Solve the problem.The parabola y2 = -6x is shifted down 3 units and left 2 units. Find an equation for the new parabola and find the new vertex.
A. (y + 2) 2 = -6(x + 3); vertex; (-3, -2)
B. (y + 3) 2 = -6(x + 2); vertex; (-2, -3)
C. (y - 3) 2 = -6(x - 2); vertex; (-2, -3)
D. (y - 2) 2 = -6(x - 3); vertex; (-3, -2)
Answer: B
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Evaluate the integral.
A. 8 cot (8? + 5) + C
B. 16 csc (8? + 5) cot (8? + 5) + C
C. -cot (8? + 5) + C
D. - 
cot (8? + 5) + C
Determine the real solutions to the system of nonlinear equations.6x2 + y2 = 366x2 - y2 = 36
A. (0, 
), (0, -
)
B. (0, 6), (0, -6)
C. (
, 0), (-
, 0)
D. (6, 0), (-6, 0)
Solve the problem.Brandon can paint a fence in 12 hours and Elaine can paint the same fence in 11 hours. How long will they take to paint the fence if they work together?
A. 5
hr
B. 5
hr
C. 11
hr
D. 5
hr
Use the Principle of Mathematical Induction to show that the statement is true for all natural numbers n.12 + 42 + 72 + . . . + (3n - 2)2 = 
What will be an ideal response?