Lesson 14
Adding and Subtracting with Scientific Notation
Problem 1
Evaluate each expression, giving the answer in scientific notation:
- \(5.3 \times 10^4 + 4.7 \times 10^4\)
- \(3.7 \times 10^6 - 3.3 \times 10^6\)
- \(4.8 \times 10^{\text-3} + 6.3 \times 10^{\text-3}\)
- \(6.6 \times 10^{\text-5} - 6.1 \times 10^{\text-5}\)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
Problem 2
- 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?
![Coordinate plane, time in minutes, 0 to 8, distance in kilometers, 0 to 5. Line segments connect the origin to 2 comma 1, 2 point 5 comma 1, 4 point 5 comma 2, 5 point 5 comma 2, 8 comma 4 point 5.](https://staging-cms-im.s3.amazonaws.com/Koa9yeYQerjR4gj4JKPAFaSE?response-content-disposition=inline%3B%20filename%3D%228-8.5.PP.C.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.PP.C.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T134039Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3dfa8b935b0e86fc74a72bc22c2038e5ebe02b98ebae16c651bb28933d7f1e02)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 6, Lesson 10.)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.
![Coordinate plane, x, number of apple, y, number of oranges.](https://staging-cms-im.s3.amazonaws.com/hUBzFZuf5v81fxSZ4FWA4uie?response-content-disposition=inline%3B%20filename%3D%228-8.4.PP.C.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%278-8.4.PP.C.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T134039Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0e196e0645001552404b31f039c9cdcd4f04f7b3429f74d47b9a37627ca66f39)
-
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?
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 5, Lesson 12.)Problem 4
Solve each equation and check your solution.
\(\text-2(3x-4)=4(x+3)+6\)
\(\frac12(z+4)-6=\text-2z+8\)
\(4w-7=6w+31\)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 4, Lesson 13.)Problem 5
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?
![Scatterplot, wingspan in millimeters, body length in millimeters. Please request assistance.](https://staging-cms-im.s3.amazonaws.com/1qwT2Gh5DaqpAMgxcZP33uZi?response-content-disposition=inline%3B%20filename%3D%228-8.6.PP.B.Image.20.png%22%3B%20filename%2A%3DUTF-8%27%278-8.6.PP.B.Image.20.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T134039Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=6ec97e84d3f40569b874f014ed48191b1f24a5ea88159b56c6d468e208ded123)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 5, Lesson 20.)Problem 6
The two triangles are similar. Find \(x\).
![Two triangles. The first has acute angles marked 46 degrees and x degrees. The second has an obtuse marked 106 degrees.](https://staging-cms-im.s3.amazonaws.com/idy2ZBdpMfi5f4Pq7iq5T8Y9?response-content-disposition=inline%3B%20filename%3D%228-8.2.B.PP.Image.08.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.B.PP.Image.08.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T134039Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=90879351713f16067c87210774efc50c7af0e68655882bebe5f983f12847a641)
Solution
Teachers with a valid work email address can click here to register or sign in for free access to Formatted Solution.
(From Unit 2, Lesson 12.)