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Math Help - [SOLVED] Help! Many algebra problems :(

  1. #16
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    2nd attempt

    Quote Originally Posted by Elite00 View Post
    ...

    13. Graph the following piecewise function and give the domain, range, and zeros.
    f (x ) = {2x + 3, x<4
    {x -1, 4 < x < 9

    ...
    Hello,

    you have f(x)=\left\{\begin{array}{l}2x+3,x<4\\x-1,4<x<9\end{array}\right.

    I've attached the graph of this function.

    From the grap you can see: The domain is d=(-\infty,4)\ \cup\ (4,9). According to the wording of this problem the 4 doesn't belong to the domain.

    The range is r=(-\infty,11)

    There is one zeroat x=-\frac{3}{2}

    EB
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  2. #17
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    Quote Originally Posted by Elite00 View Post
    ...
    15. A lab technician is trying to make an 8% solution by combining a 2% and 12% solution. If he is trying to make a 150mL solution, how many mL of each solution should be mixed?
    ...
    Hello,

    let x be the amount of the 2%-solution
    let y be the amount of the 12%-solution

    Then you get 2 simultanous equations:
    A: x+y=150
    B: 0.02*x+0.12*y=0.08*150=12

    Multiply the equation B by 50 and calculate 50*B-A:

    5y=450. Thus y = 90. Plug in this result into A. You'll get x = 60.

    EB
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  3. #18
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    Quote Originally Posted by Elite00 View Post
    ...

    20. Solve the following system of equations: { -3x + 6y – 4z = 8
    {x + 2z – 4y = -3
    {8y=z

    ...
    Hello,

    Plug in 8y for z in equation A and B.

    \begin{array}{r}A': -3x - 26y = 8\\B': x + 12y = -3 \end{array}

    Multiply B' by 3 and add A'+3*B'

    10y = -1. Thus y = -1/10. Calculate z = -4/z and finally x = -9/5

    EB
    Last edited by earboth; November 28th 2006 at 01:35 AM.
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  4. #19
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    Quote Originally Posted by Elite00 View Post
    ...
    21. Solve 4(x+5)^2 = 20. express the answer exactly and if necessary, rounded to the nearest tenth.

    22. Factor 2x^2 10x 48 =0 and solve for x

    23. Find the exact values of x in the following quadratic equation. 2x^2 5x -12 = 0

    24. Simplify the following complex number: 3 + i / 2 3i

    ...
    Hello,

    to 21.)
    4(x+5)^2 = 20\Longleftrightarrow(x+5)^2=5\Longleftrightarrow x+5=\sqrt{5}\vee x+5=-\sqrt{5}
    Thus the exact solutions are: x=-5+\sqrt{5}\ \vee \ x=-5-\sqrt{5}
    Approximate resultes: x = -2.8 or x = -7.3

    to 22.)
    2x^2 - 10x - 48 =0 \Longleftrightarrow 2(x^2-5x-24)=0 \Longleftrightarrow 2(x-8)(x+3)=0
    A produkt is zero if one of the factors is zero. Thus you'll get the solutions: x = -3 or x = 8

    to 23.)
    Use the formula you know to solve this equation: x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

    x=\frac{5\pm\sqrt{25+96}}{4}
    x=\frac{5\pm 11}{4}. Thus x = 4 or x = -3/2

    to 24.) Multiply denominator and numerator with the conjugated(?) value of the denominator:
    \frac{3+i}{2-3i} \cdot \frac{2+3i}{2+3i}=\frac{6+9i+2i+3i^2}{4-(-9)}=\frac{3+11i}{13}

    EB
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  5. #20
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    Quote Originally Posted by Elite00 View Post
    ...

    16. Graph, shade the feasible region and label the corner points for the following system of inequalities: {y < -2x -2
    {y > 1/2x
    {x > -3

    ...
    Hello,

    have a look at the attached diagram.

    EB
    Attached Thumbnails Attached Thumbnails [SOLVED] Help! Many algebra problems :(-elite_unglchggraph.gif  
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