Quantity AThe perimeter of hexagon ABCDEFQuantity BThe circumference of the circle with center O
Answer(s): B
Each side of the regular hexagon is 1, so its perimeter is 6 × 1 = 6. The circle has radius 1, so its circumference is 2(1) = 2 6.28. Since 2 > 6, Quantity B is greater.
y x = 1Quantity AQuantity B
Answer(s): C
Given y - x = 1,Hence Quantity A equals Quantity B.
Point G (not shown) and points P and S are the vertices of a right triangle with its right angle at point G.Quantity AThe x-coordinate of point GQuantity B2
Answer(s): D
The point G(x, y) must satisfy the right-angle conditionE. e.(-1 - x, 4 - y) (2 - x, 2 - y) = 0.This describes a circle (the Thales circle having PS as diameter) with centerand radius 1.8.Hence the x-coordinate of G can range continuously from about 1.3 up to about 2.33 Because xG can an be less than, equal to, or greater than 2, Quantity A may be smaller than, equal to, or larger than Quantity B.
The table summarizes the tickets purchased by a group of 12 people for a play.What is the average (arithmetic mean) price of the tickets purchased by the group?
To find the average ticket price, calculate the total amount paid and divide by the total number of tickets.Total = 6($17) + 2($16) + 2($12) + 2($11) = $102 + $32 + $24 + $22 = $180.Total tickets = 6 + 2 + 2 + 2 = 12.Average price = $180 ÷ 12 = $15
In the figure above, x + y =
In any triangle, choose one exterior angle at each vertex so that each exterior is supplementary to its interior angle.These three exterior angles always sum to 360°.For this triangle the interior apex angle is 40°, so its exterior angle is 180° - 40° = 140°Let the other two chosen exterior angles be the ones marked x° and y° along the straight base line.x + y + 140 = 360 x + y= 360 - 140 = 220.
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