answer:To evaluate each statement for correctness: **Statement ①: Equal angles are vertical angles.** - Vertical angles are the angles opposite each other when two lines cross. They are equal in measure. However, not all equal angles are vertical angles. Equal angles can also be corresponding angles or alternate angles when parallel lines are crossed by a transversal. Therefore, this statement is incorrect. **Statement ②: If angle 1 + angle 2 = 180^{circ}, then angle 1 and angle 2 are complementary angles.** - This statement is incorrect because when the sum of two angles is 180^{circ}, they are actually supplementary angles, not complementary angles. Complementary angles have a sum of 90^{circ}. **Statement ③: There is only one line perpendicular to a given line passing through a point.** - This statement is correct. Given a line in a plane, there is exactly one line that can be drawn perpendicular to it through any point not on the line. This is a fundamental property of Euclidean geometry. **Statement ④: There is only one line parallel to a given line passing through a point outside the line.** - This statement is also correct. According to the Parallel Postulate in Euclidean geometry, through a point not on a given line, there is exactly one line parallel to the given line. Given the corrections: - Statement ① is incorrect. - Statement ② is incorrectly described as correct in the standard answer; it should be considered incorrect. - Statement ③ is correct. - Statement ④ is correct. Therefore, there are 2 correct statements (③ and ④), so the correct answer is B. However, due to a misinterpretation in the explanation of statement ② in the standard solution, let's correct the approach while adhering to the original answer's conclusion for consistency: - Re-evaluating Statement ② correctly: If angle 1 + angle 2 = 180^{circ}, they are supplementary, not complementary. This was an oversight in the explanation. The correct interpretation should align with the standard solution's intent, which likely aimed to assess understanding of supplementary angles but was misstated. Given the intent to stay consistent with the original answer's conclusion and correct the oversight: Correct Statements are ③ and ④. Therefore, the correct choice, adhering to the original conclusion and correcting the explanation oversight, is: boxed{B}.

answer:**Answer:** Since (x-3)^3+2014(x-3)=1 and (2y-3)^3+2014(2y-3)=-1, adding the two equations gives: (x-3)^3+(2y-3)^3+2014(x-3)+2014(2y-3)=0, which can be rewritten as (x+2y-6)[(x-3)^2-(x-3)(2y-3)+(2y-3)^2]+2014(x+2y-6)=0, thus, (x+2y-6)[(x-3)^2-(x-3)(2y-3)+(2y-3)^2+2014]=0, since (x-3)^2-(x-3)(2y-3)+(2y-3)^2 geq 0, it must be that x+2y-6=0. Substituting 2y=6-x into z=x^2+4y^2+4x gives z=x^2+(6-x)^2+4x=2x^2-8x+36=2(x-2)^2+28 geq 28, and the minimum value is reached if and only if x=2, y=2. Therefore, the correct choice is: boxed{C}. **Analysis:** Since (x-3)^3+2014(x-3)=1 and (2y-3)^3+2014(2y-3)=-1, adding the two equations and then using the multiplication formula, we get: (x+2y-6)[(x-3)^2-(x-3)(2y-3)+(2y-3)^2]+2014(x+2y-6)=0. Since (x-3)^2-(x-3)(2y-3)+(2y-3)^2 geq 0, it follows that x+2y-6=0. Substituting 2y=6-x into z=x^2+4y^2+4x and then using the monotonicity of the quadratic function, we can obtain the result.

answer:If 63 people were equally divided into 9 cars, then to find out how many people were in one car, you would divide the total number of people by the number of cars: 63 people ÷ 9 cars = boxed{7} people per car.

answer:(1) From 2sin (A+B)- sqrt {3}=0, we get sin (A+B)= dfrac { sqrt {3}}{2}. Since triangle ABC is an acute triangle, we have A+B=120^{circ}, thus angle C=60^{circ}. So, the degree measure of angle C is boxed{60^{circ}}. (2) Since a and b are the roots of the equation x^{2}-2 sqrt {3}x+2=0, we have a+b=2 sqrt {3} and ab=2. Therefore, c^{2}=a^{2}+b^{2}-2abcos C, which simplifies to (a+b)^{2}-3ab=12-6=6. Thus, c= sqrt {6}. The length of side c is boxed{sqrt {6}}. The area of triangle ABC is S_{triangle ABC}= dfrac {1}{2}absin C= dfrac {1}{2} times 2 times dfrac { sqrt {3}}{2}= dfrac { sqrt {3}}{2}. So, the area of triangle ABC is boxed{dfrac { sqrt {3}}{2}}.