How to graph a two-step inequality - Advanced Geometry
Card 0 of 8
Let D be the region on the (x,y) coordinate plane that contains the solutions to the following inequalities:
, where 
is a positive constant
Which of the following expressions, in terms of __
_, is equivalent to the area of D?
Let D be the region on the (x,y) coordinate plane that contains the solutions to the following inequalities:
Which of the following expressions, in terms of __
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Solve and graph the following inequality:
Solve and graph the following inequality:
To solve the inequality, the first step is to add 
to both sides:
The second step is to divide both sides by 
:
To graph the inequality, you draw a straight number line. Fill in the numbers from 
to infinity. Infinity can be designated by a ray. Be sure to fill in the number 
, since the equation indicated greater than OR equal to.
The graph should look like:
To solve the inequality, the first step is to add
The second step is to divide both sides by
To graph the inequality, you draw a straight number line. Fill in the numbers from
The graph should look like:
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Which of the following lines is perpendicular to the line 
?
Which of the following lines is perpendicular to the line
The key here is to look for the line whose slope is the negative reciprocal of the original slope.
In this case, 
is the negative reciprocal of 
.
Therefore, the equation of the line which is perpendicular to the original equation is:
The key here is to look for the line whose slope is the negative reciprocal of the original slope.
In this case,
Therefore, the equation of the line which is perpendicular to the original equation is:
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Points 
and 
lie on a circle. Which of the following could be the equation of that circle?
Points
If we plug the points 
and 
into each equation, we find that these points work only in the equation 
. This circle has a radius of 
and is centered at 
.
If we plug the points
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Which inequality does this graph represent?
Which inequality does this graph represent?
The two lines represented are 
and 
. The shaded region is below both lines but above 
The two lines represented are
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What is the area of the shaded region for the following inequality:
;
What is the area of the shaded region for the following inequality:
This inequality will produce the following graph:
The shaded area is a triangle with base 7 and height 2.
To find the area, plug these values into the area formula for a triangle, 
.
In this case, we are evaluating 
, which equals 7.
This inequality will produce the following graph:
The shaded area is a triangle with base 7 and height 2.
To find the area, plug these values into the area formula for a triangle,
In this case, we are evaluating
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What is the area of the shaded region for this system of inequalities:
; 
What is the area of the shaded region for this system of inequalities:
Once graphed, the inequality will look like this:
To find the area, it is easiest to consider it as 2 congruent triangles with base 6 and height 3.
The total area will then be
, or just 
.
Once graphed, the inequality will look like this:
To find the area, it is easiest to consider it as 2 congruent triangles with base 6 and height 3.
The total area will then be
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Find the 
-intercept for the following:
Find the
.
.
.
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