Which of the following is closest to 27.8 × 9.6? A. 280 B. 300 C. 2,800 D. 3,000
2 answers:
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Part (a)
The domain is the set of allowed x inputs of a function.
The graph shows that x = 0 is not allowed because of the vertical asymptote located here. It seems like any other x value is fine though.
<h3>Domain: set of all real numbers butTo write this in interval notation, we can say which is the result of poking a hole at 0 on the real number line.
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The range deals with the y values. The graph makes it seem like it stretches on forever in both up and down directions. If this is the case, then the range is the set of all real numbers.
<h3>Range: Set of all real numbers</h3>In interval notation, we would say which is almost identical to the interval notation of the domain, except this time of course we aren't poking at hole at 0.
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Part (b)
<h3>The x intercepts are x = -4 and x = 4</h3>We can compact that to the notation
These are the locations where the blue hyperbolic curve crosses the x axis.
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Part (c)
<h3>Answer: There aren't any horizontal asymptotes in this graph.</h3>Reason: The presence of an oblique asymptote cancels out any potential for a horizontal asymptote.
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Part (d)
The vertical asymptote is located at x = 0, so the equation of the vertical asymptote is naturally x = 0. Every point on the vertical dashed line has an x coordinate of zero. The y coordinate can be anything you want.
<h3>Answer: x = 0 is the vertical asymptote</h3>=======================================================
Part (e)
The oblique or slant asymptote is the diagonal dashed line.
It goes through (0,0) and (2,6)
The equation of the line through those points is y = 3x
If you were to zoom out on the graph (if possible), then you should notice the branches of the hyperbola stretch forever upward but they slowly should approach the "fencing" that is y = 3x. The same goes for the vertical asymptote as well of course.
<h3>Answer: Oblique asymptote is y = 3x</h3>Answer:
The measure of one angle of a regular convex 20-gon is 162°
Step-by-step explanation:
* Lets explain how to solve the problem
- A convex polygon is a polygon with all the measures of its interior
angles less than 180°
- In any polygon the number of its angles equal the number of its sides
- A regular polygon is a polygon that is all angles are equal in measure
and all sides are equal in length
- The rule of the measure of an angle of a regular polygon is
, where m is the measure of each interior
angle in the polygon and n is the numbers of the sides or the angles
of the polygon
* Lets solve the problem
- The polygon is convex polygon of 20 sides (20 angles)
- The polygon is regular polygon
∵ The number of the sides of the polygon is 20 sides
∴ n = 20
∵ The polygon is regular
∴ All angles are equal in measures
∵ The measure of each angle is
∴
∴
∴
∴ m = 162
∴ The measure of one angle of a regular convex 20-gon is 162°
Answer:
x = 15
Step-by-step explanation:
Assuming 3x and x-60 are in degrees, you can use:
cos(a) = sin(a+90)
To rewrite the equation as:
sin(3x) = sin(x-60+90)
sin(3x) = sin(x+30)
3x = x+30
2x = 30
x = 15
But, solving 3x = x+30 which simplifies to x=15 is not the only solution to this equation, as you can see in below picture. Finding all solutions is a bit more work, but maybe that is not required in your case.
