Math Pool Flashcards

The diagram below shows the number of people who purchased one, two, or all three of the ice cream flavors shown. If 15 people purchased strawberry ice cream, how many people purchased chocolate ice cream?

Answer: 12

The Venn diagram shows the number of people who purchased different ice cream flavors. To find how many people purchased chocolate ice cream, sum the numbers within the chocolate circle. These are 1 (chocolate only), 4 (strawberry and chocolate), 6 (all three), and 1 (chocolate and vanilla). Adding these values gives 1 + 4 + 6 + 1 = 12 people who purchased chocolate ice cream.

Which line has a slope of -3?

Answer: 3x + y = 2

The slope-intercept form of a linear equation is y = mx + b, where 'm' represents the slope. To find the slope of the given equations, rearrange them into this form. For option C, 3x + y = 2, subtract 3x from both sides to get y = -3x + 2. In this equation, the coefficient of x is -3, which is the slope. Therefore, the line 3x + y = 2 has a slope of -3.

If g(x) = 4x - 4x, what is the value of g(3\/2)?

Answer: -2

The function is given as g(x) = 4x - 4^x. To find the value of g(3/2), substitute x = 3/2 into the function. This gives g(3/2) = 4(3/2) - 4^(3/2). First, calculate 4(3/2) = 6. Next, calculate 4^(3/2) = (√4)^3 = 2^3 = 8. Finally, subtract the second value from the first: 6 - 8 = -2.

At Bruno’s Video World, the regular price for a DVD is d dollars. How many DVDs can be purchased for x dollars when the DVDs are on sale at 20% off the regular price?

Answer: 5x\/4d\t

The regular price for a DVD is 'd' dollars. With a 20% discount, the sale price per DVD is d - 0.20d = 0.80d. To find how many DVDs can be purchased for 'x' dollars, divide the total money 'x' by the sale price per DVD: x / (0.80d). Since 0.80 is equivalent to 4/5, this expression becomes x / (4/5 d). Dividing by a fraction is the same as multiplying by its reciprocal, so x * (5 / 4d) = 5x / 4d.

In the triangle below, find the measure of angle X.

Answer: 49

The sum of the interior angles in any triangle is always 180 degrees. The diagram shows a triangle with two known angles: 88 degrees and 43 degrees. To find the measure of angle X, subtract the sum of these two angles from 180 degrees. First, add the known angles: 88 + 43 = 131 degrees. Then, subtract this sum from 180: X = 180 - 131 = 49 degrees.

If Dave drove one-third of the distance of his trip on the first day, and 60 miles on the second day, he figured out that he still had 1\/2 of the trip to drive. What was the total length, in miles, of his trip?

Answer: 360

Let the total length of the trip be T miles. Dave drove (1/3)T on the first day and 60 miles on the second day, with (1/2)T remaining. The sum of these parts equals the total trip: (1/3)T + 60 + (1/2)T = T. Combine the T terms: (1/3)T + (1/2)T = (2/6)T + (3/6)T = (5/6)T. So, (5/6)T + 60 = T. Subtract (5/6)T from both sides: 60 = T - (5/6)T = (1/6)T. Multiply by 6 to find T: T = 60 * 6 = 360 miles.

What is f(2) for the graph of f(x) below?

Answer: 1\/2

To find f(2) from the graph, locate the value x = 2 on the horizontal axis. From this point, move vertically upwards until you intersect the graph of the function f(x). Once you reach the graph, move horizontally to the left to read the corresponding y-value on the vertical axis. Following this procedure, you will find that when x = 2, the graph passes through the point (2, 1/2), meaning f(2) = 1/2.

Two sides of a triangle have sides 4 and 8. The length of the third side must be greater than_____ and less than____.

Answer: 4,12

The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. For sides 4 and 8, the third side must be greater than their difference (8 - 4 = 4) and less than their sum (4 + 8 = 12). Therefore, the length of the third side must be greater than 4 and less than 12.

Which of the following is equivalent to x2 < -2x?

Answer: -2 0

To solve the inequality x² < -2x, first move all terms to one side to get x² + 2x < 0. Factor the expression to x(x + 2) < 0. The critical points where the expression equals zero are x = 0 and x = -2. Testing intervals around these points shows that the inequality holds true when x is between -2 and 0, meaning -2 < x < 0.

6b²-24b+24=?

Answer: 6 (b-2) ²

To factor the expression 6b² - 24b + 24, first factor out the greatest common factor, which is 6, resulting in 6(b² - 4b + 4). The expression inside the parentheses, b² - 4b + 4, is a perfect square trinomial because it fits the form (a - c)² = a² - 2ac + c². Here, a = b and c = 2, so it simplifies to (b - 2)². Therefore, the fully factored expression is 6(b - 2)².