Lesson 14: Practice Problems

Problem 1

Evaluate each expression, giving the answer in scientific notation:

$5.3 \times 10^{4} + 4.7 \times 10^{4}$
$3.7 \times 10^{6} - 3.3 \times 10^{6}$
$4.8 \times 10^{- 3} + 6.3 \times 10^{- 3}$
$6.6 \times 10^{- 5} - 6.1 \times 10^{- 5}$

Problem 2 From Unit 6 Lesson 10

A graph of time in minutes vs distance in kilometers. The graph is in segments from (0,0) going up to the right with different slopes and flat segments.

Write a scenario that describes what is happening in the graph.
What is happening at 5 minutes?
What does the slope of the line between 6 and 8 minutes mean?

Problem 3

Apples cost $1 each. Oranges cost $2 each. You have $10 and want to buy 8 pieces of fruit. One graph shows combinations of apples and oranges that total to $10. The other graph shows combinations of apples and oranges that total to 8 pieces of fruit.

A graph of number of apples vs. number of oranges. Blue points start at (0,8) and go to (8,0) and orange points start at (0,5) and go to (10,0).

Name one combination of 8 fruits shown on the graph that whose cost does not total to $10.
Name one combination of fruits shown on the graph whose cost totals to $10 that are not 8 fruits all together.
How many apples and oranges would you need to have 8 fruits that cost $10 at the same time?

Problem 4

Solve each equation and check your solution.

$- 2 (3 x - 4) = 4 (x + 3) + 6$
$\frac{1}{2} (z + 4) - 6 = - 2 z + 8$
$4 w - 7 = 6 w + 31$

Problem 5 From Unit 5 Lesson 20

Ecologists measure the body length and wingspan of 127 butterfly specimens caught in a single field.

Draw a line that you think is a good fit for the data.
Write an equation for the line.
What does the slope of the line tell you about the wingspans and lengths of these butterflies?

Problem 6 From Unit 2 Lesson 12

The two triangles are similar. Find $x$ .

Two triangles on a grid. One has angles of 46 and x. The other has an angle of 106 degrees.