Question

Select the symbol that makes each of these statements true:(3 points)
165+1_π

−5⋅2+8_0


(12⋅5)+ 3_12 ⋅(5+3)
fill in the blanks with either >, <, or =

Answer 1

Let's evaluate each of the mathematical expressions step by step:

1. **Statement:** \( 165 + 1 \_ \pi \)
- Since \( \pi \) is approximately 3.14, \( 165 + 1 \pi \) calculates to about \( 165 + 3.14 \approx 168.14 \).
- So, we need to compare \( 165 \) and \( 168.14 \): \( 165 < 168.14 \).

**Conclusion:** \( 165 + 1 > \pi \)

2. **Statement:** \( -5 \cdot 2 + 8 \_ 0 \)
- The left side calculates to \( -10 + 8 = -2 \).
- We need to compare \( -2 \) and \( 0 \): \( -2 < 0 \).

**Conclusion:** \( -5 \cdot 2 + 8 < 0 \)

3. **Statement:** \( (12 \cdot 5) + 3 \_ 12 \cdot (5 + 3) \)
- Evaluating the left side: \( 12 \cdot 5 = 60 \).
- Evaluating the right side: \( 5 + 3 = 8 \) and \( 12 \cdot 8 = 96 \).
- Now we need to compare \( 60 + 3 \) to \( 96 \).

**Conclusion:** If \( 3 \) is added to \( 60 \), \( 63 < 96 \).

Combining the conclusions for each expression, we get:
1. \( 165 + 1 > \pi \)
2. \( -5 \cdot 2 + 8 < 0 \)
3. \( 60 + 3 < 96 \)

So, in summary, the correct symbols placed in the blanks are:
1. \( > \)
2. \( < \)
3. \( < \)

Therefore, the filled statements would look like:
- \( 165 + 1 > \pi \)
- \( -5 \cdot 2 + 8 < 0 \)
- \( (12 \cdot 5) + 3 < 12 \cdot (5 + 3) \)