<u>Answer:</u>
1/4
<u>Step-by-step explanation:</u>
We are to find the scale factor of the dilation that maps the pre-image of triangle ABC with vertices A(2, 5), B(6, 10) and C(9, −1) to the image triangle A'B'C' with vertices A' (0.5, 1.25), B' (1.5, 2.5), C' (2.25, −0.25).
Center of dilation is at the origin.
To find the scale factor, we will divide the corresponding vertices of the image and pre-image.
A(2, 5) ---> A' (0.5, 1.25) = ![\frac{0.5}{2} , \frac{1.25}{5}=(\frac{1}{4} , \frac{1}{4})](https://tex.z-dn.net/?f=%5Cfrac%7B0.5%7D%7B2%7D%20%2C%20%5Cfrac%7B1.25%7D%7B5%7D%3D%28%5Cfrac%7B1%7D%7B4%7D%20%2C%20%5Cfrac%7B1%7D%7B4%7D%29)
B(6, 10) ---> B' (1.5, 2.5) = ![\frac{1.5}{6} , \frac{2.5}{10}=(\frac{1}{4} , \frac{1}{4})](https://tex.z-dn.net/?f=%5Cfrac%7B1.5%7D%7B6%7D%20%2C%20%5Cfrac%7B2.5%7D%7B10%7D%3D%28%5Cfrac%7B1%7D%7B4%7D%20%2C%20%5Cfrac%7B1%7D%7B4%7D%29)
C(9, −1) ---> C' (2.25, −0.25) = ![\frac{2.25}{9} , \frac{-0.25}{-1}=(\frac{1}{4} , \frac{1}{4})](https://tex.z-dn.net/?f=%5Cfrac%7B2.25%7D%7B9%7D%20%2C%20%5Cfrac%7B-0.25%7D%7B-1%7D%3D%28%5Cfrac%7B1%7D%7B4%7D%20%2C%20%5Cfrac%7B1%7D%7B4%7D%29)
Therefore, the scale factor of the dilation is 1/4.
Answer:
600 degrees
10pi/3 rad = 10pi/3 / pi × 180° = 600 degrees.
Solve for x over the real numbers by completing the square.
(x - 8)² = 48
Take the square root of both sides:
x - 8 = 4 √(3) or x - 8 = -4 √(3)
Add 8 to both sides:
x = 8 + 4 √(3) or x - 8 = -4 √(3)
Add 8 to both sides:
Answer: x = 8 + 4 √(3) or x = 8 - 4 √(3)
A example of a Proper fraction is D =3/4