FILL BLANKIn the figure, ABCE is a square. What is the area of quadrilateral ABCD?
Answer(s): A
Area of square ABCE:Area = 8 × 8 = 64Area of triangle CDE:Triangle CDE is a right triangle:Vertical leg (CE) = 8Hypotenuse (CD) = 17Use the Pythagorean Theorem to find DE:CE2 + DE2 = CD282 + DE2 = 17264 + DE2 = 289DE2 = 225DE = 15Now area of triangle CDE:Total area of quadrilateral ABCD:ABCD = square ABCE + triangle CDE = 64 + 60 = 124
In the rectangular coordinate system, which of the following is an equation of the line passing through the points (5, 0) and (9, 2)?
To get from his house to a certain destination, George traveled a distance 4 kilometers due north, then a distance of 5 kilometers due east, and finally a distance of 6 kilometers due north. Approximately what is the straight-line distance, in kilometers, from George's house to the destination?
Answer(s): C
George's overall displacement is 10 km north (4 + 6) and 5 km east.
In the triangle shown above, x < y < z. Which of the following could be the value of b?Indicate all such values.
Answer(s): C,D
For the triangle:sides: x (left), y (right), z (base)angles at the base: left = b°, right = 40°apex angle = 180 - (b + 40) = 140 - b°Because larger sides lie opposite larger angles,x < y < z 40° < b° < 140 - b°From 40° < b°, we need b > 40.From b < 140 - b, we get 2b < 140 b < 70.Hence b must satisfy 40 < b < 70.Among the given options (35, 39, 48, 67, 71), the values in that open interval are 48 and 67.
If two adjacent vertices of a square are located at (1, 5) and (4, 1) in a rectangular coordinate plane, then the length of a side of the square is
Answer(s): B
The side of the square is the distance between the adjacent vertices (1, 5) and (4, 1). Using the distance formula:
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