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Triangle ACE, shown in the figure below, is isosceles with base . B lies on and D lies on . Segments and bisect AEC and CAE respectively. Which one of the following angle congruences is necessarily true?

(A) ∠CAE ≅ ∠BEC

(B) ∠CAD ≅ ∠AEC

(C) ∠CAE ≅ ∠ACE

(D) ∠AEC ≅ ∠ACE

(E) ∠BEC ≅ ∠DAE

The Correct Answer

The second term of an arithmetic sequence is -2, and the third term is 8. What is the first term?

(Note: An arithmetic sequence has a common difference between consecutive terms.)

(A)-12 (B) -10 (C) (D) 3 (E) 10

Correct Answer: A

For a chemistry class, Sanjay is doing an experiment that involves periodically heating a container of liquid. The graph below shows the temperature of the liquid at different times during the experiment. What is the average rate of change of temperature (in degrees Celsius per minute) during the times in which Sanjay is applying heat to this container?

(A) 4 (B) 5 (C) 8 (D) 10 (E) 20

Correct Answer: C

The town of Ashville has three bus stations (A, B, and C) that offer round-trip fares to its business district at both peak and off-peak rates. The matrices below show the average weekly sales for each station at each rate and the costs for both rates. In an average week, what are the combined peak and off-peak sales for Ashville's three bus stations?

(A)$780 (B) $1,590 (C) $1,950 (D) $2,090 (E) $2,340

Correct Answer: D

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