3. E
First, isolate the expression within the absolute value brackets:
Then divide the equation into two equations. In this first case, the expression within absolute value brackets is positive:
Next, let the expression within absolute value brackets be negative:
The two solutions are x = {8 3, 6}.
4. B
First, solve for s in terms of y:
Next, solve for y in terms of x:
Finally, substitute this value for y in the equation with s:
5. A
This is a rate question, and we are given the input and rate in order to find the output. So, we can plug the known values into the rate formula:
Jim runs h laps per hour for 2 hours, so his total distance traveled is 2h laps, which equals 2h 4 miles. Ryan runs .5h laps per hour for 1.5 hours, so in total he runs 0.75h laps. This is equal to .75h 4 miles. The difference between the distance traveled by Jim and the distance traveled by Ryan is 2h 4 – .75h 4 = 1.25h 4 miles.
6. B
This is a double percent-change problem, and so we perform each percent change one by one. First, Ken bought the shirt at a discount of 30%. The price at which he paid was:
He then sold it for 60% more than he paid:
He sold the shirt for $11.20.
7. C
The toughest part of this rate problem is translating the word problem into an equation. The point at which the trains will collide is the point at which their combined distance traveled is 255 miles. Using this fact and the rates at which the trains travel, we can find out when the collision occurs, in relation to when the trains left their respective stations. Finally, from this newly calculated information, we can find where the collision occurred. Here is the rate formula we’ll be using:
Let x represent the number of hours before the trains collide. We then have the equation:
This equation explains the situation before the collision: that the train going 45 miles per hour traveled for x hours and the train traveling 60 miles per hour traveled for x – 1 hours. Their combined distance traveled is 255. Now solve the equation for x:
3 hours pass before the trains collide. From this, we know that the collision happened 3 45 = 135 miles from the western station, and 2 60 = 120 miles from the eastern station. The halfway point between the stations is 255 2 = 127.5 miles from either station, so it happened 135 – 127.5 = 7.5 miles from the halfway point between the stations.
8. C
This problem fits the classic exponential decay model. So we plug the given information into the formula:英语作文
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