Question
8.2.1. Spiral Review
It’s time for Spiral Review! This review will help you remember some of the things you have already learned. Take your time and try your best.
Select all of the following statements that are true.
The x-axis is a horizontal line.
The y-coordinate is the second number in an ordered pair.
To reach the point move a distance of 5 units up on the y-axis and then move a distance of 2 units to the right.
The origin is the only point that is on both the x-axis and the y-axis.
The ordered pairs and name the same point.
Answer:
Sung multiplied 892.65 by a power of ten and got the product 892,650. By what power of ten did Sung multiply 892.65?
Answer:
Jeff uses 116 rubber bands to make a rubber-band ball. He estimates that he has used 448 rubber bands to make 12 rubber-band balls of the same size. Use estimation to check and explain whether his answer is reasonable or not.
Answer:
Juan has put together 325 pieces of a puzzle that has 500 pieces. He can put together 25 pieces every hour. How long will it take him to finish the puzzle?
Answer:
Emma buys a book and gives the clerk $13.00. How much did the book cost if her change is $0.33?
Answer:
It’s time for Spiral Review! This review will help you remember some of the things you have already learned. Take your time and try your best.
Select all of the following statements that are true.
The x-axis is a horizontal line.
The y-coordinate is the second number in an ordered pair.
To reach the point move a distance of 5 units up on the y-axis and then move a distance of 2 units to the right.
The origin is the only point that is on both the x-axis and the y-axis.
The ordered pairs and name the same point.
Answer:
Sung multiplied 892.65 by a power of ten and got the product 892,650. By what power of ten did Sung multiply 892.65?
Answer:
Jeff uses 116 rubber bands to make a rubber-band ball. He estimates that he has used 448 rubber bands to make 12 rubber-band balls of the same size. Use estimation to check and explain whether his answer is reasonable or not.
Answer:
Juan has put together 325 pieces of a puzzle that has 500 pieces. He can put together 25 pieces every hour. How long will it take him to finish the puzzle?
Answer:
Emma buys a book and gives the clerk $13.00. How much did the book cost if her change is $0.33?
Answer:
Answers
GPT-4o mini
Let's go through each of the questions you provided step-by-step.
### True Statements:
1. **The x-axis is a horizontal line.**
**True**. The x-axis in a Cartesian coordinate system is indeed a horizontal line.
2. **The y-coordinate is the second number in an ordered pair.**
**True**. In an ordered pair \((x, y)\), the y-coordinate is the second number.
3. **To reach the point, move a distance of 5 units up on the y-axis and then move a distance of 2 units to the right.**
**False**. The instruction is imprecise and needs a specific point. Moving 5 units up and 2 to the right does not define a single point unless a starting point is specified.
4. **The origin is the only point that is on both the x-axis and the y-axis.**
**True**. The origin \((0, 0)\) is the point at which the x-axis and the y-axis intersect.
5. **The ordered pairs and name the same point.**
**False**. Without specific ordered pairs given, we can't assume they name the same point.
### Question 1 - Power of Ten:
Sung multiplied 892.65 by a power of ten and got the product 892,650.
To find the power of ten, we notice:
\[
892.65 \times 10^n = 892,650
\]
To find how many places the decimal moved, the decimal in 892.65 moved one place to the right to become 892650 (it dropped from being between 8 and 9 to being after 892). Therefore, the power of ten is \(10^1\).
**Answer: 1 (or \(10^1\))**
### Question 2 - Estimation of Rubber Bands:
Jeff uses 116 rubber bands to make 1 rubber-band ball. To find out how many he should use for 12 balls:
\[
116 \text{ rubber bands/ball} \times 12 \text{ balls} = 1392 \text{ rubber bands}.
\]
Given Jeff estimated 448 rubber bands, we can clearly see this is an underestimate since \(116 \times 12 = 1392\).
**Answer: Jeff's estimate of 448 rubber bands for 12 balls is not reasonable. The correct amount should be approximately 1392 rubber bands.**
### Question 3 - Time to Finish Puzzle:
Juan has completed 325 pieces and has a 500-piece puzzle, so he has:
\[
500 - 325 = 175 \text{ pieces left}.
\]
He can assemble 25 pieces per hour. To find how long it will take him to finish:
\[
\frac{175 \text{ pieces}}{25 \text{ pieces/hour}} = 7 \text{ hours}.
\]
**Answer: It will take Juan 7 hours to finish the puzzle.**
### Question 4 - Cost of the Book:
Emma gave the clerk $13.00 and received $0.33 as change. To find the cost of the book:
\[
\text{Cost of the book} = 13.00 - 0.33 = 12.67.
\]
**Answer: The book cost $12.67.**
Feel free to ask if you need further clarifications or additional questions!
### True Statements:
1. **The x-axis is a horizontal line.**
**True**. The x-axis in a Cartesian coordinate system is indeed a horizontal line.
2. **The y-coordinate is the second number in an ordered pair.**
**True**. In an ordered pair \((x, y)\), the y-coordinate is the second number.
3. **To reach the point, move a distance of 5 units up on the y-axis and then move a distance of 2 units to the right.**
**False**. The instruction is imprecise and needs a specific point. Moving 5 units up and 2 to the right does not define a single point unless a starting point is specified.
4. **The origin is the only point that is on both the x-axis and the y-axis.**
**True**. The origin \((0, 0)\) is the point at which the x-axis and the y-axis intersect.
5. **The ordered pairs and name the same point.**
**False**. Without specific ordered pairs given, we can't assume they name the same point.
### Question 1 - Power of Ten:
Sung multiplied 892.65 by a power of ten and got the product 892,650.
To find the power of ten, we notice:
\[
892.65 \times 10^n = 892,650
\]
To find how many places the decimal moved, the decimal in 892.65 moved one place to the right to become 892650 (it dropped from being between 8 and 9 to being after 892). Therefore, the power of ten is \(10^1\).
**Answer: 1 (or \(10^1\))**
### Question 2 - Estimation of Rubber Bands:
Jeff uses 116 rubber bands to make 1 rubber-band ball. To find out how many he should use for 12 balls:
\[
116 \text{ rubber bands/ball} \times 12 \text{ balls} = 1392 \text{ rubber bands}.
\]
Given Jeff estimated 448 rubber bands, we can clearly see this is an underestimate since \(116 \times 12 = 1392\).
**Answer: Jeff's estimate of 448 rubber bands for 12 balls is not reasonable. The correct amount should be approximately 1392 rubber bands.**
### Question 3 - Time to Finish Puzzle:
Juan has completed 325 pieces and has a 500-piece puzzle, so he has:
\[
500 - 325 = 175 \text{ pieces left}.
\]
He can assemble 25 pieces per hour. To find how long it will take him to finish:
\[
\frac{175 \text{ pieces}}{25 \text{ pieces/hour}} = 7 \text{ hours}.
\]
**Answer: It will take Juan 7 hours to finish the puzzle.**
### Question 4 - Cost of the Book:
Emma gave the clerk $13.00 and received $0.33 as change. To find the cost of the book:
\[
\text{Cost of the book} = 13.00 - 0.33 = 12.67.
\]
**Answer: The book cost $12.67.**
Feel free to ask if you need further clarifications or additional questions!