Let's address each part of the question step-by-step.
### Plotting Points on a Number Line
We have four points to plot on a number line:
1. Point A: [tex]\( A = -1.5 \)[/tex]
- This point is at -1.5 on the number line.
2. Point B: [tex]\( B = \frac{3}{4} \)[/tex] which equals 0.75.
- This point is at 0.75 on the number line.
3. Point C: [tex]\( C = -3. \overline{3} \)[/tex]
- This point is approximately -3.3333 on the number line.
4. Point D: [tex]\( D = \sqrt{14} \)[/tex]
- The value of the square root of 14 is approximately 3.7416573867739413.
On the number line, the points can be plotted as follows:
```
-4 -3 -2 -1 0 1 2 3 4
|----|------|-------|-------|-------|-------|-------|-------|
C A B D
```
### Identifying Properties of Equations
15. Equation: [tex]\( 3 + 7 = 7 + 3 \)[/tex]
- This equation is an example of the Commutative Property of Addition. This property states that changing the order of the addends does not change the sum: [tex]\( a + b = b + a \)[/tex].
- Both sides of the equation simplify to 10, which confirms the property.
16. Equation: [tex]\( 5(2 \cdot 7) = (5 \cdot 2) \cdot 7 \)[/tex]
- This equation is an example of the Associative Property of Multiplication. This property states that the way in which factors are grouped in multiplication does not change the product: [tex]\( (a \cdot b) \cdot c = a \cdot (b \cdot c) \)[/tex].
- Simplifying both sides, [tex]\( 5 \cdot 14 \)[/tex] and [tex]\( 10 \cdot 7 \)[/tex], both give a result of 70, confirming the property.
### Summary of Results
- Points on the Number Line:
- [tex]\( A = -1.5 \)[/tex]
- [tex]\( B = 0.75 \)[/tex]
- [tex]\( C = -3.3333 \)[/tex]
- [tex]\( D = 3.7416573867739413 \)[/tex]
- Properties and Equations:
- The equation [tex]\( 3 + 7 = 7 + 3 \)[/tex] illustrates the Commutative Property of Addition.
- The equation [tex]\( 5(2 \cdot 7) = (5 \cdot 2) \cdot 7 \)[/tex] illustrates the Associative Property of Multiplication.
