17. Solve the equation using the Quadratic Formula: x2 - 7x = 30 %3D 18. Solve the equation using Factoring AND then the Quadratic Formula: x3- 27 = 0 %3D 19. Write the center-radius form of the circle. Then graph the circle: Center (3, 1), Rad 20. Determine if the equation is a circle. If so, write it in center-radius form. If not, desc graph of the equation as either Non-Existent or a Point. x2 + 8x + y2 + 4y + 16 = 0

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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### Mathematics Problem Set

1. **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.**  
   \( P(-3, 4) \) \( Q(6, -2) \)

2. **Determine whether the three points are vertices of a right triangle.**  
   \( P(-4, 3) \), \( Q(2, 5) \), \( R(-1, -6) \)

3. **Graph by plotting points. Use \( x = 0, 2, -2 \).**  
   \( y = \frac{1}{2}x + 3 \)

4. **Graph by plotting points. Use \( x = -2, -1, 2 \).**  
   \( y = \sqrt{x + 2} \)

5. **Let \( f(x) = -x^2 - 3x + 5 \). Find \( f(3) \).**

6. **Let \( g(x) = -2x + 5 \). Find \( g(x + 3) \).**

### For questions #7-11, 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)**

### Solve the problems below using appropriate methods.

12. **Find the slope, \( m \), and y-intercept, \( b \), of the following equation:**  
    \( 2x + 3y = 9 \)

### For questions #13-18, you must solve each equation using the method stated in the problem. Show work to receive credit
Transcribed Image Text:### Mathematics Problem Set 1. **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.** \( P(-3, 4) \) \( Q(6, -2) \) 2. **Determine whether the three points are vertices of a right triangle.** \( P(-4, 3) \), \( Q(2, 5) \), \( R(-1, -6) \) 3. **Graph by plotting points. Use \( x = 0, 2, -2 \).** \( y = \frac{1}{2}x + 3 \) 4. **Graph by plotting points. Use \( x = -2, -1, 2 \).** \( y = \sqrt{x + 2} \) 5. **Let \( f(x) = -x^2 - 3x + 5 \). Find \( f(3) \).** 6. **Let \( g(x) = -2x + 5 \). Find \( g(x + 3) \).** ### For questions #7-11, 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)** ### Solve the problems below using appropriate methods. 12. **Find the slope, \( m \), and y-intercept, \( b \), of the following equation:** \( 2x + 3y = 9 \) ### For questions #13-18, you must solve each equation using the method stated in the problem. Show work to receive credit
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