Response:
D. The sidelines are parallel because they are perpendicular to a common line.
Justification:
According to the perpendicular transversal theorem, when a line is perpendicular to one of two parallel lines, it is also perpendicular to the other line. Furthermore, the converse of the theorem states that if two lines are perpendicular to the same line, they must be parallel. Therefore, the sidelines are indeed parallel and also perpendicular to this single line.
Answer:
The transformation is a reflection over the x-axis followed by a translation 6 units left and 2 units down.
Step-by-step explanation:
To determine the order of transformations from ΔABC to ΔA"B"C", note that the figure first changes to ΔA'B'C', and then to ΔA''B''C''.
The transition from ΔABC to ΔA'B'C' involves a reflection over the x-axis, as ΔA'B'C' appears as a mirror image flipped vertically.
Next, moving from ΔA'B'C' to ΔA''B''C'' entails shifting the figure left by 6 units and downward by 2 units. This matches a translation by -6 in the x direction and -2 in the y direction.
Thus, the accurate description is:
Reflection across the x-axis followed by a translation of -6 units in x and -2 units in y.
Both a and b must be positive whole numbers.
The expression is 4*sqrt(30). Work Shown: Let's define circles P and Q with P representing the area of the circle with a radius of 19 and Q for a radius of 29. By using A = π*r², P calculates to 361π and Q to 841π. The resultant shaded area between circles P and Q is R = Q - P, which amounts to 480π. To ascertain the radius of a new circle S that would equal this area, we simplify R = 480π to find r = sqrt(480) leading us to r = 4*sqrt(30).
