Determine if each statement is true if
(i) ABCD is a parallelogram
(ii) ABCD is a rhombus
In each case, if true, explain why.
(a) AD ? CB
(b) ?AEC ? ?BED
(c) ?AEC ? ?AEB
(d) ?CEA ? ?BEA
(a) True for rhombi, but not for non-rhombi parallelograms. Diagonals are perpendicular in a rhombus.
(b) True for both parallelograms and rhombi; vertical angles.
(c) F (supplementary, not congruent)
(d) True for rhombi, but not for non-rhombi parallelograms. Diagonals bisect the opposite
angles in a rhombus.
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Parametric equations and a parameter interval for the motion of a particle in the xy-plane are given. Identify the particle's path by finding a Cartesian equation for it. Graph the Cartesian equation. Indicate the portion of the graph traced by the particle and the direction of motion.x = 2 sin t, y = 3 cos t, 0 ? t ? 2?
A. 
+ 
= 1
Counterclockwise from (0, 3) to (0, 3), one rotation
B. 
+ 
= 1
Counterclockwise from (0, 2) to (0, 2), one rotation
C. 
+ 
= 1
Counterclockwise from (3, 0) to (3, 0), one rotation
D. 
+ 
= 1
Counterclockwise from (2, 0) to (2, 0), one rotation
Multiply, simplifying completely. Write answers as mixed numbers whenever possible.2
× 3
A. 9
B. 7
C. 6
D. 10
The graph of a function f is given. Use the graph to answer the question.Find the values of x, if any, at which f has a relative maximum. What are the relative maxima?
A. f has a relative maximum at x = 1; the relative maximum is 1 B. f has no relative maximum C. f has a relative maximum at x = 0; the relative maximum is 1 D. f has a relative maximum at x = -1 and 1; the relative maximum is 0
Determine the number by which both sides of the equation must be multiplied or divided, as specified, to obtain just x on the left side.- 
x = 4; multiplied
A. 4
B. - 
C. -8
D. 