Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
Just want to make sure I'm correct
![### Algebraic Simplification
#### Problem Statement:
Given the expression to simplify:
\[
(7a^4 - 13a^2 + 3a) + (-3a^4 + 8a^2 - 5a)
\]
#### Step-by-Step Solution:
1. **Combine Like Terms**:
- Identify and combine the terms with the same degree of \(a\).
2. **Rewrite the Expression**:
- \(7a^4 - 13a^2 + 3a\)
- \(-3a^4 + 8a^2 - 5a\)
3. **Combine by Addition**:
- First, add the terms with \(a^4\):
\[
7a^4 + (-3a^4) = 4a^4
\]
- Next, add the terms with \(a^2\):
\[
-13a^2 + 8a^2 = -5a^2
\]
- Finally, add the linear terms (terms with \(a\)):
\[
3a - 5a = -2a
\]
4. **Write the Simplified Expression**:
\[
4a^4 - 5a^2 - 2a
\]
Thus, the simplified form of the given expression is:
\[
4a^4 - 5a^2 - 2a
\]
#### Conclusion:
By combining like terms, the original expression simplifies to \(4a^4 - 5a^2 - 2a\). This process of combining like terms helps in reducing complex algebraic expressions to their simpler forms, making them easier to handle and interpret.
This example demonstrates the foundational algebraic principle of combining like terms, which is essential for solving various algebraic problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Feb6a3e0a-0e9e-4eb9-b3f8-cac67ff0b1b6%2F7f1b81b6-dfaf-4aff-814f-9f93aa387b95%2Finwz4mp.jpeg&w=3840&q=75)
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