A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet? A. 100xy B. 100y – x C. 100x – y D. 100y / [...]
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The most important bit of information here, besides the fact the AC = 6, is the fact that the exterior angle measures 150°. This means that angle ACB measures 30° (remember, a straight line has an angle measure of 180°). Since this is a right triangle, and one of the other angles measures 90°, [...]
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What is the value of (x + y)(x + y) if xy = -3 and x2 + y2 = 10? A. 1 B. 2 C. 3 D. 4 E. 5 First we have to use the FOIL method for multiplying binomials. Using that, (x + y)(x + y) becomes x2 + 2xy + y2. If x2 + y2 [...]
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Line l contains the points (3,1) and (4,4). If line m is a different line, parallel to line l in the same coordinate plane, which of the following could be the equation of line m? A. y = 3x – 8 B. y = 1/3x – 3 C. y = -3x – 8 D. y [...]
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If Sam can do a job in 4 days that Lisa can do in 6 days and Tom can do in 2 days, how long would the job take if Sam, Lisa, and Tom worked together to complete it? A. 0.8 days B. 1.09 days C. 1.23 days D. 1.65 days E. 1.97 days The [...]
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Paint needs to be thinned to a ratio of 2 parts paint to 1.5 parts water. The painter has by mistake added water so that he has 6 litres of paint which is half water and half paint. What must he add to make the proportions of the mixture correct? A. 1 litre paint B. [...]
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If a @ b = 2(a + |b|), what is the value of 2 @ (-2 @ -1)? A. -8 B. 4 C. 0 D. -4 E. 8 We first need to solve what is inside the parentheses. What is (-2 @ -1)? Well, just plug in the values and you get the following: If a @ [...]
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What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive? A. 90 B. 95 C. 100 D. 105 E. 110 How many of you took out your calculators, added up all of these numbers, and divided by 19?? If you did that, you would have gotten the correct [...]
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A line segment containing the points (0, 0) and (12, 6) also contains: A: (6,4) B: (2,4) C: (8, 4) D: (1,0) E: (-2,-2) If the line segment contains (0,0) and (12,6), then we know that it has a sl0pe of 1/2 (to see how to determine the slope of a line, go here), and a y-intercept [...]
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The vertices of rectangle ABCD are A(-1,0), B(2,0), C(s, t), and D(-1,4). How long is diagonal AC? A. 2 B. 3 C. 4 D. 5 E. 6 In your algebra classes, you probably got used to the idea that if you see variables (in this case s and t), you need to solve for them [...]
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If Steven can mix 20 drinks in 5 minutes, Sue can mix 20 drinks in 10 minutes, and Jack can mix 20 drinks in 15 minutes, how much time will it take all 3 of them working together to mix the 20 drinks? (A) 2 minutes and 44 seconds (B) 2 minutes and [...]
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Two curves, y = px2 and y = qx2 intersect rectangle ABCD at its four corners. Which of the following expressions gives the area of the rectangle? (A) 4 · (p + q) (B) 8 · (p + q) (C) 16 · (p + q) (D) 8 · (p – q) (E) 16 · (p [...]
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A line segment containing the points (0, 0) and (12, 6) also contains: A: (6,4) B: (2,4) C: (8, 4) D: (1,0) E: (0,-6) First, we need to figure out the equation for this line. Using the slope formula, we know that the slope of this line is 1/2. Furthermore, we know that that the y-intercept is 0 [...]
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A radioactive chemical decays 20 percent each day. If 48 pounds of this chemical remain today, how many pounds of this chemical were present two days ago? A. 75 B. 72 C. 70 D. 66 E. 60 We first need to go back to the day before. If 48 pounds of this chemical remain, and [...]
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A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 100 revolutions. How many revolutions does the second wheel make in covering d feet? A. 100xy B. 100y – x C. 100x – y D. 100y / [...]
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