Determine whether each regular polygon tessellates the plane. Explain.
2 answers:
Answer:
b. no; measure of interior angle = 135°
Step-by-step explanation:
A regular polygon can only tessellate the plane when its interior angle divides 360 degrees.
The polygons that tessellate are - the square, the equilateral triangle, and the regular hexagon.
The octagon cannot tessellate because its internal angle does not divide 360 degrees. Tessellation means an arrangement of polygons in a repeated pattern without overlapping.
The internal angle of an octagon is 135 degrees. When we divide 360 by 135 we get,
Its not a complete number this is why octagons do not tessellate.
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Answer:
The value of x = -1 makes the denominator of the function equal to zero. That is why this value is not included in the domain of f(x)
Step-by-step explanation:
We have the following expression
Since the division between zero is not defined then the function f(x) can not include the values of x that make the denominator of the function zero.
Now we search that values of x make 0 the denominator factoring the polynomial
We need two numbers that when adding them get as a result -1 and when multiplying those numbers, obtain -2 as a result.
These numbers are -2 and 1
Then the factors are:
We do the same with the numerator
We need two numbers that when adding them get as a result 4 and when multiplying those numbers, obtain 3 as a result.
These numbers are 3 and 1
Then the factors are:
Therefore
Note that only if
So since is not included in the domain the function has a discontinuity in