Numbers and Their Application to Math and Science

Odd Solutions for HW Numbers Lesson 12

1. Aunt Ethel hands you $15 in quarters (q) and dimes (d). Name five ordered pairs (q,d) representing the change she might have given you. Graph the points. What relation do you observe?
   A. (60,0), (0,150), (20,100), (40,50), (50,25).
   The line 5q + 2d = 300 (25x + 10y = 1500).

2. 
   
3. Prove that "If two lines are parallel to the same line, then they are parallel to each other."
   A. Given line a is parallel to line b and b is parallel to line c. Since parallel lines have the same slopes then m_a = m_b and m_b = m_c. By the Law of Transitivity, m_a = m_c. Equal sloped lines are parallel, thus line a and line c are parallel.

4. 
   Classify the line of the following as vertical, horizontal, or oblique (neither):

5. x + y = 2
   A. oblique
   
6. 
   
7. 3x - 2y = 1
   A. oblique
   
8. 
   
9. Graph y = 3x + 2.
   A. The line crosses the y-axis at (0,2) and the x-axis at (-2/3,0).

11. Determine if the following system of equations is inconsistent, independent, or dependent:
    2x - 3y = 5
    10x - 15y = 25 A. dependent
    
12. 
    
13. Find a perpendicular line to the given line: 4x - y = 3.
    Answers vary: x + 4y = 3; 2x + 8y = 4; 3x + 12y = 3.
    
14. 
    
15. Graph the equation x² + y² = 4. Is it a relation or function?
    A. relation (circle, radius=2, centered at (0,0).

17. Graph the function y = x² - 4x + 4. Find the domain and range.
    A. Domain is all reals. The range: y 0.

19. Determine if the equation has real solutions. 4x² - 13x + 11 = 0.
    A. NO. D=13² - 4(4)(11) = 169 - 176 = -7

21. Read sections 3.6 and 3.7 in your geometry textbook and do question 9 in both.
    • (3.6) 9: (2-4)/(6-1)=-2/5.
    • (3.7) 9: If two nonvertical lines are perpendicular, then the product of their slopes is -1.
      If the product of the slopes of two nonvertical lines is -1, then the lines are perpendicular.

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