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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![### Algebra and Geometry Problem Set
#### 1. Distance and Midpoint
Find (a) the distance \( d(P, Q) \) and (b) the coordinates of the midpoint \( M \) of line segment \( PQ \).
- Write the answer as a simplified radical.
- Points: \( P(-3, 4) \) \( Q(6, -2) \)
#### 2. Right Triangle Verification
Determine whether the three points are vertices of a right triangle.
- Points: \( P(-4, 3) \), \( Q(2, 5) \), \( R(1, -6) \)
#### 3. Graphing Linear Equations by Plotting Points
Graph the equation by plotting points. Use \( x = 0, 2, -2 \).
\[ y = \frac{1}{2} x + 3 \]
#### 4. Graphing Square Root Functions by Plotting Points
Graph the equation by plotting points. Use \( x = -2, -1, 2 \).
\[ y = \sqrt{x + 2} \]
#### 5. Function Evaluation
Let \( f(x) = -x^2 - 3x + 5 \). Find \( f(3) \).
#### 6. Another Function Evaluation
Let \( g(x) = -2x + 5 \). Find \( g(x + 3) \).
#### 7-11. Writing Equations of Lines
Write an equation of the line with the given conditions. You may write your answer in \( y = mx + b \) or \( Ax + By = C \) form, or, in \( x = a \) or \( y = b \) form, when applicable.
7. Through \((-3, 5)\); Slope = \(-2\).
8. Through \( (5, -2) \); Slope = 0.
9. Slope = \( \frac{2}{3} \); y-intercept \( (0, -4) \).
10. Undefined slope; Through \( (5, 2) \).
11. Parallel to \( 2x + 4y = 9 \); Through \( (6, 1) \).
#### 12. Finding Slope and Intercepts
Find the slope, \( m \), and y-intercept, \( b](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa8f54919-3719-4a11-8884-2432a8f20fd9%2F80d53629-fa85-4833-a260-a7a1fa24e95b%2Fswywxur.jpeg&w=3840&q=75)
Transcribed Image Text:### Algebra and Geometry Problem Set
#### 1. Distance and Midpoint
Find (a) the distance \( d(P, Q) \) and (b) the coordinates of the midpoint \( M \) of line segment \( PQ \).
- Write the answer as a simplified radical.
- Points: \( P(-3, 4) \) \( Q(6, -2) \)
#### 2. Right Triangle Verification
Determine whether the three points are vertices of a right triangle.
- Points: \( P(-4, 3) \), \( Q(2, 5) \), \( R(1, -6) \)
#### 3. Graphing Linear Equations by Plotting Points
Graph the equation by plotting points. Use \( x = 0, 2, -2 \).
\[ y = \frac{1}{2} x + 3 \]
#### 4. Graphing Square Root Functions by Plotting Points
Graph the equation by plotting points. Use \( x = -2, -1, 2 \).
\[ y = \sqrt{x + 2} \]
#### 5. Function Evaluation
Let \( f(x) = -x^2 - 3x + 5 \). Find \( f(3) \).
#### 6. Another Function Evaluation
Let \( g(x) = -2x + 5 \). Find \( g(x + 3) \).
#### 7-11. Writing Equations of Lines
Write an equation of the line with the given conditions. You may write your answer in \( y = mx + b \) or \( Ax + By = C \) form, or, in \( x = a \) or \( y = b \) form, when applicable.
7. Through \((-3, 5)\); Slope = \(-2\).
8. Through \( (5, -2) \); Slope = 0.
9. Slope = \( \frac{2}{3} \); y-intercept \( (0, -4) \).
10. Undefined slope; Through \( (5, 2) \).
11. Parallel to \( 2x + 4y = 9 \); Through \( (6, 1) \).
#### 12. Finding Slope and Intercepts
Find the slope, \( m \), and y-intercept, \( b
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