Answer:
94 children, 64 students, and 47 adults attended the movie theater.
Step-by-step explanation:
Let; a be for adults, s for students, and c for children.
Make a system to solve for the amount of people.
c/a = 2
a + 2a + s = 205
3a + s = 205
Simplify.
s = 205 - 3a
s = 205 - 3a
c = 2a
Plug it in.
5c + 7s + 12a = 1482
10a + 7(205 -3a) + 12a = 1482
10a + 1435 - 21a + 12a = 1482
a + 1435 = 1482
a = 47
Substitute.
c = 2(47)
c = 94
Solve.
s = 205 - 3(47)
s = 64
4.67= 4 67/100
67 is a prime number, so the only fraction 67 hundredths can be represented by is 67/100.
Answer:
27
Step-by-step explanation:
Area of Triangle x 2 = 3 * 3
The reason I did not divide it by 2 is because of how the other triangle is bound to have the same area. Just leave it as it is because later you're going to reach the same answer.
3 * 3 = 9
Rectangle Area = 6 * 3 = 18
18 + 9 = 27
The complex solutions come in pairs and the only difference between them is the sign between the real and imaginary part, so one of the other two solutions is

. The third solution can be easily found using the rational root theorem, and it's equal to -1.
Answer:
B. More than one quadrilateral exists with the given conditions, and all instances must be isosceles trapezoids.
Step-by-step explanation:
In a parallelogram, adjacent angles are supplementary. They are only congruent if the parallelogram is a rectangle. In this problem, adjacent angles are both congruent and acute. If this were a triangle, it would guarantee the triangle is isosceles.
The fact that opposite angles are supplementary guarantees that the fourth side of the figure is parallel to the base between the acute angles. That makes the figure an isosceles trapezoid. Unless specific angles and side lengths are specified, the description matches <em>any</em> isosceles trapezoid.