Answer:
Minimum angle = 108°
Step-by-step explanation:
From the figure attached,
Minimum angle to overlap the star onto itself is the angle of rotation from point A to B.
Let the angle between A and B measure a°.
If we complete a star pentagon by joining the vertices of the star,
Formula to measure the internal angle of a polygon is,
Measure of internal angle = 
Measure of ∠ABC = 
= 108°
Since, one side star divides the interior angle into three equal parts,
Measure of interior angle =
= 36°
From ΔAOB,
m(∠OAB) + m(∠AOB) + m(∠ABO) = 180° [Sum of interior angles of a triangle = 180°]
36° + a + 36° = 180°
a + 72° = 180°
a = 180 - 72
a = 108°
Therefore, by the minimum angle of rotation of 108° star will overlap onto itself.
Answer:
The duration is 135 minutes ie. 2 hours and 15 minutes
If (.) represent multplication the answer is
2/5×35=14
if (.) represent decimal the answer is
2/ 5.35= 40/107
1. 1/49
2. 1/625
3. 1/8
4. 1/216
5. 1/64
6. 25/121?
7. 1/256
8. -1/531441?
9. a^4/9
10. 1/12t^3
11. 25/b^4
12. 7/r^7
13. 4x^5/y^3
14. 3g^3
I hope this is all right, if it's not I apologize.
The transformation of a function may involve any change. The function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
<h3>How does the transformation of a function happen?</h3>
The transformation of a function may involve any change.
Usually, these can be shifted horizontally (by transforming inputs) or vertically (by transforming output), stretched (multiplying outputs or inputs) etc.
If the original function is y = f(x), assuming the horizontal axis is the input axis and the vertical is for outputs, then:
Horizontal shift (also called phase shift):
- Left shift by c units, y=f(x+c) (same output, but c units earlier)
- Right shift by c units, y=f(x-c)(same output, but c units late)
Vertical shift
- Up by d units: y = f(x) + d
- Down by d units: y = f(x) - d
Stretching:
- Vertical stretch by a factor k: y = k \times f(x)
- Horizontal stretch by a factor k: y = f(\dfrac{x}{k})
The function f(x)=x^(1/3) is transformed to form the function of h(x)=(2x)^(1/3)+5. Therefore, the transformation made to the function is,
Vertically stretched by a factor of 2^(1/3) ⇒ 2^(1/3) × x^(1/3) = (2x)^(1/3)
Up by 5 units ⇒ (2x)^(1/3) + 5
Hence, the function f(x) is vertically stretched and shifted 5 units upwards to form h(x).
Learn more about Transforming functions:
brainly.com/question/17006186
#SPJ1