Trevor is analyzing a circle, y² + x² = 100, and a linear function g(x). Will they intersect? y² + x² = 100 g(x) x g(x) 2 -1 -22 0 -20 1 -18 € -10 -8 -6 -4 -2 -2 O Yes, at positive x coordinates O Yes, at negative x coordinates O Yes, at negative and positive x coordinates O No, they will not intersect 2 4 6 8
Trevor is analyzing a circle, y² + x² = 100, and a linear function g(x). Will they intersect? y² + x² = 100 g(x) x g(x) 2 -1 -22 0 -20 1 -18 € -10 -8 -6 -4 -2 -2 O Yes, at positive x coordinates O Yes, at negative x coordinates O Yes, at negative and positive x coordinates O No, they will not intersect 2 4 6 8
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Title: Analyzing the Intersection of a Circle and a Linear Function**
**Problem:**
Trevor is analyzing a circle, \(y^2 + x^2 = 100\), and a linear function \(g(x)\). Will they intersect?
**Mathematical Representations:**
1. **Circle Equation:**
\[
y^2 + x^2 = 100
\]
This is the equation of a circle centered at the origin (0,0) with a radius of 10. The graph of the circle is displayed on a Cartesian plane with the x and y axes marked from -10 to 10 in both directions.
2. **Linear Function:**
\[
g(x)
\]
Given values for the linear function \(g(x)\):
\[
\begin{array}{|c|c|}
\hline
x & g(x) \\
\hline
-1 & -22 \\
0 & -20 \\
1 & -18 \\
\hline
\end{array}
\]
This table shows three points for the linear function \(g(x)\).
**Question:**
**Will the Circle and the Linear Function Intersect?**
1. **Graph Analysis:**
On the provided graph:
- The circle is centered at the origin with a radius of 10 (plotted in blue).
- There is no explicit plot of the linear function \(g(x)\) on the graph.
2. **Choices:**
- **Yes, at positive x coordinates**
- **Yes, at negative x coordinates**
- **Yes, at negative and positive x coordinates**
- **No, they will not intersect**
**Step-by-Step Solution:**
1. **Understand the Circle Equation:**
\[ y^2 + x^2 = 100 \]
The maximum value for \(y\) or \(x\) is 10, given the radius.
2. **Analyze the Linear Function Points:**
\[
\begin{array}{ccc}
x & g(x) \\
-1 & -22 \\
0 & -20 \\
1 & -18 \\
\end{array}
\]
- The given \(g(x)\) points suggest](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F355372c0-0b06-4568-8d9a-cddd4364f7ea%2F057978f8-8c8f-43ed-b3dc-84e8ac801a5c%2F16iqs4b_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Analyzing the Intersection of a Circle and a Linear Function**
**Problem:**
Trevor is analyzing a circle, \(y^2 + x^2 = 100\), and a linear function \(g(x)\). Will they intersect?
**Mathematical Representations:**
1. **Circle Equation:**
\[
y^2 + x^2 = 100
\]
This is the equation of a circle centered at the origin (0,0) with a radius of 10. The graph of the circle is displayed on a Cartesian plane with the x and y axes marked from -10 to 10 in both directions.
2. **Linear Function:**
\[
g(x)
\]
Given values for the linear function \(g(x)\):
\[
\begin{array}{|c|c|}
\hline
x & g(x) \\
\hline
-1 & -22 \\
0 & -20 \\
1 & -18 \\
\hline
\end{array}
\]
This table shows three points for the linear function \(g(x)\).
**Question:**
**Will the Circle and the Linear Function Intersect?**
1. **Graph Analysis:**
On the provided graph:
- The circle is centered at the origin with a radius of 10 (plotted in blue).
- There is no explicit plot of the linear function \(g(x)\) on the graph.
2. **Choices:**
- **Yes, at positive x coordinates**
- **Yes, at negative x coordinates**
- **Yes, at negative and positive x coordinates**
- **No, they will not intersect**
**Step-by-Step Solution:**
1. **Understand the Circle Equation:**
\[ y^2 + x^2 = 100 \]
The maximum value for \(y\) or \(x\) is 10, given the radius.
2. **Analyze the Linear Function Points:**
\[
\begin{array}{ccc}
x & g(x) \\
-1 & -22 \\
0 & -20 \\
1 & -18 \\
\end{array}
\]
- The given \(g(x)\) points suggest
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