8th Grade Benchmark C

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The square root of a number is the value that, when multiplied by itself, gives the original number. In this case, the square root of 4 is 2, because 2 multiplied by itself equals 4. Among the given options, the only perfect square for which 2 is the square root is 16, because 2 multiplied by itself equals 16. Therefore, the correct answer is 16.

When a figure is reflected over the y-axis, the x-coordinates of the points remain the same, but the y-coordinates change sign. In this case, angle B is a vertex of quadrilateral ABCD, and when it is reflected over the y-axis, it becomes angle F in quadrilateral EFGH. Therefore, angle B is congruent to angle F.

Q'R' is the segment that is congruent to QR. This means that Q'R' and QR have the same length.

Graph A is the most likely scatter plot that Quincy created because it shows a random distribution of points with no clear pattern or trend. In a scatter plot, the points represent individual data points, and in this case, the points are scattered across the graph without any obvious relationship between age and height. Graphs B, C, and D show either a positive or negative correlation between age and height, which is not indicated in the question.

The correct answer is the sequence that involves a horizontal shift of 11 units to the right and a vertical shift of 3 units down. This transformation will move each letter in the word "PODS" to the right by 11 units and downward by 3 units, resulting in the word "P'O'D'S'".

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Since lines HI and JK are parallel, angle HBA and angle BCK are corresponding angles. Corresponding angles are congruent when the lines are parallel. Therefore, the measure of angle BCK is also 63 degrees. However, the options provided do not include 63 degrees. Therefore, the answer is not available.

The correct answer is D because a linear function is a function that can be represented by a straight line on a graph. Option D is the only option that represents a straight line when graphed, indicating that it is a linear function.

The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). In this case, the slope is -3, indicating that for every 1 unit increase in x, y decreases by 3 units. The y-intercept represents the value of y when x is equal to 0. In this case, the y-intercept is 4, meaning that the graph intersects the y-axis at the point (0, 4). Therefore, the correct answer is slope of -3, y-intercept of 4.

Based on the graph, the y-axis represents the allowance received by Herbie and the x-axis represents the number of weeks. The graph shows that for every 4 weeks, the allowance received by Herbie is $48. Therefore, the correct answer is $48.

The given answer, "reflection over the x-axis," best describes the transformation from PQRS to P'Q'R'S'. This is because a reflection over the x-axis would result in the points being mirrored across the x-axis. In other words, any point above the x-axis would be reflected to a point below the x-axis, and vice versa. This transformation would change the orientation of the quadrilateral, flipping it upside down.

The figure DART is dilated by a factor of 2, which means that each point in the figure is multiplied by 2 in both the x and y coordinates. Therefore, the new coordinates for point D would be (-3*2, 4*2) = (-6, 8). Comparing this with the given answer choices, we can see that the new coordinates (-6, 8) match with point A. Therefore, the correct answer is A.

The correct answer is the first graph. It represents a function because for every input value (x-coordinate), there is only one output value (y-coordinate). In other words, there are no vertical lines that intersect the graph at more than one point.

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The coordinates of the new figure after rotating 180 degrees about the origin can be found by changing the signs of both x and y coordinates of each point. The new coordinates are L(6,-8), M(4,-2), and N(9,-3).

The answer is 7 in cubed because "in cubed" refers to raising a number to the power of 3. So, 7 in cubed means 7^3, which equals 343.

The solution to the given system of linear equations can be found by solving the equations simultaneously. By adding the two equations, we can eliminate the x variable and solve for y. The resulting equation is -y = 2, which gives us y = -2. Substituting this value of y into either of the original equations, we can solve for x. Plugging in y = -2 into the first equation, we get 2x - 7(-2) = 12, which simplifies to 2x + 14 = 12. Solving for x, we find x = -1. Therefore, the solution to the system of equations is (-1, -2).

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To find the slope of a line passing through two points, we can use the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the coordinates are (-7, -6) and (3, 0). Plugging these values into the formula, we get (0 - (-6)) / (3 - (-7)), which simplifies to 6 / 10 or 3/5. Therefore, the slope of the line passing through these points is 3/5.

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To solve the equation, we need to simplify both sides. First, distribute 11 to (y-2), which gives us 11y - 22. Then, combine like terms by adding 3y and 7y on the right side, which gives us 10y. Simplifying further, we have 11y + 10y - 22 = 14. Combining like terms again, we get 21y - 22 = 14. To isolate y, we add 22 to both sides, resulting in 21y = 36. Finally, we divide both sides by 21, giving us y = 36/21, which simplifies to 12/7. Therefore, the answer is 12/7.

Based on the given information, Ray claims that he can bicycle 5 miles to the local pool in 20 minutes. Looking at the graph provided by Danny, it shows that Ray's ride to the local YMCA took 20 minutes as well. Since the distance is the same for both rides, but Ray's ride took the same amount of time at a faster speed, it can be concluded that Ray bicycles at a faster speed than Danny. Therefore, the correct answer is Ray, because he bicycles 15 miles an hour and Danny bicycles 12 miles an hour.

The formula for the volume of a cylinder is V= (pi)r^2h. Since the radius of the lid is given as 1.5 inches, we can substitute this value into the formula. We are also given that the volume of the can of cherries needed is 22 cubic inches. By rearranging the formula to solve for h, we can find the height. Plugging in the values, we have 22 = (pi)(1.5^2)h. Solving for h gives us h ≈ 3 inches. Therefore, the height of the can of cherries needed to make a pie is 3 inches.

The distance between two points in a coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The formula is: distance = sqrt((x2-x1)^2 + (y2-y1)^2). In this case, the x-coordinates of K and J are 2 and -4 respectively, and the y-coordinates are 1 and -7 respectively. Plugging these values into the formula, we get: distance = sqrt(((-4)-(2))^2 + ((-7)-(1))^2) = sqrt((-6)^2 + (-8)^2) = sqrt(36 + 64) = sqrt(100) = 10 units. Therefore, the distance between point K and J is 10 units.

The rate of change of a line can be found by calculating the difference in the y-coordinates divided by the difference in the x-coordinates of two points on the line. In this case, the difference in the y-coordinates is -2 - 6 = -8, and the difference in the x-coordinates is 1 - (-2) = 3. Therefore, the rate of change is -8/3, which can be simplified to -4/3.

According to the graph, the price of Kramer's cheese is higher than Sophie's cheese. The difference between the prices is $2, with Sophie's cheese being $2 less per pound than Kramer's cheese.