spiral review week 12
this worksheet will be collected on friday.
monday (unit 5 – lesson 2)
solve using order of operations.
1) 5(6 + 2²) − 16 ÷2 2) 40 ÷ 2² + 3 + (3×7) + 7 − 5

tuesday (unit 5 – lesson 7)
combine like terms.
5a² + 8a + 7a² + 3a + 7 − 6a - 2 7b + 6b² + 4² − 5b − 9

Question

spiral review week 12
this worksheet will be collected on friday.
monday (unit 5 – lesson 2)
solve using order of operations.
1)  5(6 + 2²) − 16 ÷2        2)  40 ÷ 2² + 3 + (3×7) + 7 − 5

tuesday (unit 5 – lesson 7)
combine like terms.
5a² + 8a + 7a² + 3a + 7 − 6a - 2        7b + 6b² + 4² − 5b − 9

Accepted Answer

### Problem 1: $ 5(6 + 2^2) - 16 \div 2 $
# Explanation:
## Step 1: Simplify the exponent
First, we simplify the exponent $ 2^2 $.
$ 2^2 = 4 $
So the expression becomes $ 5(6 + 4) - 16 \div 2 $

## Step 2: Simplify the parentheses
Next, we simplify the expression inside the parentheses $ 6 + 4 $.
$ 6 + 4 = 10 $
Now the expression is $ 5(10) - 16 \div 2 $

## Step 3: Perform multiplication and division
Now we perform the multiplication $ 5(10) $ and the division $ 16 \div 2 $.
$ 5(10) = 50 $
$ 16 \div 2 = 8 $
The expression now is $ 50 - 8 $

## Step 4: Perform subtraction
Finally, we subtract $ 8 $ from $ 50 $.
$ 50 - 8 = 42 $

# Answer:
$ 42 $

### Problem 2: $ 40 \div 2^2 + 3 + (3 \times 7) + 7 - 5 $
# Explanation:
## Step 1: Simplify the exponent and parentheses
First, simplify the exponent $ 2^2 $ and the expression inside the parentheses $ 3 \times 7 $.
$ 2^2 = 4 $
$ 3 \times 7 = 21 $
The expression becomes $ 40 \div 4 + 3 + 21 + 7 - 5 $

## Step 2: Perform division
Next, perform the division $ 40 \div 4 $.
$ 40 \div 4 = 10 $
Now the expression is $ 10 + 3 + 21 + 7 - 5 $

## Step 3: Perform addition and subtraction from left to right
First, add $ 10 + 3 $:
$ 10 + 3 = 13 $
Then add $ 13 + 21 $:
$ 13 + 21 = 34 $
Next, add $ 34 + 7 $:
$ 34 + 7 = 41 $
Finally, subtract $ 5 $ from $ 41 $:
$ 41 - 5 = 36 $

# Answer:
$ 36 $

### Problem 3: $ 5a^2 + 8a + 7a^2 + 3a + 7 - 6a - 2 $
# Explanation:
## Step 1: Identify like terms
The like terms are:
- $ 5a^2 $ and $ 7a^2 $ (both have $ a^2 $)
- $ 8a $, $ 3a $, and $ -6a $ (both have $ a $)
- $ 7 $ and $ -2 $ (constants)

## Step 2: Combine the $ a^2 $ terms
$ 5a^2 + 7a^2 = 12a^2 $

## Step 3: Combine the $ a $ terms
$ 8a + 3a - 6a = (8 + 3 - 6)a = 5a $

## Step 4: Combine the constant terms
$ 7 - 2 = 5 $

## Step 5: Combine all the simplified terms
Putting it all together, we get $ 12a^2 + 5a + 5 $

# Answer:
$ 12a^2 + 5a + 5 $

### Problem 4: $ 7b + 6b^2 + 4^2 - 5b - 9 $
# Explanation:
## Step 1: Simplify the exponent
First, simplify the exponent $ 4^2 $.
$ 4^2 = 16 $
The expression becomes $ 7b + 6b^2 + 16 - 5b - 9 $

## Step 2: Identify like terms
The like terms are:
- $ 7b $ and $ -5b $ (both have $ b $)
- $ 16 $ and $ -9 $ (constants)
- $ 6b^2 $ (only term with $ b^2 $)

## Step 3: Combine the $ b $ terms
$ 7b - 5b = 2b $

## Step 4: Combine the constant terms
$ 16 - 9 = 7 $

## Step 5: Combine all the simplified terms
Putting it all together, we get $ 6b^2 + 2b + 7 $

# Answer:
$ 6b^2 + 2b + 7 $

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1: \( 5(6 + 2^2) - 16 \div 2 \)

Step 1: Simplify the exponent

Step 2: Simplify the parentheses

Step 3: Perform multiplication and division

Step 4: Perform subtraction

Step 1: Simplify the exponent and parentheses

Step 2: Perform division

Step 3: Perform addition and subtraction from left to right

Step 1: Identify like terms

Step 2: Combine the \( a^2 \) terms

Step 3: Combine the \( a \) terms

Step 4: Combine the constant terms

Step 5: Combine all the simplified terms

Answer:

Problem 2: \( 40 \div 2^2 + 3 + (3 \times 7) + 7 - 5 \)