Find the exact value of each variable that represents a side length in a right triangle.

5 right triangles. Top left, Side lengths are: h, 8, 10. Top center, Side lengths are: 6, k, 6 point 5. Top right, side lengths are: 2, m, 5. Bottom left, Side lengths are: square root 10, n, 10. Bottom right, Side lengths are: p, square root 68, square root 85.

In each part, and represent the length of a leg of a right triangle, and represents the length of its hypotenuse. Find the unknown length, given the other two lengths.

What is the exact length of each line segment? Explain or show your reasoning. (Each grid square represents 1 square unit.)

A line segment labeled “q” on a square grid. The line segment starts at an intersection point on the grid and slants upward and to the right to an end point that is 4 units to the right and 5 units up.

In 2015, there were roughly high school football players and professional football players in the United States. About how many times more high school football players are there? Explain how you know.

Evaluate:

Here is a scatter plot of weight vs. age for different Dobermanns. The model represented by is graphed with the scatter plot. Here, represents age in weeks, and represents weight in pounds.

Scatter plot with line of best fit. Horizontal axis, age in weeks, scale 0 to 25, by 5’s. Vertical axis, weight in pounds, scale 0 to 80, by 20’s. Line of best fit, slope=2.45, y intercept=1.22. 

1. What is the slope and what does it mean in this situation?
2. Based on this model, how heavy would you expect a newborn Dobermann to be?