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Intern  B
Joined: 02 Nov 2017
Posts: 32
Location: India
GPA: 3.87
In the coordinate plane there is the area of the region shaded surroun  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 17% (00:06) correct 83% (02:54) wrong based on 6 sessions

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In the coordinate plane there is the area of the region shaded surrounded by 3 inequalities. Which of the following options can be these inequalities?

1) $$x>0$$
2) $$y>0$$
3) $$y<-3x+8$$
4) $$y>(\frac{1}{2})x+4$$
5) $$y>(-\frac{1}{2})x+4$$

A. 1), 3), 5)
B. 1), 3), 4)
C. 2), 3), 5)
D. 2), 3), 4)
E. 2), 4), 5)

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Originally posted by indu1954 on 23 Mar 2019, 19:36.
Last edited by Bunuel on 24 Mar 2019, 01:46, edited 2 times in total.
Renamed the topic.
Math Expert V
Joined: 02 Aug 2009
Posts: 8320
Re: In the coordinate plane there is the area of the region shaded surroun  [#permalink]

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indu1954 wrote:
Topic-Function

In the coordinate plane there is the area of the region shaded surrounded by 3 inequalities. Which of the following options can be these inequalities?

1) x>0 2) y>0 3) y<-3x+8 4) y>(1/2)x+4 5) y>(-1/2)x+4
A. 1), 3), 5) B. 1), 3), 4) C. 2), 3), 5) D. 2), 3), 4) E. 2), 4), 5)

Hi..

In very simple terms,
You should note that the area is surrounded by three straight lines..
So if you substitute the inequality sign(< and >) with equality sign (=) in all 5 options, you should be able to get equation of these lines....

The next thing you can say that the two lines apart from y axis are having negative slope, because y and x have opposite effects, one increases the other decreases.
So the options that have negative coefficient of X while positive of y can be the equation of line..
Choice 3 and 5 have negative slope given by coefficients of x, -3 and -1/2.

Now we are left with the third side ..
So on y_axis, X is always 0, so x=0 is the third side, so 1,3,5

A

Of course if you want to get a bit more on theory , you can decide on the inequality sign < and > in option 3 and 5. But here you can answer without getting into any other details
_________________ Re: In the coordinate plane there is the area of the region shaded surroun   [#permalink] 23 Mar 2019, 22:18
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# In the coordinate plane there is the area of the region shaded surroun  