Simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.
1 answer:
<h2>Answer:</h2>
<u>x>0 and working with real numbers</u>
OR
<u>x<0 and working with imaginary/complex numbers</u>
OR
<u>Leave it like the following for both systems(Real/Complex) numbers</u>
<u>First simplify</u>
<u>Find a perfect square and a non perfect square, which when you multiply the two squares it gives you</u>
<u>Now get the square root of</u> <u>if we are working with real numbers and x > 0</u>
<u>If x not > 0 then just leave as</u>
<u>Now combine it all</u>
OR
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Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.
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The equation of the first line can be found as follows:
the slope is
, thus, the equation is:
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the slope is
,
thus the equation of the second line is :
We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,
so we write the inequalities so that they do not hold for (0, 4)
line 1:
y≥x+4
4≥0+4=4 is true, so we change the sign and write : y≤x+4
similarly, line 2:
y≤-2x+3
4≤-2*0+3=3, which is not true, so we have the correct direction.
Note that since the lines were solid, we include the equality case:
Answer:
the shaded region is the solution to the system of inequalities:
i) y≤x+4
ii) y≤-2x+3
The second line, through (1, 1) and (2, -1) is the purple line.
Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.
Both lines are included, since they are solid lines.
The equation of the first line can be found as follows:
the slope is
The equation of the second line can be found as follows:
the slope is
thus the equation of the second line is :
We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,
so we write the inequalities so that they do not hold for (0, 4)
line 1:
y≥x+4
4≥0+4=4 is true, so we change the sign and write : y≤x+4
similarly, line 2:
y≤-2x+3
4≤-2*0+3=3, which is not true, so we have the correct direction.
Note that since the lines were solid, we include the equality case:
Answer:
the shaded region is the solution to the system of inequalities:
i) y≤x+4
ii) y≤-2x+3