Lesson 4: Practice Problems

Problem 1

Find the exact length of each line segment.
Estimate the length of each line segment to the nearest tenth of a unit. Explain your reasoning.

Problem 2

Plot each number on the $x$ -axis: $\sqrt{16}, \sqrt{35}, \sqrt{66}$ . Consider using the grid to help.

Problem 3

Use the fact that $\sqrt{7}$ is a solution to the equation $x^{2} = 7$ to find a decimal approximation of $\sqrt{7}$ whose square is between 6.9 and 7.1.

Problem 4 From Unit 7 Lesson 14

Graphite is made up of layers of graphene. Each layer of graphene is about 200 picometers, or $200 \times 10^{- 12}$ meters, thick. How many layers of graphene are there in a 1.6-mm-thick piece of graphite? Express your answer in scientific notation.

Problem 5 From Unit 6 Lesson 6

Here is a scatter plot that shows the number of assists and points for a group of hockey players. The model, represented by $y = 1.5 x + 1.2$ , is graphed with the scatter plot.

A scatter plot showing assists (horizontal:0-60) and points (vertical:0-80). A line is drawn through the points with a positive slope.

What does the slope mean in this situation?
Based on the model, how many points will a player have if he has 30 assists?

Problem 6 From Unit 3 Lesson 5

The points $(12, 23)$ and $(14, 45)$ lie on a line. What is the slope of the line?