1. 2x and 6y Because
What is the smallest angle of rotational symmetry that maps a regular pentagon onto itself?
2 answers:
Consider the regular pentagon ABCDE, with center (of mass) O.
The central angle O is a complete angle, so its measure is 360°.
It is divided into 5 equal parts, so each of them has a measure of 360°/5=72°.
If we rotate the pentagon, with point O as the center of the rotation, we can map A to any of the other points.
The smallest angle of rotation is the angle which mas A to E, 72°.
Answer: 72°
The central angle O is a complete angle, so its measure is 360°.
It is divided into 5 equal parts, so each of them has a measure of 360°/5=72°.
If we rotate the pentagon, with point O as the center of the rotation, we can map A to any of the other points.
The smallest angle of rotation is the angle which mas A to E, 72°.
Answer: 72°
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The set of inequalities y ≤ x² - 3 and y > -x² + 2 do not have a solution
<h3>How to modify the graphs</h3>The attached figure 1 represents the missing piece in the question
From the graph, we have:
f(x) = x² - 3
g(x) = -x² + 2
Next, we change the equations to inequalities as follows:
y ≤ x² - 3
y > -x² + 2
To modify the graph, we then perform the following transformations:
- Shift the function g(x) down by 2 units
- Reflect across the x-axis
- Shift the function g(x) down by 3 units
After the modifications in (a), we have:
y ≤ x² - 3 and y > -x² + 2
Next, we plot the graph of the inequalities
From the graph of the inequalities, the curves of the inequalities have no point of intersection
Hence, the set of inequalities do not have a solution
Read more about inequalities at:
#SPJ1
ANSWER: Exact Form:
2
Decimal Form: 24.08318915
STEP-BY-STEP EXPLANATION:
(-12,1) (12,-1)
Use the distance formula to determine the distance between the two points.
Distance =
Substitute the actual values of the points into the distance formula.
Multiply -1 BY -12
Add 12 and 12
Raise 24 to the power of 2
Rewrite 580 as ·145
Factor 4 out of 580
Rewrite 4 as
Pull terms out from under the radical.
2
The result can be shown in multiple forms.
Exact Form:
2
Decimal Form: 24.08318915