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What is the correct form of the partial fraction decomposition for ?

Question illustration
A
StartFraction A Over x + 2 EndFraction + StartFraction B Over (x + 2) squared EndFraction
Option A
B
StartFraction A Over x + 2 EndFraction + StartFraction B x + C Over (x + 2) squared EndFraction
Option B
C
StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C Over (x + 2) squared EndFraction
Option C
D
StartFraction A Over x EndFraction + StartFraction B Over x + 2 EndFraction + StartFraction C x + D Over (x + 2) squared EndFraction
Option D
3

Which expression represents the correct form for the quotient and remainder, written as partial fractions, of ?

Question illustration
A
A + StartFraction B Over x + 3 EndFraction + StartFraction C Over 2 x minus 7 EndFraction
Option A
B
A + StartFraction B x + C Over x + 3 EndFraction + StartFraction D x + E Over 2 x minus 7 EndFraction
Option B
C
A x + B + StartFraction C Over x + 3 EndFraction + StartFraction D Over 2 x minus 7 EndFraction
Option C
D
A x + B + StartFraction C x + D Over x + 3 EndFraction + StartFraction E x + F Over 2 x minus 7 EndFraction
Option D
4

What is the partial fraction decomposition of ?

Question illustration
A
StartFraction 1 Over 3 x EndFraction + StartFraction x minus 2 Over 4 x squared + 9 EndFraction
Option A
B
StartFraction 1 Over 3 x EndFraction + StartFraction x + 2 Over 4 x squared + 9 EndFraction
Option B
C
StartFraction negative 2 Over 3 x EndFraction + StartFraction x minus 1 Over 4 x squared + 9 EndFraction
Option C
D
StartFraction negative 2 Over 3 x EndFraction + StartFraction x + 1 Over 4 x squared + 9 EndFraction
Option D
9

The graph below shows the transformation from triangle 1 to triangle 2.Which sequence of steps would transform triangle 1 to triangle 2?

Question illustration
A
reflect across the y-axis; rotate 180° counterclockwise about the origin
B
reflect across the x-axis; rotate 270° counterclockwise about the origin
C
reflect across the y-axis; rotate 90° counterclockwise about the origin
D
rotate 90° counterclockwise about the origin; rotate 270° counterclockwise about the origin

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