Question
Choose the inequality that matches this situation.
Sarah will spend at most $26 on candy. Each item costs $3, and she has a coupon for a $5 discount.
Sarah will spend at most $26 on candy. Each item costs $3, and she has a coupon for a $5 discount.
Answers
Answer
what is the sighn
Answer
choose the inequality that matches this situation.
Company A charges $312 to power-wash the siding of a house plus $12 for each window. Company B charges $36 per window, and the price includs the siding. How many windows must a house have to make the total cost from Company A be less expensive than Company B?
Company A charges $312 to power-wash the siding of a house plus $12 for each window. Company B charges $36 per window, and the price includs the siding. How many windows must a house have to make the total cost from Company A be less expensive than Company B?
Answer
Choose the inequality that matches this situation.
Company A charges a fee of $25 plus $0.20 per brouchure to print and deliver them. Company B charges $0.30 per brochure. How many would need to be ordered for Company A to cost more than Company B
Solve this equation for x:
5(2x + 3) = 7x - 3
Company A charges a fee of $25 plus $0.20 per brouchure to print and deliver them. Company B charges $0.30 per brochure. How many would need to be ordered for Company A to cost more than Company B
Solve this equation for x:
5(2x + 3) = 7x - 3
Answer
What is it called when heat and pressure change one type of rock into another?(1 point)
Responses
erosion
erosion
metamorphism
metamorphism
crystallization
crystallization
deposition
deposition
What is the theory that Earth’s surface is composed of several rock plates that fit together like the pieces of a puzzle?(1 point)
Responses
geological shift
geological shift
plate tectonics
plate tectonics
metamorphism
metamorphism
divergent plate boundary
Where are most deposits of natural resources found?(1 point)
Responses
at present and past plate boundaries
at present and past plate boundaries
in the earth's oceans
in the earth's oceans
in very tall mountain ranges
in very tall mountain ranges
near rivers and streams
near rivers and streams
Responses
erosion
erosion
metamorphism
metamorphism
crystallization
crystallization
deposition
deposition
What is the theory that Earth’s surface is composed of several rock plates that fit together like the pieces of a puzzle?(1 point)
Responses
geological shift
geological shift
plate tectonics
plate tectonics
metamorphism
metamorphism
divergent plate boundary
Where are most deposits of natural resources found?(1 point)
Responses
at present and past plate boundaries
at present and past plate boundaries
in the earth's oceans
in the earth's oceans
in very tall mountain ranges
in very tall mountain ranges
near rivers and streams
near rivers and streams
Answer
What does discovery of giant rabbit fossils on an island in the Mediterranean Sea tell scientists about the Earth’s changing landforms?(1 point)
Responses
The island had been underwater in the past.
The island had been underwater in the past.
The island had remained unchanged since its formation.
The island had remained unchanged since its formation.
The island was formed by a volcanic eruption in the past.
The island was formed by a volcanic eruption in the past.
The island had to be connected to the mainland in the past.
Responses
The island had been underwater in the past.
The island had been underwater in the past.
The island had remained unchanged since its formation.
The island had remained unchanged since its formation.
The island was formed by a volcanic eruption in the past.
The island was formed by a volcanic eruption in the past.
The island had to be connected to the mainland in the past.
Answered by
GPT-4o mini
To represent the situation with an inequality, let's define the variable:
- Let \( x \) be the number of candy items Sarah buys.
The cost of each candy item is $3, so the total cost for \( x \) items will be \( 3x \). Additionally, Sarah has a coupon for a $5 discount, which means her total cost after applying the discount will be \( 3x - 5 \).
Since Sarah will spend at most $26, we can set up the inequality as follows:
\[
3x - 5 \leq 26
\]
This inequality represents the situation where Sarah's total spending on candy, after applying the discount, does not exceed $26.
- Let \( x \) be the number of candy items Sarah buys.
The cost of each candy item is $3, so the total cost for \( x \) items will be \( 3x \). Additionally, Sarah has a coupon for a $5 discount, which means her total cost after applying the discount will be \( 3x - 5 \).
Since Sarah will spend at most $26, we can set up the inequality as follows:
\[
3x - 5 \leq 26
\]
This inequality represents the situation where Sarah's total spending on candy, after applying the discount, does not exceed $26.
Answered by
GPT-4o mini
In the inequality we set up, the sign used is "less than or equal to" (≤). This indicates that the amount Sarah spends after using her coupon can be equal to or less than $26.
The complete inequality is:
\[
3x - 5 \leq 26
\]
The complete inequality is:
\[
3x - 5 \leq 26
\]
Answered by
GPT-4o mini
Let's define the variable:
- Let \( x \) be the number of windows.
**Company A's cost:**
- Fixed cost for power-washing the siding: $312.
- Additional cost for \( x \) windows: $12 per window.
- Total cost for Company A:
\[
\text{Cost}_A = 312 + 12x
\]
**Company B's cost:**
- Cost for \( x \) windows at $36 each:
- Total cost for Company B:
\[
\text{Cost}_B = 36x
\]
We want to find out when Company A's cost is less than Company B's cost:
\[
312 + 12x < 36x
\]
To isolate \( x \), we can first subtract \( 12x \) from both sides:
\[
312 < 36x - 12x
\]
\[
312 < 24x
\]
Finally, we can divide both sides by 24:
\[
\frac{312}{24} < x
\]
\[
13 < x
\]
This means that \( x > 13 \).
So the inequality that matches the situation is:
\[
312 + 12x < 36x
\]
- Let \( x \) be the number of windows.
**Company A's cost:**
- Fixed cost for power-washing the siding: $312.
- Additional cost for \( x \) windows: $12 per window.
- Total cost for Company A:
\[
\text{Cost}_A = 312 + 12x
\]
**Company B's cost:**
- Cost for \( x \) windows at $36 each:
- Total cost for Company B:
\[
\text{Cost}_B = 36x
\]
We want to find out when Company A's cost is less than Company B's cost:
\[
312 + 12x < 36x
\]
To isolate \( x \), we can first subtract \( 12x \) from both sides:
\[
312 < 36x - 12x
\]
\[
312 < 24x
\]
Finally, we can divide both sides by 24:
\[
\frac{312}{24} < x
\]
\[
13 < x
\]
This means that \( x > 13 \).
So the inequality that matches the situation is:
\[
312 + 12x < 36x
\]
Answered by
GPT-4o mini
First, let's set up the inequality for the given situation with Company A and Company B.
### Company A's cost:
- Fixed fee: $25
- Cost per brochure: $0.20
- Total cost for \( x \) brochures:
\[
\text{Cost}_A = 25 + 0.20x
\]
### Company B's cost:
- Cost per brochure: $0.30
- Total cost for \( x \) brochures:
\[
\text{Cost}_B = 0.30x
\]
We want to find when Company A's cost is **more** than Company B's cost:
\[
25 + 0.20x > 0.30x
\]
### Now solve the inequality:
1. Subtract \( 0.20x \) from both sides:
\[
25 > 0.30x - 0.20x
\]
\[
25 > 0.10x
\]
2. Divide both sides by \( 0.10 \):
\[
\frac{25}{0.10} > x
\]
\[
250 > x
\]
or
\[
x < 250
\]
The inequality that matches the situation is:
\[
25 + 0.20x > 0.30x
\]
---
### Now, solving the equation:
**Equation:**
\[
5(2x + 3) = 7x - 3
\]
1. Distribute on the left side:
\[
10x + 15 = 7x - 3
\]
2. Subtract \( 7x \) from both sides:
\[
10x - 7x + 15 = -3
\]
\[
3x + 15 = -3
\]
3. Subtract 15 from both sides:
\[
3x = -3 - 15
\]
\[
3x = -18
\]
4. Divide both sides by 3:
\[
x = -6
\]
So, the solution to the equation \( 5(2x + 3) = 7x - 3 \) is:
\[
x = -6
\]
### Company A's cost:
- Fixed fee: $25
- Cost per brochure: $0.20
- Total cost for \( x \) brochures:
\[
\text{Cost}_A = 25 + 0.20x
\]
### Company B's cost:
- Cost per brochure: $0.30
- Total cost for \( x \) brochures:
\[
\text{Cost}_B = 0.30x
\]
We want to find when Company A's cost is **more** than Company B's cost:
\[
25 + 0.20x > 0.30x
\]
### Now solve the inequality:
1. Subtract \( 0.20x \) from both sides:
\[
25 > 0.30x - 0.20x
\]
\[
25 > 0.10x
\]
2. Divide both sides by \( 0.10 \):
\[
\frac{25}{0.10} > x
\]
\[
250 > x
\]
or
\[
x < 250
\]
The inequality that matches the situation is:
\[
25 + 0.20x > 0.30x
\]
---
### Now, solving the equation:
**Equation:**
\[
5(2x + 3) = 7x - 3
\]
1. Distribute on the left side:
\[
10x + 15 = 7x - 3
\]
2. Subtract \( 7x \) from both sides:
\[
10x - 7x + 15 = -3
\]
\[
3x + 15 = -3
\]
3. Subtract 15 from both sides:
\[
3x = -3 - 15
\]
\[
3x = -18
\]
4. Divide both sides by 3:
\[
x = -6
\]
So, the solution to the equation \( 5(2x + 3) = 7x - 3 \) is:
\[
x = -6
\]
Answered by
GPT-4o mini
Here are the correct responses to your questions:
1. **What is it called when heat and pressure change one type of rock into another?**
- **Response:** **metamorphism**
2. **What is the theory that Earth’s surface is composed of several rock plates that fit together like the pieces of a puzzle?**
- **Response:** **plate tectonics**
3. **Where are most deposits of natural resources found?**
- **Response:** **at present and past plate boundaries**
If you have any more questions or need further clarification, feel free to ask!
1. **What is it called when heat and pressure change one type of rock into another?**
- **Response:** **metamorphism**
2. **What is the theory that Earth’s surface is composed of several rock plates that fit together like the pieces of a puzzle?**
- **Response:** **plate tectonics**
3. **Where are most deposits of natural resources found?**
- **Response:** **at present and past plate boundaries**
If you have any more questions or need further clarification, feel free to ask!
Answered by
GPT-4o mini
The discovery of giant rabbit fossils on an island in the Mediterranean Sea suggests that:
- **Response:** **The island had to be connected to the mainland in the past.**
This is because the presence of land mammals, like rabbits, typically indicates that there was once a land connection between the island and a larger landmass, as these animals would have needed a pathway to migrate to the island. If you have any further questions or need clarification, feel free to ask!
- **Response:** **The island had to be connected to the mainland in the past.**
This is because the presence of land mammals, like rabbits, typically indicates that there was once a land connection between the island and a larger landmass, as these animals would have needed a pathway to migrate to the island. If you have any further questions or need clarification, feel free to ask!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.