.50 Admission for adults = $4

  63. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    "2200 people enter the fair and $5050 is collected" means c+a = 2200 1.50c + 4a=5050 = 15c+40a = 50500 (keep integers as long as possible Substitute (because c has a coefficient of 1) c=2200-a so 15(2200-a) + 40a = 50500 expand 33000 -15a + 40a = 50500

  64. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    40a-15a = 50500-33000 25a = 17500 a=17500/25 = 700 c=2200-700=1500 Check 1.5c+4a=2250+2800=5050 good!

  65. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You will find that once the variables are defined, everything else look easy. What do you think?

  66. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It seems so complicated >_<

  67. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    *-*

  68. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you want to tell me which part is harder to understand?

  69. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    It looks complicated probably because I show all the work. If I skipped or jumped some steps, it will look easy, but a little harder to follow.

  70. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm.... :/

  71. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now your turn! The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number

  72. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    First define variables, use meaningful names, like t = tens digit u = units digit. so far so good?

  73. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    When you have a number like 25, then t=2, u=5, and 10t+u = 25.

  74. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    "The sum of the digits of a two-digit number is 7" can you form an equation with that?

  75. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    7u+t=27?

  76. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Here, we are saying the equivalent of 2+5=7, so t+u=7 will do. now "When the digits are reversed, the number is increased by 27. "

  77. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    t+u=27?

  78. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    10t+u is the original number 10u+t is the number reversed (units digit becomes 10's digit) so 10u+t = 10t+u + 27 (increased by 27)

  79. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Simplifying this equation, we get 9u-9t=27 or u-t=3 combined with u+t=7 we solve for t=2, u=5, or the original number is 25.

  80. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Check: 52-25=27, ok.

  81. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :/

  82. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @pooja195

  83. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    .

  84. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm typing up an example.

  85. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\large \frac{5}{x^2-1}+\frac{4}{x^2+2x+1}\)

  86. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So first factorize the denominators:

  87. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\frac{5}{(x+1)(x-1)}+\frac{4}{(x+1)^2}\)

  88. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you find the common denominator? between (x+1)(x-1) and (x+1)^2

  89. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    it would be (x-1)

  90. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and then x+1 on the other side?

  91. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    "common" denominator of two expressions must contain ALL the factors, and is the same for all the terms. So start with one of the two , say (x+1)(x-1) and add factors to it so that it contains every expression.

  92. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Say we start with (x+1)(x-1), surely it contains (x+1)(x-1) , which is the first expression.

  93. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Question is, does it contain the second expression (x+1)^2?

  94. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the answer is no. What do we need to do? Multiply by another (x+1), so we end up with a common denominator of (x+1)(x-1)(x+1).

  95. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So going back to the question: \(\Large \frac{5\color{red}{(x+1)}}{(x+1)(x-1)\color{red}{(x+1)}}+\frac{4\color{blue}{(x-1)}}{(x+1)^2\color{blue}{(x-1)}}\) notice that now both denominators are identical.

  96. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\Large \frac{5\color{red}{(x+1)}}{(x+1)^2(x-1)}+\frac{4\color{blue}{(x-1)}}{(x+1)^2(x-1)}\)

  97. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and that's the same as \(\Large \frac{5\color{red}{(x+1)}+4\color{blue}{(x-1)}}{(x+1)^2(x-1)}\)

  98. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Next step is to expand and simplify the numerator: \(\Large \frac{5x+5+4x-4}{(x+1)^2(x-1)}=\frac{9x+1}{(x+1)^2(x-1)}\) and that's the end of the calculations.

  99. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I read these but only half .-. @mathmate

  100. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Did you understand as far as you read?

  101. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes but now we can start studying for the finals :P >_<

  102. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Here's the diagnostic test, as far as I have done. I will add other things on.

  103. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @pooja195 you there?

  104. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i iz here

  105. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, let's get started. Any questions on chapter 1?

  106. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Say, 4^d=64, what is "d".

  107. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    need help?

  108. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yeah :/

  109. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    4^0=?

  110. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    1

  111. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Very good! 4^1=

  112. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    4

  113. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Just two rules: Anything raised to the power of 0 is 1, anything raised to the power of 1 is the base itself, like 4^1=4

  114. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    4^2=

  115. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    16

  116. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Remember, \(4^2=4.4\), \(4^3=4.4.4\), \(4^4=4.4.4.4\), etc.

  117. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so 4^3=?

  118. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    64

  119. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so 3?

  120. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    compare 4^3=64, 4^d=64 so what is d? yes, d=3

  121. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Great! Now try 8=2^z. what is z?

  122. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2*2*2 2^3

  123. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and z=?

  124. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    3

  125. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good! Now a difficult one: \(-3^2=\)?

  126. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    -9? or if its (-3)^2 it would be 9

  127. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Exactly, that's where many students make mistakes. when in doubt, use PEMDAS which says that exponentiation goes before subtraction (negative), so what you did was correct. (-3)^2 would raise the power of -3, so (-3)*(-3)=+9. Well done!

  128. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and -3^2=-9.

  129. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Try the following: 1^3= 3=3^j, j= 1=4^h, h= 3^r=81, r= (-2)^3=

  130. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Laws of exponent: 2^n = 2.2.2.....2 (n times) \(a^m \times a^n = a^{m+n}\) \(\large a^{-m}=\frac{1}{a^m}\) \(\large a^{\frac{1}{2}}=\sqrt a\) \(\Large a^{-\frac{1}{2}}=\frac{1}{\sqrt a}\)

  131. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now practice: \(\Large (\frac{1}{2})^2=\) \(\Large (0.2)^3=(\frac{2}{10})^3=(\frac{1}{5})^3=\frac{1}{125}\) Express \(\large 3^{-8}\) with a positive exponent. \(\large 3^{-8}\) =

  132. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    O_O

  133. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433336557931:dw|

  134. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What is that??

  135. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Helps you see where numbers belong. R includes all numbers you're studying (i.e. does not include complex numbers) Inside of R is divided into Q (rational) and Q' (irrationals) Q' (irrationals) include numbers like sqrt(2), \(\pi\), sin(10\(^\circ \)), etc. Q (rationals) include \(all\) integers (Z), and all naturals (N). Decimals (2.5) repeating decimals (2.33333...), fractions (7/3) all belong to rationals, but not Z and N. All N belong to Z, but negative integers are in Z but not in N. See if you can read these relations from the diagram.

  136. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    @pooja195

  137. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

  138. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Solve x+4<7 (page 324)

  139. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x<3

  140. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok... too easy for you?

  141. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes xD

  142. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Write an inequality to show the max. no. of apples I can buy if I have $4.8 and apples cost $0.60 each.

  143. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    * possible number of apples

  144. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    O_O i dunno this...

  145. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x+0.60<4.8?

  146. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I have $4.80, and apples cost 0.60 each. So the maximum number of apples I can buy is $4.80/0.60 =?

  147. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    8

  148. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good, and the minimum?

  149. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    would i subtract?

  150. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Well, the minimum would be zero. I don't have to buy any. So the answer would be:

  151. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x=8?

  152. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x<8

  153. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That's the maximum number of apples. If we ask for the possible number, then it would be:

  154. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    4? o.L

  155. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I can buy anything from 0 to 8, so \(\large 0\le x \le 8\), where x is the number of apples.

  156. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ooo >_<

  157. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Does that make sense?

  158. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yea

  159. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Word problems!

  160. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Try 4x-3=21

  161. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    solve.

  162. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x=6

  163. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent! now solve -5x+10=30

  164. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x=-4

  165. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good!

  166. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now solve \(-5x+10\le30\)

  167. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~x \ge-4\]

  168. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Very good!!! you actually know the rules!

  169. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Why is it \(\ge\) and not \(\le\) ?

  170. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    because when you divide by a negative you always need to flip the signs

  171. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent! What if you multiply by a negative?

  172. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Keep the sign as it is DO NOT change it :)

  173. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Is x/(-1) equal to x*(-1)? why would the rule be different?

  174. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    idk its just like that .-.

  175. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Actually, whether you multiply or divide by a negative, you flip the direction of the > or < sign. You can remember that precisely because x*(-1) is the same as x/(-1). So can you now solve

  176. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\Large \frac{5}{3}(x-5)=6\)

  177. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\frac{ 5 }{ 3 }x-\frac{ 25 }{ 3 }=6\]

  178. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    There is a trick to solving equations with fractional coefficients!

  179. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I would multiply by the denominator, or LCM of the denominator if there are many.

  180. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    This way, we end up with an equation with integer coefficients.

  181. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\Large \frac{5}{3}(x-5)=6\) \(\Large 3*\frac{5}{3}(x-5)=3*6\) \(\Large 5(x-5)=18\) and then go from here

  182. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~5x-25=18\] \[\huge~5x=43\] \[\huge~x=\frac{ 43}{ 5 }\]

  183. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Exactly!

  184. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Any questions before we move on to linear equations?

  185. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ...and graphing?

  186. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no, but lets skip graphing :/

  187. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You're willing to forfeit the points?

  188. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nvm -_-

  189. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What is a linear equation in slope-intercept form?

  190. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    y=mx+b

  191. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good! Can you find a line with a slope of 2 that passes through (2,4)?

  192. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Point slope formula \[\huge~y-y1=m(x-x1)\] \[\huge~y-4=2(x-2)\] \[\huge~y-4=2x-4\] \[\huge~y=2x\]

  193. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent. What form of equation did you use?

  194. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I call it point-slope form. Not many school teach this form.

  195. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    *schools

  196. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i wrote it on top xD

  197. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry, I didn't see it!

  198. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    itz okz :-)

  199. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now how about a line that passes through 2 points. Can you find it?

  200. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The points are (2,5), (7,15)

  201. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Find slope first \[\huge~\frac{ y2-y1 }{ x2-x1 }\] \[\huge~\frac{ 15-5 }{ 7-2}=\frac{ 10 }{ 5 }=5\] Point slope formula \[\huge~y-y1=m(x-x1)\] Pick a point right? \[\huge~y-5=5(x-2)\] \[\huge~y-5=5x-10\] \[\huge~y=5x-5\]

  202. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you got 90% for this one!

  203. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    -_-

  204. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Spot the error!

  205. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i dont see it .-.

  206. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Wait i simplified

  207. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    All the steps are perfect, but 10/5=2 !!!!

  208. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    >_<

  209. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Are you going to make me redo all the work????? ;-;

  210. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That's no problem. That's how I would correct, more for steps.

  211. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No!

  212. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

  213. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If your steps are good, that's what's important.

  214. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    But do be careful in tests and exams.

  215. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok :)

  216. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Translate into a mathematical inequality: Ken's age (k) is at least four years older than Pete's (p).

  217. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~K \ge 4+p\]

  218. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :/

  219. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Great! It wasn't easy for you, but you did it!

  220. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Now try: Liz (L) has at least 4 times less flowers than Priya (P).

  221. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    At least 4 times could mean 5 times!

  222. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    * could be

  223. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Idk know this one .-.

  224. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    When in doubt, put numbers in. Say Liz has $10, how much should Priya have?

  225. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    $40, $50, $60, anything $40 or more, right?

  226. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry, change flowers to $...:(

  227. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So if L=10, P=40, so we write \(\Large 4L \le P\)

  228. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i knew it!

  229. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    That's what you would have done?

  230. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i was thinking something similiar

  231. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    4p

  232. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Good. Be careful, many students would write L\(\le\) 4P.

  233. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    XD

  234. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so using numbers, you can check your work.

  235. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Right

  236. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    How are we doing so far?

  237. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Great :)

  238. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Pace? 1=too slow, 10=too fast.

  239. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    5

  240. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, we're on the right track.

  241. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Gimme a minute, I have to flip the pages. You can go get a glass of water, you talked a lot! lol

  242. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    XD

  243. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Heard about compound inequalities? (6.5)

  244. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  245. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Have you done interval notation?

  246. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no

  247. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Like (5,8(, or ]5, 8]

  248. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nope

  249. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    They are usually used to solve compound inequalities.

  250. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Since you haven't done it, we'll describe by words.

  251. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You mean and and or ?

  252. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[x+3<5~~or~~~5<x+3\]

  253. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    like that?

  254. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes.

  255. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you try to solve x<-5 or x>-4

  256. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    They are already solved. -

  257. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Excellent!

  258. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Change to and: Can you try to solve x<-5 and x>-4

  259. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    still the same :/ ?

  260. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No, I'll draw the number line.

  261. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433387503479:dw|

  262. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Solution for or is shown in the graph. But for and, there is no number that satisfies the and condition. No number can be less than -5 and greater than -4 at the same time, so answer is "no solution".

  263. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    How about solving: x>4 and x<10 Use the number line if necessary

  264. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Feel free to show intermediate steps progressively. You don't have to wait till you typed up everything.

  265. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1433387789387:dw|

  266. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The answer is correct graphically. How would you write it mathematically?

  267. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x>4 and x<10

  268. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You can write it as \(4\lt x\lt10\) whe it is a range

  269. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    But be careful about the difference between \(\le\) and \(\lt\) etc

  270. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Moving onto 6.6 unless you have questions.

  271. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Solve |x|=2

  272. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    +2 -2

  273. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Very good. I see that your book does not write the answer in set notation, for example: x={-2,2}

  274. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Neither does your teacher?

  275. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Nope

  276. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, no problem. Solve |x|<2

  277. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x<2 and x>−2

  278. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Again, these two "and" inequalities make a range between -2 and +2 so we write -2<x<2. ok?

  279. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok

  280. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    solve |x-3| =5

  281. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    x−3=5 x=8 x−3=−5 x=-2

  282. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    So x=8 or -2 Good, you know your stuff! This is encouraging! what do you think?

  283. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Its easy :)

  284. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Even better!

  285. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now solve |2x-7| -3=6

  286. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    add 3 to both sides 2x-7=9 x=8 2x-7=-9 x=-1

  287. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Very good! It's still easy?

  288. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes

  289. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    We move onto abs. inequalities.

  290. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    solve |4-3x| -2 \(\le\) 7

  291. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Do you want me to show the work?

  292. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Not in this case, will save some time.

  293. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \[\huge~x \ge \frac{ -5 }{ 3} ~~~and ~~~x \le \frac{ 13 }{ 3 }\]

  294. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you check if it is x>=13/3

  295. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    −3x+4−4≥−9−4 I subtracted 4 from both sides −3x≥−13 i divided and flipped the signs it should be \[\huge~\frac{ 13 }{ -3 }\]

  296. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I have 4-3x <= -9 (second case) -3x <= -13 3x >= 13 so x>=13/3 do you agree?

  297. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    oh right the negatives cancel

  298. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, they do (after flipping sign)

  299. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and then u flipped .-.

  300. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    xD

  301. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    LOL

  302. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Looks like you're good till 6.7 (perhaps as you expected).

  303. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sorry, didn't achieve 2 chapters, not even one, but we're efficient.

  304. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    No dull moment. :)

  305. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :)

  306. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If we have time later on, we may go back to word problems.

  307. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    NO

  308. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Sure, we'll continue with 6.8 then.

  309. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    The NO is a tell-tale sign! :)

  310. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    -_-

  311. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\color{blue}{\text{Originally Posted by}}\) @mathmate If we have time later on, we may go back to word problems. \(\color{blue}{\text{End of Quote}}\) NONONONONONON!!!

  312. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Not today. Want to do word problems when you're fresh. We'll move on to graphics in 2 variables. p.367

  313. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Can you tell me in a few words about graphing linear inequalities in two variables?

  314. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    :/

  315. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Use words like region, feasible, vertical, horizontal lines, etc

  316. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, so I'll do it.

  317. mathmate
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ... another time! :)

  318. pooja195
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes :)

  319. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.