Answer: The answer is (D) Reflection across the line y = -x.
Step-by-step explanation: In figure given in the question, we can see two triangles, ΔABC and ΔA'B'C' where the second triangle is the result of transformation from the first one.
(A) If we rotate ΔABC 180° counterclockwise about the origin, then the image will coincide with ΔA'B'C'. So, this transformation can take place here.
(B) If we reflect ΔABC across the origin, then also the image will coincide with ΔA'B'C' and so this transformation can also take place.
(C) If we rotate ΔABC through 180° clockwise about the origin, the we will see the image will be same as ΔA'B'C'. Hence, this transformation can also take place.
(D) Finally, if we reflect ΔABC across the line y = -x, the the image formed will be different from ΔA'B'C', in fact, it is ΔA'D'E', as shown in the attached figure. So, this transformation can not take place here.
Thus, the correct option is (D).
Answer:
3x-4y
Step-by-step explanation:
combine like terms. 2x+x=3x.
-5y+y=-4y
We can find the slope of this line by using the slope formula:

We'll use the points (-6, 0) and (0, -3)
(-3 - 0) / (0 + 6) = -3/6 = -0.5
The slope of the line is A, -1/2
Answer:
it is 70% full
Step-by-step explanation:
When it is 30 % empty it means it is 70% full
0.7x=0.3x+30
0.7x-0.3x=30
Given,
The coordinates of the point on the circle is (-4, -2).
The coordinates of the center of the circle is (-8, -10).
Reuired
The length of the center of the circle.
By using the distance formula, the radius of the circle can be calculated.
The distance formula is,

Substituting the value of the coordinates of the points,
![\begin{gathered} Distance=\sqrt{(-10-(-2))^2+(-8-(-4))^2} \\ =\sqrt{(-10+2)^2+(-8+4)^2} \\ =\sqrt{(-8)^2+(-4)^2} \\ =\sqrt{64+16} \\ =\sqrt{80} \\ =\sqrt{4\times4\times5} \\ =4\sqrt[]{5} \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20Distance%3D%5Csqrt%7B%28-10-%28-2%29%29%5E2%2B%28-8-%28-4%29%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%7B%28-10%2B2%29%5E2%2B%28-8%2B4%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%7B%28-8%29%5E2%2B%28-4%29%5E2%7D%20%5C%5C%20%3D%5Csqrt%7B64%2B16%7D%20%5C%5C%20%3D%5Csqrt%7B80%7D%20%5C%5C%20%3D%5Csqrt%7B4%5Ctimes4%5Ctimes5%7D%20%5C%5C%20%3D4%5Csqrt%5B%5D%7B5%7D%20%5Cend%7Bgathered%7D)
Hence,