Yes. There can be a line perpendicular to the given line at every point on it,
and you know how many different points there are on it ...
You can't. There are an infinite number of possible rectangles with a given area.
For any given subset, yes, because there are an infinite number of irrational numbers for each rational number. But for the set of ALL real numbers, both are infinite in number, even though the vast majority of real numbers would be irrational.
Because you would need an infinite length of paper to print out the ticket.
Only one
Equilateral triangles
Through a given plane, an infinite number of lines can be drawn perpendicular to it. For any point on the plane, there exists exactly one line that is perpendicular to the plane at that point. However, since there are infinitely many points on the plane, this leads to an infinite number of perpendicular lines overall.
Through a given point, an infinite number of lines can be drawn perpendicular to a given plane. Since any line that extends from the point to the plane at a right angle can be considered perpendicular, and this can occur at various angles around the point, there are no restrictions on the direction of these lines as long as they maintain the perpendicular relationship. Hence, the answer is infinite lines.
Any line whose slope is the negative reciprocal of that line's slope will be perpendicular to it. Given the format in which it's written, we can see that this line's slope is -8. This means that any line with a slope of 1/8 will be perpendicular to it. The most obvious one being: y = x/8 + 6 But there are an infinite number of lines with that slope, and thus an infinite number of lines that are perpendicular to the given one. For example, the line: y = x/8 + 258734095874390587423 is just as valid an answer.
Yes it's quite possible if need be.
Yes, but only in principle. In practice, you won't live long enough. Putting it in more positive terms: No matter how many lines have already been drawn perpendicular to a given line [segment], there's always enough room for a lot more of them.
Since there are an infinite number of prime numbers, there are infinite numbers with any given number of prime factors.
a circle?
Only one line can be drawn perpendicular to a given line at a specific point on that line in a plane. This is based on the definition of perpendicular lines, which intersect at a right angle (90 degrees). The uniqueness of this perpendicular line arises from the geometric properties of Euclidean space.
In a plane, there are infinitely many lines that can serve as perpendicular bisectors of a given segment. The unique perpendicular bisector of a segment is a specific line that divides the segment into two equal parts at a right angle. However, any line parallel to this unique bisector, at any distance, can also be considered a perpendicular bisector if it intersects the segment at its midpoint. Thus, while the unique perpendicular bisector exists, an infinite number of lines can be drawn parallel to it.
an infinite number; no limit
You can't. There are an infinite number of possible rectangles with a given area.
Given a line, there are an infinite number of different planes that it lies in.