6.6 Symmetries of Regular
Polygons
A Solidify Understanding Task
A line that reflects a figure onto itself is called a line of symmetry. A figure that can be carried onto
itself by a rotation is said to have rotational symmetry. A diagonal of a polygon is any line
segment that connects non-consecutive vertices of the polygon.
For each of the following regular polygons, describe the rotations and reflections that carry it onto
itself: (be as specific as possible in your descriptions, such as specifying the angle of rotation)
1. An equilateral triangle
2. A square
3. A regular pentagon
4. A regular hexagon
The angles ACD and Angle ABE are congruent so there measure is equal.
3x+14=50
3x= 50-14
3x= 36
X= 36/3=12
If the -8 is under the square root, then...

OR
If the -8 is not under the square root, then...

Either way, we replace x with -3 and simplify.
For more information, refer to the direct substitution rule for limits.
Step-by-step explanation:
Use formula to find the slope/gradient

(-5, -1) = (x1, y1)
(5, 11) = (x2, y2)
So,

Answer:
95% Confidence interval for the variance:

95% Confidence interval for the standard deviation:

Step-by-step explanation:
We have to calculate a 95% confidence interval for the standard deviation σ and the variance σ².
The sample, of size n=8, has a standard deviation of s=2.89 miles.
Then, the variance of the sample is

The confidence interval for the variance is:

The critical values for the Chi-square distribution for a 95% confidence (α=0.05) interval are:

Then, the confidence interval can be calculated as:

If we calculate the square root for each bound we will have the confidence interval for the standard deviation:
