0. If a = 3, then 5o = 15. If 2 = 1, then a = 3. So

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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**In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures.**

1.  
   \(1, -2, 3, -4, \ldots\)

2.  
   \(0, 2, 6, 12, 20, \ldots\)

3.  
   \(Z, Y, X, W, V, \ldots\)

4.  
   \(A, D, G, J, M, \ldots\)

5.  
   **A sequence of geometric shapes:**
   - Sequence contains an equilateral triangle, square, and pentagon.
   - Next likely two shapes could be hexagon, heptagon (progressive increase in number of sides).

6.  
   **A series of stacked cubes forming steps:**
   - The sequence appears to show increasing complexity or number of cubes in each step.

**In Exercises 7–10, make and test a conjecture about the given quantity.**

7.  
   The sum of an even integer and an odd integer.

8.  
   The product of any two even integers.

9.  
   The quotient of a number and its reciprocal.

10.  
   The quotient of two negative integers.

**In Exercises 11–14, find a counterexample to show that the conjecture is false.**

11.  
    The product of two positive numbers is always greater than either number.

12.  
    If \( n \) is a nonzero integer, then \( n + \frac{1}{n} \) is always greater than 1.

13.  
    If two angles are supplements of each other, then one of the angles must be acute.

14.  
    A line divides \(\overline{MN}\) into two line segments. So, the line is a segment bisector of \(\overline{MN}\).

**In Exercises 15–18, use the Law of Detachment to determine what you can conclude from the given information, if possible.**

15.  
    If you download a GIF, then your device crashes.  
    You downloaded a GIF.

16.  
    If a quadrilateral is a square, then it has four right angles.  
    Quadrilateral \(QRST\) has four right angles.

17.  
    If a point divides a line segment into two congruent line segments, then
Transcribed Image Text:**In Exercises 1–6, describe the pattern. Then write or draw the next two numbers, letters, or figures.** 1. \(1, -2, 3, -4, \ldots\) 2. \(0, 2, 6, 12, 20, \ldots\) 3. \(Z, Y, X, W, V, \ldots\) 4. \(A, D, G, J, M, \ldots\) 5. **A sequence of geometric shapes:** - Sequence contains an equilateral triangle, square, and pentagon. - Next likely two shapes could be hexagon, heptagon (progressive increase in number of sides). 6. **A series of stacked cubes forming steps:** - The sequence appears to show increasing complexity or number of cubes in each step. **In Exercises 7–10, make and test a conjecture about the given quantity.** 7. The sum of an even integer and an odd integer. 8. The product of any two even integers. 9. The quotient of a number and its reciprocal. 10. The quotient of two negative integers. **In Exercises 11–14, find a counterexample to show that the conjecture is false.** 11. The product of two positive numbers is always greater than either number. 12. If \( n \) is a nonzero integer, then \( n + \frac{1}{n} \) is always greater than 1. 13. If two angles are supplements of each other, then one of the angles must be acute. 14. A line divides \(\overline{MN}\) into two line segments. So, the line is a segment bisector of \(\overline{MN}\). **In Exercises 15–18, use the Law of Detachment to determine what you can conclude from the given information, if possible.** 15. If you download a GIF, then your device crashes. You downloaded a GIF. 16. If a quadrilateral is a square, then it has four right angles. Quadrilateral \(QRST\) has four right angles. 17. If a point divides a line segment into two congruent line segments, then
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given 

if a=3 , then 5a=15

if 12a=121 ,then a=3

 

 

 

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