What is the value of (13)2?
Answer(s): B
This problem does not have to be computed, because the two symbols cancel each other. The radical sign () in (13) tells you to find the square root of 13. But the exponent (2) tells you to square the answer that is, to multiply the square root of 13 by itself. This would get you back to 13.
Mr. Langendorfer drove his car steadily at 40 miles per hour for 120 miles. He then increased his speed and drove the next 120 miles at 60 miles per hour.What was his average speed?
Answer(s): A
To find the average rate of speed (mph), divide the distance he covered by the time he spent traveling (R = D/ T). In this example, begin by finding the distance traveled.120 + 120 = 240 miles (distance)Next find the length of time he traveled.At the beginning of his trip, he drove 120 miles at 40 mph.120 / 40 = 3 hours (first part of trip)Later, he increased his speed.120 / 60 = 2 hours (second part of trip)Altogether, he traveled for 5 hours. Now apply the formula for finding his average rate of speed D/T = 240/5 = 48 mph (rate of speed)
An architect designs two walls of a museum to meet at an angle of 120 degrees.What is an angle of this size called?
An angle of 180 degrees is a straight angle. An angle of 90 degrees is a right angle. An angle greater than 90 degrees but less than 180 degrees is an obtuse angle. An angle less than 90 degrees is an acute angle.
Solve the following equations for x.5x + 4y = 27x - 2y=11
Answer(s): D
To solve these equations for x, begin by finding a way to eliminate y.Multiply both sides of the second equation by 2.2(x - 2y) = 2 × 112x - 4y = 22Add the new form of the second equation to the first equation, and solve for x.5x + 4y = 272x - 4y = 22(+4 cancels -4)7x = 49x = 7
If a is a negative number, and ab is a positive number, then which of the following must be true?
Answer(s): C
The product of a negative number and a positive number is always negative. The product of two negative numbers is always a positive number. Since ab is positive and a is negative, b must be negative, too.
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