Nys Grade 8 Math Assessment

Explanation
The given expression can be simplified by combining like terms. The terms 12ab, 8ab, and 5ab all have the same variables (a and b), so we can add their coefficients (the numbers in front of the variables) together. 12ab + 8ab + 5ab equals 25ab. Therefore, the simplified expression is 25ab.

Explanation
Graph D shows the change in temperature of the water in the beaker over time. The graph starts at 20°C and gradually increases to 60°C after 8 minutes. Then, it continues to increase to 100°C after 16 minutes and remains at 100°C for the next 8 minutes. This matches the given information in the question, making graph D the correct representation of the temperature change over time.

Explanation
The term "hypotenuse" best describes AC in the right triangle shown. The hypotenuse is the side opposite the right angle and is the longest side of the triangle. In this case, AC is the side opposite the right angle and is longer than the other two sides (legs) of the triangle.

Explanation
In a rectangle, the diagonal is the hypotenuse of a right triangle formed by the length and width of the rectangle. Using the Pythagorean theorem, we can find the length of the diagonal. Let's assume the length of the rectangle is x and the width is y. The diagonal (d) can be calculated as d = sqrt(x^2 + y^2). Since the garden is divided into two equal sections, the length and width are equal, so we can substitute x = y. Therefore, d = sqrt(2x^2) = sqrt(2) * x. Given that the length of the garden is 13 meters, the length of the diagonal is 13 * sqrt(2) = 13 meters.

Explanation
Based on the survey results, 209 out of 643 skateboarders preferred wood skateboards. To estimate the percentage, we can divide the number of skateboarders who preferred wood (209) by the total number of skateboarders surveyed (643) and multiply by 100. This calculation gives us approximately 32.5%. Since we are looking for the most reasonable estimation, the closest option is 30%, which is the correct answer.

Explanation
The scale on the map shows that 1 inch represents 344 miles. Therefore, to find the actual distance between the two cities, we need to multiply the distance on the map (2 inches) by the scale factor (344 miles). This gives us 2 inches * 344 miles/inch = 688 miles.