Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.3: Hyperbolas
Problem 44E
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Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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QUestion15
The diagram features two quadrilaterals on a coordinate plane:
1. Quadrilateral \(ABCD\) positioned in the first quadrant.
2. Quadrilateral \(JKLM\) positioned in the third quadrant.
### Axes:
- **X-axis**: Horizontal axis of the coordinate plane
- **Y-axis**: Vertical axis of the coordinate plane
### Vertices:
- **\(ABCD\)**:
- \(A\) is positioned at top right.
- \(B\) is located slightly below and to the left of \(A\).
- \(C\) is below \(B\).
- \(D\) is to the right of \(C\).
- **\(JKLM\)**:
- \(J\) is positioned to the top right.
- \(K\) is to the left of \(J\).
- \(L\) is below \(K\).
- \(M\) is right of \(L\).
### Given Angles:
- \(\angle A = 82^\circ\)
- \(\angle B = 104^\circ\)
- \(\angle L = 121^\circ\)
### Unknown Angle:
- \(\angle M\)
The task is to determine the measure of \(\angle M\).
Given the angles and the nature of rigid motions, which preserve angles and relative side lengths:
- Rigid motions include translations, rotations, and reflections.
- The sum of angles in any quadrilateral is \(360^\circ\).
### Calculation:
Sum of angles in \(JKLM\):
\[ \angle J + \angle K + \angle L + \angle M = 360^\circ \]
Given:
\[ \angle J \equiv \angle A = 82^\circ \]
\[ \angle K \equiv \angle B = 104^\circ \]
\[ \angle L = 121^\circ \]
To find \(\angle M\):
\[ 82^\circ + 104^\circ + 121^\circ + \angle M = 360^\circ \]
\[ 307^\circ + \angle M = 360^\circ \]
\[ \angle M = 360](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffeb8ca9d-9969-400c-8a44-95370ebd76d8%2F635757d9-d650-43ab-a651-64e0947897c7%2Faf9ems_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Rigid Motions in Geometry**
In the diagram below, a sequence of rigid motions maps the quadrilateral \(ABCD\) onto \(JKLM\).
The diagram features two quadrilaterals on a coordinate plane:
1. Quadrilateral \(ABCD\) positioned in the first quadrant.
2. Quadrilateral \(JKLM\) positioned in the third quadrant.
### Axes:
- **X-axis**: Horizontal axis of the coordinate plane
- **Y-axis**: Vertical axis of the coordinate plane
### Vertices:
- **\(ABCD\)**:
- \(A\) is positioned at top right.
- \(B\) is located slightly below and to the left of \(A\).
- \(C\) is below \(B\).
- \(D\) is to the right of \(C\).
- **\(JKLM\)**:
- \(J\) is positioned to the top right.
- \(K\) is to the left of \(J\).
- \(L\) is below \(K\).
- \(M\) is right of \(L\).
### Given Angles:
- \(\angle A = 82^\circ\)
- \(\angle B = 104^\circ\)
- \(\angle L = 121^\circ\)
### Unknown Angle:
- \(\angle M\)
The task is to determine the measure of \(\angle M\).
Given the angles and the nature of rigid motions, which preserve angles and relative side lengths:
- Rigid motions include translations, rotations, and reflections.
- The sum of angles in any quadrilateral is \(360^\circ\).
### Calculation:
Sum of angles in \(JKLM\):
\[ \angle J + \angle K + \angle L + \angle M = 360^\circ \]
Given:
\[ \angle J \equiv \angle A = 82^\circ \]
\[ \angle K \equiv \angle B = 104^\circ \]
\[ \angle L = 121^\circ \]
To find \(\angle M\):
\[ 82^\circ + 104^\circ + 121^\circ + \angle M = 360^\circ \]
\[ 307^\circ + \angle M = 360^\circ \]
\[ \angle M = 360
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