Find the scale factor WARM-UP 6x2 17xi-3 = 0 1x 18x-3 6x+1x 1 18 (x – 3)(6x + 1) = 0 2x + 1 3x + 5, 3x +5 (x– 3) = 0 2x 6x2 +10a 18 3x + 5 x = 3 2x + 3 2x + 1 9x +15 18(2x + 1) = (3x + 5)(2x + 3) 36x + 18 = 6x2 + 19x + 15 0 = 6x2 – 17x - 3 +3 or (6x +1) = 0 or x= 6. -- %3D %3D
Find the scale factor WARM-UP 6x2 17xi-3 = 0 1x 18x-3 6x+1x 1 18 (x – 3)(6x + 1) = 0 2x + 1 3x + 5, 3x +5 (x– 3) = 0 2x 6x2 +10a 18 3x + 5 x = 3 2x + 3 2x + 1 9x +15 18(2x + 1) = (3x + 5)(2x + 3) 36x + 18 = 6x2 + 19x + 15 0 = 6x2 – 17x - 3 +3 or (6x +1) = 0 or x= 6. -- %3D %3D
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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I need to find the answer for the left sides of the shapes
![**Warm-Up: Find the Scale Factor**
1. **Diagrams**:
- Two triangles are shown.
- The smaller triangle has sides labeled \(2x + 1\) and \(2x + 3\).
- The larger triangle has sides labeled \(3x + 5\) and 18.
2. **Scale Factor Calculation**:
\[
\frac{18}{2x + 3} = \frac{3x + 5}{2x + 1}
\]
3. **Cross-Multiplication**:
\[
18(2x + 1) = (3x + 5)(2x + 3)
\]
4. **Expanding the Equation**:
- \(18 \times (2x + 1)\) gives \(36x + 18\).
- \((3x + 5)(2x + 3)\) is expanded using a factorization box:
- Top row: \(2x, 3\)
- Left column: \(3x, 5\)
- Inside the box: \(6x^2, 10x, 9x, 15\)
Combining terms gives:
\[
6x^2 + 19x + 15
\]
5. **Setting the Equation**:
\[
36x + 18 = 6x^2 + 19x + 15
\]
6. **Rearranging the Equation**:
\[
0 = 6x^2 - 17x - 3
\]
7. **Factoring the Quadratic**:
\[
6x^2 - 17x - 3 = 0
\]
- Factor as \((x - 3)(6x + 1) = 0\)
8. **Finding Solutions**:
- Solving \((x - 3) = 0\) gives:
\[
x = 3
\]
- Solving \((6x + 1) = 0\) gives:
\[
x = -\frac{1}{6}
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Transcribed Image Text:**Warm-Up: Find the Scale Factor**
1. **Diagrams**:
- Two triangles are shown.
- The smaller triangle has sides labeled \(2x + 1\) and \(2x + 3\).
- The larger triangle has sides labeled \(3x + 5\) and 18.
2. **Scale Factor Calculation**:
\[
\frac{18}{2x + 3} = \frac{3x + 5}{2x + 1}
\]
3. **Cross-Multiplication**:
\[
18(2x + 1) = (3x + 5)(2x + 3)
\]
4. **Expanding the Equation**:
- \(18 \times (2x + 1)\) gives \(36x + 18\).
- \((3x + 5)(2x + 3)\) is expanded using a factorization box:
- Top row: \(2x, 3\)
- Left column: \(3x, 5\)
- Inside the box: \(6x^2, 10x, 9x, 15\)
Combining terms gives:
\[
6x^2 + 19x + 15
\]
5. **Setting the Equation**:
\[
36x + 18 = 6x^2 + 19x + 15
\]
6. **Rearranging the Equation**:
\[
0 = 6x^2 - 17x - 3
\]
7. **Factoring the Quadratic**:
\[
6x^2 - 17x - 3 = 0
\]
- Factor as \((x - 3)(6x + 1) = 0\)
8. **Finding Solutions**:
- Solving \((x - 3) = 0\) gives:
\[
x = 3
\]
- Solving \((6x + 1) = 0\) gives:
\[
x = -\frac{1}{6}
\]
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