The scale factor which used to perform the dilation was 0.4
Step-by-step explanation:
If point (x , y) is dilated about the origin by a scale factor k, then
- Its image is point (kx , ky)
- If k > 1, then kx > x and ky > y
- If 0 < k < 1, then kx < x and ky < y
∵ Δ RST is dilated about the origin O to create Δ R'S'T'
- Assume that the scale factor is k
∵ Point R is (3 , 9)
∴ x = 3 and y = 9
∵ Point R' is (1.2 , 3.6)
∴ kx = 1.2 and ky = 3.6
∵ x = 3 and kx = 1.2
- Substitute x in kx to find k
∴ k(3) = 1.2
∴ 3k = 1.2
- Divide both sides by 3
∴ k = 0.4
To check your answer use the y-coordinates of R and R' to find k
∵ y = 9 and ky = 3.6
- Substitute the value of y in ky to find k
∵ k(9) = 3.6
∴ 9k = 3.6
- Divide both sides by 9
∴ k = 0.4
∴ The scale factor is 0.4
The scale factor which used to perform the dilation was 0.4
Learn more:
You can learn more about dilation in brainly.com/question/3552621
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The fraction of the image in blue with respect to the <em>entire</em> hexagon is 
.
<h3>
Estimation of the ratio of the shaded region area to the entire area</h3>
Initially we proceed to create auxiliar constructions , represented by red line segments, to re-define the hexagon as a sum of standard figures. According to the figure, we find two types of triangles (type-1 and type-2), and the following relationship between the two types:
(1)
Where:
- Area of a type-1 triangle.
- Area of a type-2 triangle.
The formulae for the area of the shaded region (
) and the <em>entire</em> hexagon (
) are, respectively:
<h3>Shaded region</h3>
(2)
<h3>Entire hexagon</h3>
(3)
And the fraction of the image in blue is:
The fraction of the image in blue with respect to the <em>entire</em> hexagon is . 
To learn more on hexagons, we kindly invite to check this verified question: brainly.com/question/4083236
<h2>
Answer with explanation:</h2>
The given function : 
Using completing the squares, we have
[∵ 
]
(1)
Comparing (1) to the standard vertex form 
, the vertex of function is at (h,k)=(-1,-4)
For x-intercept, put f(x)=0 in (1), we get
Square root on both sides, we get
∴ x intercepts : x= (-3,0) and (1,0)
For y-intercept put x=0 in (1), we get
∴ y intercept : (0,-3)
Axis of symmetry : 
In , a=1 and b=2
Axis of symmetry=
DCAB would be 100. I'm pretty sure DCAB would be 100 because if DDAC is 20 that means the letters D,C, and A are 5. So if D,C, and A are all equal to 5 then B is equal to 85.
