Sure, let's break down each expression step-by-step to match it with the correct value.
### 1. Expression: [tex]\(4 + 8 \left(\frac{1}{4} + 2\right)\)[/tex]
Step-by-Step Solution:
1. Inside parentheses first: [tex]\(\frac{1}{4} + 2 = \frac{1}{4} + \frac{8}{4} = \frac{9}{4} = 2.25\)[/tex]
2. Multiplication: [tex]\(8 \times 2.25 = 18\)[/tex]
3. Addition: [tex]\(4 + 18 = 22\)[/tex]
So, the value for [tex]\(4 + 8 \left(\frac{1}{4} + 2\right)\)[/tex] is 22.
### 2. Expression: [tex]\(0.25 \cdot 4^3 - 1\)[/tex]
Step-by-Step Solution:
1. Exponentiation first: [tex]\(4^3 = 64\)[/tex]
2. Multiplication: [tex]\(0.25 \times 64 = 16\)[/tex]
3. Subtraction: [tex]\(16 - 1 = 15\)[/tex]
So, the value for [tex]\(0.25 \cdot 4^3 - 1\)[/tex] is 15.
### 3. Expression: [tex]\(1 + 5 \cdot 2 + (1 + 3)^2\)[/tex]
Step-by-Step Solution:
1. Inside parentheses first: [tex]\((1 + 3) = 4\)[/tex]
2. Exponentiation: [tex]\(4^2 = 16\)[/tex]
3. Multiplication: [tex]\(5 \times 2 = 10\)[/tex]
4. Addition: [tex]\(1 + 10 + 16 = 27\)[/tex]
So, the value for [tex]\(1 + 5 \cdot 2 + (1 + 3)^2\)[/tex] is 27.
### Matching Values to Expressions
- [tex]\(4 + 8 \left(\frac{1}{4} + 2\right)\)[/tex] matches with 22
- [tex]\(0.25 \cdot 4^3 - 1\)[/tex] matches with 15
- [tex]\(1 + 5 \cdot 2 + (1 + 3)^2\)[/tex] matches with 27
Let's pair them:
[tex]\(4 + 8 \left(\frac{1}{4} + 2\right)\)[/tex] ⟹ 22
[tex]\(0.25 \cdot 4^3 - 1\)[/tex] ⟹ 15
[tex]\(1 + 5 \cdot 2 + (1 + 3)^2\)[/tex] ⟹ 27
