a.) The orientation of ABCD is clockwise, as is the orientation of A'B'C'D'. This means the transformation involves a even number of reflections (may be 0). The orientation of AB is North, and the orientation of A'B' is West, so a rotation of 90° CCW (or equivalent) is involved. We can find the point of intersection of the perpendicular bisectors of AA' and BB' (at (-1, -1)) to determine a suitable center of rotation.
ABCD can be transformed to A'B'C'D' by ...
- rotation 90° CCW about the point (-1, -1)
b.) Rotation by 90° can also be accomplished by reflection across a diagonal line. Since we want the orientation to remain unchanged, we need another reflection to put the figure into its final position. A suitable alternate sequence for mapping ABCD to A'B'C'D' is ...
- reflection across the line y=x
- reflection across the line x=-1
Answer:
an infinite number of pounds of $4 nuts
Step-by-step explanation:
If <em>any</em> nuts worth less than $4 per pound are put into the mix with nuts worth $4 per pound, the value of the mix will be less than $4 per pound.
The mix Randall proposes cannot be made.
Answer:
8/3
Step-by-step explanation:
the slope is 8/3 i am sure
Answer: Let length = 2x + 3
Let width = x
Area = 54 ft2
length × width = Area
x(2x + 3) = 54
2x2 + 3x = 54
2x2 + 3x - 54 = 0
(2x - 9)(x + 6) = 0
x = 9/2 and x = -6
x = 4.5 and x = -6
We accept x = 4.5 because length cannot be a negative value. Substituting this value into the dimensions:
width = 4.5 ft
length = 2(4.5) + 3 = 9 + 3 = 12 ft
Step-by-step explanation: