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Answer:
x intercept of CD = 17
Step-by-step explanation:
We are given a line AB with its end coordinates. and Another line segment CD which is perpendicular to AB. We have the coordinates of C , and we are asked to find the x intercept of line CD.
For that we need to find the equation of CD
we have coordinates of C , and hence if we have slope of CD we can find equation of CD
Slope of CD can be determine with the help of slope of AB as CD⊥ AB
So, the slope of CD
Hence we start from determining slope of AB
slope is given as
Hence
There fore
(∵ Product of Slopes of two perpendicular lines is always -1)
Now we find the equation of CD with the help of slope -1 and coordinates of C(5,12)
Hence we have our equation , now in order to find the x intercept we keep y = 0 in it and solve for x
Hence the x intercept is 17
Answer:
See attached. (Both inequalities graph to the same region.)
Step-by-step explanation:
To graph an inequality, you first replace the inequality symbol by an equal sign. Then you graph the line (or curve) described by the equation. If the inequality symbol includes the "or equal to" case, then the line (or curve) is solid and is part of the solution set. If not, then the line (or curve) is dashed and is <em>not part of the solution set</em>.
Here, the line x+y=5, will bound the solution set, but is not part of it.
Note that the line -x -y = -5 (from the second inequality) is the same ilne.
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After you have graphed the boundary of the solution region, you need to determine which side of the boundary has the solutions. I find it easy to do this by locating an x- or y-term with a positive coefficient and seeing which side of the inequality symbol that lies on. Here, both the x-term and the y-term lie on the "is greater than" side of the symbol, so the half-plane is shaded above and to the right of the line, where x- and y-values are greater than they are on the line.
In the second inequality, you can multiply the whole thing by -1 to get
... x + y > 5 . . . . same as the first inequality
or you can add (x+y) to both sides to get
... 0 < -5 +x +y
Once again, the x- and y-values that satisfy this are greater than those that are on the boundary line.
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The graph seems to show only one equation. Both are there, but the dashed blue line sits on top of the dashed red line, so you can't see it. The purple shading indicates both red and blue shading in the same area.
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Of course you graph the boundary line the way you would any linear equation. In this form, it is not too difficult to see that both the x- and y-intercepts are 5. (When x=0, y=5; and when y=0, x=5 for the boundary line's equation x+y=5.) Draw the dotted line through these intercept points, add shading above, and you have your graph.
