lesson 2-1a
variables and expressions
evaluate each expression to find the missing values in the tables.
1.
| n | $n + 8^2$ |
| ---- | ---- |
| 7 | 71 |
| 9 | |
| 22 | |
| 35 | |
2.
| n | $25 - n$ |
| ---- | ---- |
| 20 | 5 |
| 5 | |
| 18 | |
| 9 | |
3.
| n | $n \bullet 7$ |
| ---- | ---- |
| 8 | 56 |
| 9 | |
| 11 | |
| 12 | |
4.
| n | $24 \div n$ |
| ---- | ---- |
| 2 | 12 |
| 6 | |
| 4 | |
| 8 | |
5.
| n | $n + 15$ |
| ---- | ---- |
| 35 | |
| 5 | |
| 20 | |
| 85 | |
6.
| n | $n \bullet 2^3$ |
| ---- | ---- |
| 7 | |
| 4 | |
| 10 | |
| 13 | |
7. a car is traveling at a speed of 55 miles per hour. you want to write an algebraic expression to show how far the car will travel in a certain number of hours. what will be your constant? your variable?
8. shawn evaluated the algebraic expression $x \div 4$ for $x = 12$ and gave an answer of 8. what was his error? what is the correct answer?

Question

lesson 2-1a
variables and expressions
evaluate each expression to find the missing values in the tables.
1.
| n | $n + 8^2$ |
| ---- | ---- |
| 7 | 71 |
| 9 |  |
| 22 |  |
| 35 |  |
2.
| n | $25 - n$ |
| ---- | ---- |
| 20 | 5 |
| 5 |  |
| 18 |  |
| 9 |  |
3.
| n | $n \bullet 7$ |
| ---- | ---- |
| 8 | 56 |
| 9 |  |
| 11 |  |
| 12 |  |
4.
| n | $24 \div n$ |
| ---- | ---- |
| 2 | 12 |
| 6 |  |
| 4 |  |
| 8 |  |
5.
| n | $n + 15$ |
| ---- | ---- |
| 35 |  |
| 5 |  |
| 20 |  |
| 85 |  |
6.
| n | $n \bullet 2^3$ |
| ---- | ---- |
| 7 |  |
| 4 |  |
| 10 |  |
| 13 |  |
7. a car is traveling at a speed of 55 miles per hour. you want to write an algebraic expression to show how far the car will travel in a certain number of hours. what will be your constant? your variable?
8. shawn evaluated the algebraic expression $x \div 4$ for $x = 12$ and gave an answer of 8. what was his error? what is the correct answer?

Accepted Answer

### Problem 1:
# Explanation:
## Step1: Calculate $8^2$
$8^2 = 64$
## Step2: For $n = 9$, evaluate $n + 8^2$
$9 + 64 = 73$
## Step3: For $n = 22$, evaluate $n + 8^2$
$22 + 64 = 86$
## Step4: For $n = 35$, evaluate $n + 8^2$
$35 + 64 = 99$
# Answer:
For $n = 9$: $73$; For $n = 22$: $86$; For $n = 35$: $99$

### Problem 2:
# Explanation:
## Step1: For $n = 5$, evaluate $25 - n$
$25 - 5 = 20$
## Step2: For $n = 18$, evaluate $25 - n$
$25 - 18 = 7$
## Step3: For $n = 9$, evaluate $25 - n$
$25 - 9 = 16$
# Answer:
For $n = 5$: $20$; For $n = 18$: $7$; For $n = 9$: $16$

### Problem 3:
# Explanation:
## Step1: For $n = 9$, evaluate $n \cdot 7$
$9 \times 7 = 63$
## Step2: For $n = 11$, evaluate $n \cdot 7$
$11 \times 7 = 77$
## Step3: For $n = 12$, evaluate $n \cdot 7$
$12 \times 7 = 84$
# Answer:
For $n = 9$: $63$; For $n = 11$: $77$; For $n = 12$: $84$

### Problem 4:
# Explanation:
## Step1: For $n = 6$, evaluate $24 \div n$
$24 \div 6 = 4$
## Step2: For $n = 4$, evaluate $24 \div n$
$24 \div 4 = 6$
## Step3: For $n = 8$, evaluate $24 \div n$
$24 \div 8 = 3$
# Answer:
For $n = 6$: $4$; For $n = 4$: $6$; For $n = 8$: $3$

### Problem 5:
# Explanation:
## Step1: For $n = 35$, evaluate $n + 15$
$35 + 15 = 50$
## Step2: For $n = 5$, evaluate $n + 15$
$5 + 15 = 20$
## Step3: For $n = 20$, evaluate $n + 15$
$20 + 15 = 35$
## Step4: For $n = 85$, evaluate $n + 15$
$85 + 15 = 100$
# Answer:
For $n = 35$: $50$; For $n = 5$: $20$; For $n = 20$: $35$; For $n = 85$: $100$

### Problem 6:
# Explanation:
## Step1: Calculate $2^3$
$2^3 = 8$
## Step2: For $n = 7$, evaluate $n \cdot 2^3$
$7 \times 8 = 56$
## Step3: For $n = 4$, evaluate $n \cdot 2^3$
$4 \times 8 = 32$
## Step4: For $n = 10$, evaluate $n \cdot 2^3$
$10 \times 8 = 80$
## Step5: For $n = 13$, evaluate $n \cdot 2^3$
$13 \times 8 = 104$
# Answer:
For $n = 7$: $56$; For $n = 4$: $32$; For $n = 10$: $80$; For $n = 13$: $104$

### Problem 7:
# Brief Explanations:
The formula for distance is $d = vt$, where $v$ is speed (constant), $t$ is time (variable). Here, speed $v = 55$ mph (constant), time (number of hours) is the variable (let's say $h$).
# Answer:
Constant: $55$ (speed in miles per hour); Variable: Number of hours (let's denote it as $h$)

### Problem 8:
# Brief Explanations:
To evaluate $x \div 4$ for $x = 12$, we do $12 \div 4 = 3$. Shawn's error was likely adding $4$ to $12$ (getting $16$? No, he got $8$, maybe he subtracted or miscalculated. Correctly, $12 \div 4 = 3$.
# Answer:
Error: Shawn miscalculated $12 \div 4$ (likely a wrong operation like $12 - 4 = 8$ or incorrect division). Correct answer: $3$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Problem 1:

Step1: Calculate \(8^2\)

Step2: For \(n = 9\), evaluate \(n + 8^2\)

Step3: For \(n = 22\), evaluate \(n + 8^2\)

Step4: For \(n = 35\), evaluate \(n + 8^2\)

Step1: For \(n = 5\), evaluate \(25 - n\)

Step2: For \(n = 18\), evaluate \(25 - n\)

Step3: For \(n = 9\), evaluate \(25 - n\)

Step1: For \(n = 9\), evaluate \(n \cdot 7\)

Step2: For \(n = 11\), evaluate \(n \cdot 7\)

Step3: For \(n = 12\), evaluate \(n \cdot 7\)

Answer:

Problem 2: