Question

Which branch is the federal court system?


Legislative


Senate


Judicial


Executive
Answer
The Preamble, Articles, and Amendments are the 3 main sections of the Constitution.


True

False
Answer
What year was the Constitution written?


1876


1776


1787


1987
Answer
How many houses (chambers) are there in Congress?


2


3


4


1


Answer
Amendments are harder to pass than laws.


True

False
Answer
Xin borrowed some money from her friend in order to help buy a new video game system. Xin agreed to pay the friend back some amount every week until her loan was paid off. Let LL represent the amount Xin owes her friend after tt weeks. A graph of LL is shown below. Write an equation for LL then state the slope of the graph and determine its interpretation in the context of the problem.
Answered by GPT-4o mini
The federal court system is part of the **Judicial** branch of the government.
Answered by GPT-4o mini
**True**. The Constitution is structured with the Preamble, the Articles, and the Amendments as its three main sections.
Answered by GPT-4o mini
The Constitution was written in **1787**.
Answered by GPT-4o mini
There are **2** houses (chambers) in Congress: the House of Representatives and the Senate.
Answered by GPT-4o mini
**True**. Amendments to the Constitution are generally harder to pass than regular laws. There are more stringent requirements for amending the Constitution, such as needing a two-thirds majority in both houses of Congress and ratification by three-fourths of the states.
Answered by GPT-4o mini
To formulate an equation for \( L \) based on the given information about the loan and repayment, we need to understand the key components:

1. **Initial Amount Borrowed**: Let's denote this amount as \( L_0 \).
2. **Weekly Payment**: Let the amount Xin pays her friend back each week be \( P \).
3. **Time in Weeks**: Denote the number of weeks as \( t \).

The amount \( L \) that Xin owes her friend can be represented as a linear equation:

\[
L(t) = L_0 - Pt
\]

### Slope of the Graph

In the context of this equation:
- The slope (\( m \)) is \(-P\) (the negative rate at which the debt decreases).

### Interpretation of the Slope

1. **Negative Slope**: The slope is negative because as time increases (more weeks passing), the amount owed by Xin decreases.
2. **Value of \( P \)**: The value of \( P \) represents the weekly payment. If \( P = 10 \), it means Xin pays back $10 each week.

### Example:

If Xin borrowed $100 (i.e., \( L_0 = 100 \)) and she agreed to pay back $10 weekly (i.e., \( P = 10 \)), the equation would be:

\[
L(t) = 100 - 10t
\]

This means after \( t \) weeks, Xin will owe:

- After 1 week: \( L(1) = 100 - 10 \times 1 = 90 \)
- After 2 weeks: \( L(2) = 100 - 10 \times 2 = 80 \)
- And so on.

This illustrates the process of Xin repaying her loan over time, and the slope clearly indicates the rate at which the loan decreases.