Through which angle of rotation does the image of a regular pentagon coincide with its preimage?
2 answers:
<u>Answer-</u>
<em>When rotated a angle of 72°, a regular pentagon coincides with its pre-image.</em>
<u>Solution-</u>
A polygon is regular when all angles are equal and all sides are equal. So, when a pentagon's all 5 angles and sides are equal then it's called as a regular pentagon.
The angel subtended by two consecutive radius of a regular pentagon(i.e the line joining vertices and the center of the pentagon) at the center is 72°.
Due to its symmetry when a regular pentagon is rotated 72° around its center(both clockwise and counter-clockwise), it produces same pentagon as before.
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The shortest distance they have to travel to return to their starting point is 9.4 miles.
Explanation
The joggers run 8 mile north and then runs 5 miles west. we have to calculate the shortest distance they have to travel to return to their starting point.
The distance traveled north and west respectively makes the height and base of a right angled triangle.
to find the shortest distance to the starting point, the hypotenuse has to be determined.
height h=8 miles
base b=5 miles
using pythagoras theorem
The shortest distance to the starting point is 9.4 miles
Answer:
The answer to your question is the first option
Step-by-step explanation:
64
Process
1.- Find the prime factors of 64
64 2
32 2
16 2
8 2
4 2
2 2
1
64 = 2⁶
2.- Express 64 as a fractional exponent
64
3.- Simplify
64
64
64
4.- Result
64