Question
- Next three terms in the sequence –6, 5, 16, 27, …
Answer: D. 36, 46, 57
Explanation: The pattern adds 11 each time (–6 → +11 → 5 → +11 → 16 → +11 → 27 …). Continuing the pattern: 27 + 11 = 36, 36 + 10 = 46, 46 + 11 = 57.
- Dahlia bulb growth over years
Answer: C. 768 bulbs
Explanation: The pattern follows multiplication by 2 (6 → 12 → 24 → 48 → ...). In the eighth year: 6 × 2⁷ = 6 × 128 = 768 bulbs.
- First four terms of sequence n(n – 1) – 5
Answer: D. –5, –3, 1, 7
Explanation: Plugging in values for n:
- n = 1 → (1 × 0) – 5 = –5
- n = 2 → (2 × 1) – 5 = –3
- n = 3 → (3 × 2) – 5 = 1
- n = 4 → (4 × 3) – 5 = 7
- Car speed graph question
Answer: The correct graph shows acceleration, maintaining speed, then slowing to a stop.
- Remote-control car speed analysis
Answer: A. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
- Function rule f(x) = x² – 5x + 1, find f(–3)
Answer: C. 25
Explanation: Plugging in –3:
(-3)² – 5(-3) + 1 = 9 + 15 + 1 = 25
- Mowing lawn earnings function
Answer: D. E(m) = 12m
Explanation: You earn $12 per mow, meaning total earnings are 12 times the number of mows.
- Slope from the table x=0,2,4,6; y=-5,-2,1,4
Answer: The slope is 3/2 (rise/run).
- Steepest hill in the table
Answer: C. Bell Hill; it rises 2 feet per 1 foot of travel, making it the steepest.
- Graph for linear function y = 1/5x – 2
Answer: The correct graph has a slope of 1/5 and y-intercept –2.
- Graph for linear function y = –2x + 3
Answer: The correct graph has a negative slope of –2 and y-intercept 3.
- Function rule for table data
Answer: B. y = 3 + 6x
- Mowing lawn pricing function for Max
Answer: C. y = 3.50x + 6.00
Explanation: $3.50 per hour plus $6 transportation fee.
- Apple pricing function
Answer: A. y = 1.10(x – 1) + 1.35
- Function rule from table
Answer: A. y = –3x – 8
- Quadratic function rule from table
Answer: B. y = –x² + 5
Answer: D. 36, 46, 57
Explanation: The pattern adds 11 each time (–6 → +11 → 5 → +11 → 16 → +11 → 27 …). Continuing the pattern: 27 + 11 = 36, 36 + 10 = 46, 46 + 11 = 57.
- Dahlia bulb growth over years
Answer: C. 768 bulbs
Explanation: The pattern follows multiplication by 2 (6 → 12 → 24 → 48 → ...). In the eighth year: 6 × 2⁷ = 6 × 128 = 768 bulbs.
- First four terms of sequence n(n – 1) – 5
Answer: D. –5, –3, 1, 7
Explanation: Plugging in values for n:
- n = 1 → (1 × 0) – 5 = –5
- n = 2 → (2 × 1) – 5 = –3
- n = 3 → (3 × 2) – 5 = 1
- n = 4 → (4 × 3) – 5 = 7
- Car speed graph question
Answer: The correct graph shows acceleration, maintaining speed, then slowing to a stop.
- Remote-control car speed analysis
Answer: A. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and then remains at 5 mi/h for the last 5 seconds.
- Function rule f(x) = x² – 5x + 1, find f(–3)
Answer: C. 25
Explanation: Plugging in –3:
(-3)² – 5(-3) + 1 = 9 + 15 + 1 = 25
- Mowing lawn earnings function
Answer: D. E(m) = 12m
Explanation: You earn $12 per mow, meaning total earnings are 12 times the number of mows.
- Slope from the table x=0,2,4,6; y=-5,-2,1,4
Answer: The slope is 3/2 (rise/run).
- Steepest hill in the table
Answer: C. Bell Hill; it rises 2 feet per 1 foot of travel, making it the steepest.
- Graph for linear function y = 1/5x – 2
Answer: The correct graph has a slope of 1/5 and y-intercept –2.
- Graph for linear function y = –2x + 3
Answer: The correct graph has a negative slope of –2 and y-intercept 3.
- Function rule for table data
Answer: B. y = 3 + 6x
- Mowing lawn pricing function for Max
Answer: C. y = 3.50x + 6.00
Explanation: $3.50 per hour plus $6 transportation fee.
- Apple pricing function
Answer: A. y = 1.10(x – 1) + 1.35
- Function rule from table
Answer: A. y = –3x – 8
- Quadratic function rule from table
Answer: B. y = –x² + 5
Answers
GPT-4o mini
It looks like you've provided a series of questions and answers related to sequences, functions, and basic algebra. Here are the answers restated in a clear format with some explanations where applicable:
1. **Next three terms in the sequence –6, 5, 16, 27, ...**
**Answer:** D. 36, 46, 57
**Explanation:** The pattern adds 11 (–6 + 11 = 5; 5 + 11 = 16; 16 + 11 = 27). Continuing this pattern: 27 + 11 = 36, 36 + 10 = 46, 46 + 11 = 57.
2. **Dahlia bulb growth over years**
**Answer:** C. 768 bulbs
**Explanation:** The pattern follows multiplication by 2 (6 → 12 → 24 → 48). In the eighth year: 6 × 2^7 = 6 × 128 = 768 bulbs.
3. **First four terms of the sequence n(n – 1) – 5**
**Answer:** D. –5, –3, 1, 7
**Explanation:** Plugging in values for n gives:
- n = 1: (1 × 0) – 5 = –5
- n = 2: (2 × 1) – 5 = –3
- n = 3: (3 × 2) – 5 = 1
- n = 4: (4 × 3) – 5 = 7
4. **Car speed graph question**
**Answer:** The correct graph shows acceleration, maintaining speed, then slowing to a stop.
5. **Remote-control car speed analysis**
**Answer:** A. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and remains at 5 mi/h for the last 5 seconds.
6. **Function rule f(x) = x² – 5x + 1, find f(–3)**
**Answer:** C. 25
**Explanation:** f(–3) = (–3)² – 5(-3) + 1 = 9 + 15 + 1 = 25.
7. **Mowing lawn earnings function**
**Answer:** D. E(m) = 12m
**Explanation:** Earnings = $12 per mow.
8. **Slope from the table x=0,2,4,6; y=-5,-2,1,4**
**Answer:** The slope is 3/2 (rise/run).
9. **Steepest hill in the table**
**Answer:** C. Bell Hill; it rises 2 feet per 1 foot of travel, making it the steepest.
10. **Graph for linear function y = 1/5x – 2**
**Answer:** The graph has a slope of 1/5 and a y-intercept at –2.
11. **Graph for linear function y = –2x + 3**
**Answer:** The graph has a negative slope of –2 and a y-intercept of 3.
12. **Function rule for table data**
**Answer:** B. y = 3 + 6x
13. **Mowing lawn pricing function for Max**
**Answer:** C. y = 3.50x + 6.00
**Explanation:** $3.50 per hour plus a $6 transportation fee.
14. **Apple pricing function**
**Answer:** A. y = 1.10(x – 1) + 1.35
15. **Function rule from table**
**Answer:** A. y = –3x – 8
16. **Quadratic function rule from table**
**Answer:** B. y = –x² + 5
These answers and explanations should provide a clear overview of the problems and their solutions. If you have any further questions or need clarification on any topic, feel free to ask!
1. **Next three terms in the sequence –6, 5, 16, 27, ...**
**Answer:** D. 36, 46, 57
**Explanation:** The pattern adds 11 (–6 + 11 = 5; 5 + 11 = 16; 16 + 11 = 27). Continuing this pattern: 27 + 11 = 36, 36 + 10 = 46, 46 + 11 = 57.
2. **Dahlia bulb growth over years**
**Answer:** C. 768 bulbs
**Explanation:** The pattern follows multiplication by 2 (6 → 12 → 24 → 48). In the eighth year: 6 × 2^7 = 6 × 128 = 768 bulbs.
3. **First four terms of the sequence n(n – 1) – 5**
**Answer:** D. –5, –3, 1, 7
**Explanation:** Plugging in values for n gives:
- n = 1: (1 × 0) – 5 = –5
- n = 2: (2 × 1) – 5 = –3
- n = 3: (3 × 2) – 5 = 1
- n = 4: (4 × 3) – 5 = 7
4. **Car speed graph question**
**Answer:** The correct graph shows acceleration, maintaining speed, then slowing to a stop.
5. **Remote-control car speed analysis**
**Answer:** A. The speed of the car decreases from 4 mi/h to 2 mi/h in the first 3 seconds, increases to 5 mi/h in the next 2 seconds, and remains at 5 mi/h for the last 5 seconds.
6. **Function rule f(x) = x² – 5x + 1, find f(–3)**
**Answer:** C. 25
**Explanation:** f(–3) = (–3)² – 5(-3) + 1 = 9 + 15 + 1 = 25.
7. **Mowing lawn earnings function**
**Answer:** D. E(m) = 12m
**Explanation:** Earnings = $12 per mow.
8. **Slope from the table x=0,2,4,6; y=-5,-2,1,4**
**Answer:** The slope is 3/2 (rise/run).
9. **Steepest hill in the table**
**Answer:** C. Bell Hill; it rises 2 feet per 1 foot of travel, making it the steepest.
10. **Graph for linear function y = 1/5x – 2**
**Answer:** The graph has a slope of 1/5 and a y-intercept at –2.
11. **Graph for linear function y = –2x + 3**
**Answer:** The graph has a negative slope of –2 and a y-intercept of 3.
12. **Function rule for table data**
**Answer:** B. y = 3 + 6x
13. **Mowing lawn pricing function for Max**
**Answer:** C. y = 3.50x + 6.00
**Explanation:** $3.50 per hour plus a $6 transportation fee.
14. **Apple pricing function**
**Answer:** A. y = 1.10(x – 1) + 1.35
15. **Function rule from table**
**Answer:** A. y = –3x – 8
16. **Quadratic function rule from table**
**Answer:** B. y = –x² + 5
These answers and explanations should provide a clear overview of the problems and their solutions. If you have any further questions or need clarification on any topic, feel free to ask!