Question
Kylie is writing a persuasive essay for English class. The essay has to present her opinion and evidence for constructing that opinion. The essay has to have a minimum word count of 150 words and a maximum word count of 500 words.
Which compound inequality represents the length, w, of the essay?
500 ≤ w ≤ 150
150 ≥ w
500 ≤ w
150 ≤ w ≤ 500
Which compound inequality represents the length, w, of the essay?
500 ≤ w ≤ 150
150 ≥ w
500 ≤ w
150 ≤ w ≤ 500
Answers
Answer
graph this compound inequality: 2.5 < x < 4.5 the symbol < has a line under it open or closed circle? left or right?
Answer
The image shows a number line ranging from -5 to 5 with increments of 1. Above the number line, there’s a compound inequality: 2.5 ≤ x ≤ 4.5. The number line has two orange points at 2.5 and 4.5, both with closed circles, indicating that these values are included in the solution set. Arrows extend between these points, showing that all numbers between 2.5 and 4.5 are part of the solution.
Answer
where do i put it close or open and left or right?? WHAT LINE AND WHERE DO I PUT IT
Answer
THANK YOU guys close circle to the right on 2.5 and close circle to the left on 4.5
Which scenario fits the compound inequality?
Jill’s best friend lives less than 2.5 miles from her house, but more than 4.5 miles from their school.
It is good to choose a hotel with ratings with more than 2.5 stars.
In terms of percent, the salinity of most sea water is between 2.5 and 4.5.
The grade point average of Mrs. Green’s class is less than 4.5.
Which scenario fits the compound inequality?
Jill’s best friend lives less than 2.5 miles from her house, but more than 4.5 miles from their school.
It is good to choose a hotel with ratings with more than 2.5 stars.
In terms of percent, the salinity of most sea water is between 2.5 and 4.5.
The grade point average of Mrs. Green’s class is less than 4.5.
Answer
The image shows four number lines, each representing different inequalities. The question asks which graph represents the compound inequality ( x \leq \frac{5}{4} ) or ( x \geq \frac{5}{2} ).
The first number line shows values greater than -0.5.
The second number line shows values less than or equal to 1.25.
The third number line shows values less than or equal to 1.25 and greater than or equal to 2.5.
The fourth number line shows values greater than -0.5 and less than or equal to 2.5.
The first number line shows values greater than -0.5.
The second number line shows values less than or equal to 1.25.
The third number line shows values less than or equal to 1.25 and greater than or equal to 2.5.
The fourth number line shows values greater than -0.5 and less than or equal to 2.5.
Answered by
GPT-4o mini
The correct compound inequality that represents the length, \( w \), of Kylie’s essay is:
**150 ≤ w ≤ 500**
This inequality states that the length of the essay must be at least 150 words and no more than 500 words, which aligns with the requirements given.
**150 ≤ w ≤ 500**
This inequality states that the length of the essay must be at least 150 words and no more than 500 words, which aligns with the requirements given.
Answered by
GPT-4o mini
To graph the compound inequality \( 2.5 < x < 4.5 \):
1. **Identify the type of circles to use:**
- Since the inequality uses strict inequalities (no "or equal to" symbols), you will use **open circles** for both 2.5 and 4.5.
2. **Position the open circles:**
- Place an open circle at **2.5** and another open circle at **4.5**.
- This indicates that 2.5 and 4.5 are NOT included in the solution set.
3. **Shade the region:**
- Shade the area between the two open circles to represent all the values of \( x \) that are greater than 2.5 and less than 4.5.
### On a number line, it looks like this:
```
2.5 3 4 4.5
o----|----|----o
↑
shading
```
- The open circles at 2.5 and 4.5 indicate that these endpoints are not included, and the shaded line between them represents all values of \( x \) that satisfy the inequality \( 2.5 < x < 4.5 \).
1. **Identify the type of circles to use:**
- Since the inequality uses strict inequalities (no "or equal to" symbols), you will use **open circles** for both 2.5 and 4.5.
2. **Position the open circles:**
- Place an open circle at **2.5** and another open circle at **4.5**.
- This indicates that 2.5 and 4.5 are NOT included in the solution set.
3. **Shade the region:**
- Shade the area between the two open circles to represent all the values of \( x \) that are greater than 2.5 and less than 4.5.
### On a number line, it looks like this:
```
2.5 3 4 4.5
o----|----|----o
↑
shading
```
- The open circles at 2.5 and 4.5 indicate that these endpoints are not included, and the shaded line between them represents all values of \( x \) that satisfy the inequality \( 2.5 < x < 4.5 \).
Answered by
GPT-4o mini
Based on the description you've provided, the compound inequality represented is actually \( 2.5 \leq x \leq 4.5 \). Here’s how to interpret and graph it:
1. **Closed Circles:**
- Since the inequality includes "less than or equal to" (≤) for both endpoints, you would use **closed circles** at both 2.5 and 4.5. This indicates that both 2.5 and 4.5 are included in the solution set.
2. **Shading:**
- You would shade the region between 2.5 and 4.5 on the number line. This shows that all numbers between these two points (including 2.5 and 4.5 themselves) are part of the solution.
### Graphing Steps:
- Place a **closed circle** at **2.5** and another **closed circle** at **4.5**.
- Shade the line segment between these two closed circles.
### On a number line, the representation looks like this:
```
-5 -4 -3 -2 -1 0 1 2 3 4 5
| |
o===============================o
2.5 4.5
```
- The **closed circles** indicate that the endpoints 2.5 and 4.5 are included in the solution set, while the shaded region represents all values of \( x \) that satisfy the inequality \( 2.5 \leq x \leq 4.5 \).
1. **Closed Circles:**
- Since the inequality includes "less than or equal to" (≤) for both endpoints, you would use **closed circles** at both 2.5 and 4.5. This indicates that both 2.5 and 4.5 are included in the solution set.
2. **Shading:**
- You would shade the region between 2.5 and 4.5 on the number line. This shows that all numbers between these two points (including 2.5 and 4.5 themselves) are part of the solution.
### Graphing Steps:
- Place a **closed circle** at **2.5** and another **closed circle** at **4.5**.
- Shade the line segment between these two closed circles.
### On a number line, the representation looks like this:
```
-5 -4 -3 -2 -1 0 1 2 3 4 5
| |
o===============================o
2.5 4.5
```
- The **closed circles** indicate that the endpoints 2.5 and 4.5 are included in the solution set, while the shaded region represents all values of \( x \) that satisfy the inequality \( 2.5 \leq x \leq 4.5 \).
Answered by
GPT-4o mini
I apologize for any confusion! Based on your previous message about the compound inequality \(2.5 \leq x \leq 4.5\), here's how to accurately represent it on a number line:
### Steps:
1. **Choose Circles:**
- Use **closed circles** for both 2.5 and 4.5, because the inequality includes equal to (≤).
2. **Position the Circles:**
- Place a **closed circle** at **2.5** on the number line.
- Place another **closed circle** at **4.5** on the number line.
3. **Shading:**
- Shade the line **between** the two closed circles:
- Starting from 2.5 to 4.5, shade all the points in that range. This indicates that all numbers between 2.5 and 4.5, including 2.5 and 4.5 themselves, are part of the solution.
### Placement and Direction on a Number Line:
- You do not put an open circle here, since the points are included.
- The **shaded area** will extend **to the right** from 2.5 to 4.5.
### Visual Representation on a Number Line:
```
-5 -4 -3 -2 -1 0 1 2 3 4 5
| |
•=======================• (2.5 and 4.5 are closed circles)
2.5 4.5
```
### Summary:
- **Closed circles** at **2.5** and **4.5**.
- Shade the line **to the right** from **2.5** to **4.5** (including the endpoints).
This properly represents the compound inequality \(2.5 \leq x \leq 4.5\) on the number line!
### Steps:
1. **Choose Circles:**
- Use **closed circles** for both 2.5 and 4.5, because the inequality includes equal to (≤).
2. **Position the Circles:**
- Place a **closed circle** at **2.5** on the number line.
- Place another **closed circle** at **4.5** on the number line.
3. **Shading:**
- Shade the line **between** the two closed circles:
- Starting from 2.5 to 4.5, shade all the points in that range. This indicates that all numbers between 2.5 and 4.5, including 2.5 and 4.5 themselves, are part of the solution.
### Placement and Direction on a Number Line:
- You do not put an open circle here, since the points are included.
- The **shaded area** will extend **to the right** from 2.5 to 4.5.
### Visual Representation on a Number Line:
```
-5 -4 -3 -2 -1 0 1 2 3 4 5
| |
•=======================• (2.5 and 4.5 are closed circles)
2.5 4.5
```
### Summary:
- **Closed circles** at **2.5** and **4.5**.
- Shade the line **to the right** from **2.5** to **4.5** (including the endpoints).
This properly represents the compound inequality \(2.5 \leq x \leq 4.5\) on the number line!
Answered by
GPT-4o mini
To find the scenario that fits the compound inequality \(2.5 \leq x \leq 4.5\), we need to identify which option indicates that a value is between 2.5 and 4.5, inclusive of both endpoints.
Let's analyze the scenarios:
1. **Jill’s best friend lives less than 2.5 miles from her house, but more than 4.5 miles from their school.**
- This scenario does not fit because it describes values outside of the range 2.5 to 4.5.
2. **It is good to choose a hotel with ratings with more than 2.5 stars.**
- This does not fit either, because it talks about ratings greater than 2.5 without specifying an upper limit.
3. **In terms of percent, the salinity of most sea water is between 2.5 and 4.5.**
- This fits the compound inequality \(2.5 \leq x \leq 4.5\), as it indicates that the salinity is greater than or equal to 2.5 and less than or equal to 4.5.
4. **The grade point average of Mrs. Green’s class is less than 4.5.**
- This scenario does not fit since it does not indicate a lower limit of 2.5.
### Conclusion:
The correct scenario that fits the compound inequality \(2.5 \leq x \leq 4.5\) is:
**In terms of percent, the salinity of most sea water is between 2.5 and 4.5.**
Let's analyze the scenarios:
1. **Jill’s best friend lives less than 2.5 miles from her house, but more than 4.5 miles from their school.**
- This scenario does not fit because it describes values outside of the range 2.5 to 4.5.
2. **It is good to choose a hotel with ratings with more than 2.5 stars.**
- This does not fit either, because it talks about ratings greater than 2.5 without specifying an upper limit.
3. **In terms of percent, the salinity of most sea water is between 2.5 and 4.5.**
- This fits the compound inequality \(2.5 \leq x \leq 4.5\), as it indicates that the salinity is greater than or equal to 2.5 and less than or equal to 4.5.
4. **The grade point average of Mrs. Green’s class is less than 4.5.**
- This scenario does not fit since it does not indicate a lower limit of 2.5.
### Conclusion:
The correct scenario that fits the compound inequality \(2.5 \leq x \leq 4.5\) is:
**In terms of percent, the salinity of most sea water is between 2.5 and 4.5.**
Answered by
GPT-4o mini
To determine which graph represents the compound inequality \( x \leq \frac{5}{4} \) or \( x \geq \frac{5}{2} \), let's break down the compound inequality:
1. **Understanding the Inequalities:**
- \( x \leq \frac{5}{4} \) means all values **less than or equal to** \( \frac{5}{4} \) (which is 1.25).
- \( x \geq \frac{5}{2} \) means all values **greater than or equal to** \( \frac{5}{2} \) (which is 2.5).
2. **Combining the Inequalities:**
- The compound inequality states that \( x \) can either be less than or equal to \( 1.25 \) or greater than or equal to \( 2.5 \). This means that there are two segments of valid \( x \) values that do not overlap:
- All values of \( x \) less than or equal to \( 1.25\) (with a closed circle at \( 1.25 \)).
- All values of \( x \) greater than or equal to \( 2.5\) (with a closed circle at \( 2.5 \)).
3. **Evaluating the Number Lines:**
- **First Number Line:** Values greater than -0.5. (Not the correct choice)
- **Second Number Line:** Values less than or equal to \( 1.25 \). (Part of the inequality but incomplete as it doesn't capture the greater values)
- **Third Number Line:** Values less than or equal to \( 1.25 \) and greater than or equal to \( 2.5 \). (Correct choice, as it shows both segments of the inequality properly)
- **Fourth Number Line:** Values greater than -0.5 and less than or equal to \( 2.5 \). (Not the correct choice)
### Conclusion:
The correct graph that represents the compound inequality \( x \leq \frac{5}{4} \) or \( x \geq \frac{5}{2} \) is the **third number line,** which shows values less than or equal to \( 1.25 \) and contains values greater than or equal to \( 2.5 \).
1. **Understanding the Inequalities:**
- \( x \leq \frac{5}{4} \) means all values **less than or equal to** \( \frac{5}{4} \) (which is 1.25).
- \( x \geq \frac{5}{2} \) means all values **greater than or equal to** \( \frac{5}{2} \) (which is 2.5).
2. **Combining the Inequalities:**
- The compound inequality states that \( x \) can either be less than or equal to \( 1.25 \) or greater than or equal to \( 2.5 \). This means that there are two segments of valid \( x \) values that do not overlap:
- All values of \( x \) less than or equal to \( 1.25\) (with a closed circle at \( 1.25 \)).
- All values of \( x \) greater than or equal to \( 2.5\) (with a closed circle at \( 2.5 \)).
3. **Evaluating the Number Lines:**
- **First Number Line:** Values greater than -0.5. (Not the correct choice)
- **Second Number Line:** Values less than or equal to \( 1.25 \). (Part of the inequality but incomplete as it doesn't capture the greater values)
- **Third Number Line:** Values less than or equal to \( 1.25 \) and greater than or equal to \( 2.5 \). (Correct choice, as it shows both segments of the inequality properly)
- **Fourth Number Line:** Values greater than -0.5 and less than or equal to \( 2.5 \). (Not the correct choice)
### Conclusion:
The correct graph that represents the compound inequality \( x \leq \frac{5}{4} \) or \( x \geq \frac{5}{2} \) is the **third number line,** which shows values less than or equal to \( 1.25 \) and contains values greater than or equal to \( 2.5 \).
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