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  1. #1
    Junior Member
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    graph

    could you please help me work this problems out? please!


    FIRST PROBLEM
    The equation:

    |x/2| + |y/2| = 5

    encloses a certain region on a coordinate plane. What is the area of this region?


    SECOND PROBLEM
    How many different numbers are there such that ax + b = c (a,b,and c are constants) ?
    1. c>b
    2. a>1

    A. Statement 1. is sufficient
    B. Statement 2. is sufficient
    C. Statements 1. and 2. together are sufficient
    D. Each statement alone is sufficient
    E. Both statements together are not sufficient



    thank you
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  2. #2
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    Quote Originally Posted by simone View Post
    could you please help me work this problems out? please!


    FIRST PROBLEM
    The equation:

    |x/2| + |y/2| = 5

    encloses a certain region on a coordinate plane. What is the area of this region?

    ...
    Hi,

    use the property of an absolute value:

    | x | = \left\{\begin{array}{lr}x , & \text{ if } \geq 0 \\ -x , & \text{ if } < 0 \end{array} \right.

    You get 4 different equations:
    <br />
\left|\frac y2\right|+\left|\frac x2 \right| = 5 ~\iff~\left\{\begin{array}{lr}y \geq0 \wedge x\geq 0\rightarrow & y = -x+10 \\y \geq 0 \wedge x < 0 \rightarrow & y = x+10 \\y < 0 \wedge x\geq 0 \rightarrow & y = x-10 \\ y < 0 \wedge x < 0 \rightarrow & y = -x-10\end{array}\right.

    These 4 lines form a square: see attachment.

    If these lines are supposed to enclose a region as stated in the text of your problem then you have to replace the = sign by a \leq sign.
    Attached Thumbnails Attached Thumbnails graph-doppelabswert.gif  
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