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Question 84645: Could I possibly get some help on these problems?
Write the equation of the line passing through
(4,4) and (4,2).
Write the equation of the line which has y-intercept (0,5) and is perpendicular to the line with equation y=-3x+1.
A roof rises 9.75 ft. over a horizontal distance of 17.24 ft. What is the slope of the roof to the nearest hundreth?
Given f(x)=5x2-3x+1, find f(-2).
thank you for your time and help.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! ******************
Write the equation of the line passing through (4,4) and (4,2).
.
The "trick" to this problem is to note that the value of x in both of the given points is
the same. So you can say that based on these two points, the value of y can be anything
but the value of x always equals 4. So the equation that reflects this situation
is x = 4. That is the answer to this question. (The graph of this equation is a vertical
line that crosses the x-axis at +4.)
.
******************
Write the equation of the line which has y-intercept (0,5) and is perpendicular to the line with equation y=-3x+1.
.
For two lines to be perpendicular their slopes must be negative inverses of each other.
For example, if one of the lines has a slope of 4, to be perpendicular to it the other
line must have a slope of -1/4. In this case, the given line has a slope of -3. (You can
tell that because -3 is the multiplier of the x term in the equation of the line.) Therefore,
the slope of a line that is perpendicular to the given line must be -1/(-3). This simplifies
to +1/3. The slope intercept form of an equation can be used. This form is:
.
y = mx + b
.
where m is the slope and b is the value where the graph crosses the y-axis. We have
figured out that the slope of the perpendicular line is +1/3 so we can substitute
that into the slope intercept form. When we do that the equation becomes:
.
y = (1/3)x + b
.
The problem also tells you that the y-intercept point of the perpendicular line is (0,5).
This means that the value of y where the graph of the perpendicular crosses the y-axis
is +5. But that point is represented by b in the equation. Therefore, substitute
+5 for b and the equation of the perpendicular line becomes:
.
y = (1/3)x + 5
.
and this is the equation you were asked to find.
.
*************************
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A roof rises 9.75 ft. over a horizontal distance of 17.24 ft. What is the slope of the roof to the nearest hundreth?
.
Slope is defined as rise divided by horizontal distance which is called run. In this
problem you are told that the rise is 9.75 feet and the run is 17.24 feet. So the slope (m)
is:
.
m = 9.75/17.24
.
Using a calculator you can reduce this:
.
m = 9.75/17.24 = 0.565545243
.
and to the nearest hundredth this rounds to 0.57
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The answer to this problem is that the slope is 0.57
.
********************
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Given  find f(-2).
.
All that this problem is asking you to do is to evaluate f(x) when x = -2. So all you
need to do is substitute -2 for x and calculate out the answer.
.
When x is -2, then  becomes:
.
.
Since  and  the problem becomes:
.
.
and this simplifies to:
.
.
The answer is f(-2) = 27
*********************
Hope this helps you to understand these four problems a little better.
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