Question
a number multiplied by 54 the result is positive number less than 54 which of these was multiplied by 54
Answers
Answered by
GPT-4o mini
To find a number that, when multiplied by 54, results in a positive number less than 54, we can set up the following mathematical expression:
Let \( x \) be the number we are looking for. The condition can be expressed as:
\[
0 < 54x < 54
\]
To determine the possible values for \( x \), we can divide the entire inequality by 54 (noting that since 54 is positive, we do not need to flip the inequality signs):
\[
0 < x < 1
\]
This means \( x \) must be a positive number that is less than 1.
Thus, any number satisfying \( 0 < x < 1 \) can be multiplied by 54 to yield a positive result less than 54. For example, \( x = 0.5 \) or \( x = 0.1 \) would work, since:
- \( 54 \times 0.5 = 27 \) (which is less than 54)
- \( 54 \times 0.1 = 5.4 \) (which is also less than 54)
In conclusion, any positive number less than 1 when multiplied by 54 will fulfill the condition.
Let \( x \) be the number we are looking for. The condition can be expressed as:
\[
0 < 54x < 54
\]
To determine the possible values for \( x \), we can divide the entire inequality by 54 (noting that since 54 is positive, we do not need to flip the inequality signs):
\[
0 < x < 1
\]
This means \( x \) must be a positive number that is less than 1.
Thus, any number satisfying \( 0 < x < 1 \) can be multiplied by 54 to yield a positive result less than 54. For example, \( x = 0.5 \) or \( x = 0.1 \) would work, since:
- \( 54 \times 0.5 = 27 \) (which is less than 54)
- \( 54 \times 0.1 = 5.4 \) (which is also less than 54)
In conclusion, any positive number less than 1 when multiplied by 54 will fulfill the condition.
Answer
A: A number less then zero
B: a number between zero and one
C: a number greater than one
D: zero
B: a number between zero and one
C: a number greater than one
D: zero
Answered by
GPT-4o mini
To determine which option results in a product that is positive and less than 54 when multiplied by 54, let's analyze each option:
**A: A number less than zero**
- If a number is less than zero (negative), then multiplying it by 54 will yield a negative product (e.g., \( 54 \times (-1) = -54 \)). This does not satisfy the condition of being a positive number.
**B: A number between zero and one**
- If a number is between zero and one (e.g., \( 0.5 \)), then multiplying it by 54 will yield a positive product that is less than 54 (e.g., \( 54 \times 0.5 = 27 \)). This satisfies the condition.
**C: A number greater than one**
- If a number is greater than one (e.g., \( 2 \)), then multiplying it by 54 will yield a product greater than 54 (e.g., \( 54 \times 2 = 108 \)). This does not satisfy the condition of being less than 54.
**D: Zero**
- Multiplying zero by any number results in zero (e.g., \( 54 \times 0 = 0 \)). While this is not negative, it does not satisfy the requirement of being a positive number.
### Conclusion:
The only option that results in a product that is a positive number less than 54 is **B: a number between zero and one**.
**A: A number less than zero**
- If a number is less than zero (negative), then multiplying it by 54 will yield a negative product (e.g., \( 54 \times (-1) = -54 \)). This does not satisfy the condition of being a positive number.
**B: A number between zero and one**
- If a number is between zero and one (e.g., \( 0.5 \)), then multiplying it by 54 will yield a positive product that is less than 54 (e.g., \( 54 \times 0.5 = 27 \)). This satisfies the condition.
**C: A number greater than one**
- If a number is greater than one (e.g., \( 2 \)), then multiplying it by 54 will yield a product greater than 54 (e.g., \( 54 \times 2 = 108 \)). This does not satisfy the condition of being less than 54.
**D: Zero**
- Multiplying zero by any number results in zero (e.g., \( 54 \times 0 = 0 \)). While this is not negative, it does not satisfy the requirement of being a positive number.
### Conclusion:
The only option that results in a product that is a positive number less than 54 is **B: a number between zero and one**.
Answer
use properties of rational numbers to multiply the following -2.2 x (-60.4)
Answered by
GPT-4o mini
To multiply the rational numbers \(-2.2\) and \(-60.4\), we can follow these steps:
1. **Identify the signs**: Both numbers are negative.
2. **Multiply the absolute values**: Ignore the signs and multiply the positive versions of the numbers.
\[
2.2 \times 60.4
\]
3. **Calculating \(2.2 \times 60.4\)**:
- You can perform the multiplication directly:
\[
2.2 \times 60.4 = 2.2 \times (60 + 0.4) = (2.2 \times 60) + (2.2 \times 0.4)
\]
- Calculate \(2.2 \times 60\):
\[
2.2 \times 60 = 132
\]
- Next, calculate \(2.2 \times 0.4\):
\[
2.2 \times 0.4 = 0.88
\]
- Now sum these results:
\[
132 + 0.88 = 132.88
\]
4. **Determine the sign**: Since both numbers are negative, we multiply two negatives, which results in a positive.
\[
-2.2 \times -60.4 = 132.88
\]
### Final Answer:
\[
-2.2 \times -60.4 = 132.88
\]
1. **Identify the signs**: Both numbers are negative.
2. **Multiply the absolute values**: Ignore the signs and multiply the positive versions of the numbers.
\[
2.2 \times 60.4
\]
3. **Calculating \(2.2 \times 60.4\)**:
- You can perform the multiplication directly:
\[
2.2 \times 60.4 = 2.2 \times (60 + 0.4) = (2.2 \times 60) + (2.2 \times 0.4)
\]
- Calculate \(2.2 \times 60\):
\[
2.2 \times 60 = 132
\]
- Next, calculate \(2.2 \times 0.4\):
\[
2.2 \times 0.4 = 0.88
\]
- Now sum these results:
\[
132 + 0.88 = 132.88
\]
4. **Determine the sign**: Since both numbers are negative, we multiply two negatives, which results in a positive.
\[
-2.2 \times -60.4 = 132.88
\]
### Final Answer:
\[
-2.2 \times -60.4 = 132.88
\]
Answer
The altitude of an airplane is decreasing at a rate of 42 feet per second what is the change in altitude of the airplane over a period of 27 seconds
Answered by
GPT-4o mini
To find the change in altitude of the airplane over a period of 27 seconds, given that it is decreasing at a rate of 42 feet per second, you can use the formula for change in altitude:
\[
\text{Change in altitude} = \text{Rate} \times \text{Time}
\]
In this case:
- Rate = -42 feet per second (the negative sign indicates a decrease)
- Time = 27 seconds
Now, plug in the values:
\[
\text{Change in altitude} = -42 \, \text{feet/second} \times 27 \, \text{seconds}
\]
Now, calculate:
\[
\text{Change in altitude} = -1134 \, \text{feet}
\]
### Conclusion:
The change in altitude of the airplane over a period of 27 seconds is a decrease of **1134 feet**.
\[
\text{Change in altitude} = \text{Rate} \times \text{Time}
\]
In this case:
- Rate = -42 feet per second (the negative sign indicates a decrease)
- Time = 27 seconds
Now, plug in the values:
\[
\text{Change in altitude} = -42 \, \text{feet/second} \times 27 \, \text{seconds}
\]
Now, calculate:
\[
\text{Change in altitude} = -1134 \, \text{feet}
\]
### Conclusion:
The change in altitude of the airplane over a period of 27 seconds is a decrease of **1134 feet**.
Answer
-26 x (-58/221)
Answered by
GPT-4o mini
To multiply \(-26\) by \(-\frac{58}{221}\), you can follow these steps:
1. **Multiply the absolute values**: Ignore the signs for the moment and multiply the numbers.
\[
26 \times 58 = 1508
\]
2. **Determine the sign**: Since both numbers are negative, the product will be positive.
Thus, the final result will be:
\[
-26 \times -\frac{58}{221} = \frac{1508}{221}
\]
3. **Simplify if possible**: Now we check if \(\frac{1508}{221}\) can be simplified.
- 1508 divided by 221 is approximately equal to \(6.818\). However, for the exact value, we can calculate \(1508 \div 221\), which does not yield a whole number, hence the fraction is in its simplest form.
So, the final answer is:
\[
\frac{1508}{221}
\]
If you prefer a decimal approximation, you can calculate:
\[
\frac{1508}{221} \approx 6.818
\]
### Final Answer:
\[
-26 \times -\frac{58}{221} = \frac{1508}{221} \quad \text{or} \quad \approx 6.818
\]
1. **Multiply the absolute values**: Ignore the signs for the moment and multiply the numbers.
\[
26 \times 58 = 1508
\]
2. **Determine the sign**: Since both numbers are negative, the product will be positive.
Thus, the final result will be:
\[
-26 \times -\frac{58}{221} = \frac{1508}{221}
\]
3. **Simplify if possible**: Now we check if \(\frac{1508}{221}\) can be simplified.
- 1508 divided by 221 is approximately equal to \(6.818\). However, for the exact value, we can calculate \(1508 \div 221\), which does not yield a whole number, hence the fraction is in its simplest form.
So, the final answer is:
\[
\frac{1508}{221}
\]
If you prefer a decimal approximation, you can calculate:
\[
\frac{1508}{221} \approx 6.818
\]
### Final Answer:
\[
-26 \times -\frac{58}{221} = \frac{1508}{221} \quad \text{or} \quad \approx 6.818
\]
Answer
A: 116/17
B: -84\221
C: 2873/29
D: 58\17
B: -84\221
C: 2873/29
D: 58\17
Answered by
GPT-4o mini
Let's find which of these options is equivalent to the result we calculated, \(\frac{1508}{221}\).
### Check each option:
1. **Option A: \(\frac{116}{17}\)**
- Dividing numerator by denominator:
\[
\frac{116}{17} \approx 6.8235
\]
2. **Option B: \(-\frac{84}{221}\)**
- This is a negative fraction and cannot be equal to \(\frac{1508}{221}\), which is positive.
3. **Option C: \(\frac{2873}{29}\)**
- Dividing numerator by denominator:
\[
\frac{2873}{29} = 99.069 \quad (\text{not equivalent to } \frac{1508}{221})
\]
4. **Option D: \(\frac{58}{17}\)**
- Dividing numerator by denominator:
\[
\frac{58}{17} \approx 3.41176 \quad (\text{not equivalent to } \frac{1508}{221})
\]
### Summary:
From this analysis, none of the options A, B, C, or D are equivalent to \(\frac{1508}{221}\).
To clarify the calculations, we can check the approximate decimal value of \(\frac{1508}{221}\):
- It can be calculated as:
\[
1508 \div 221 \approx 6.818 \quad \text{(which is the result we obtained)}
\]
Since none of the options are equal to this value, it seems there is no correct choice among the options provided. If you need further assistance or a different context, feel free to ask!
### Check each option:
1. **Option A: \(\frac{116}{17}\)**
- Dividing numerator by denominator:
\[
\frac{116}{17} \approx 6.8235
\]
2. **Option B: \(-\frac{84}{221}\)**
- This is a negative fraction and cannot be equal to \(\frac{1508}{221}\), which is positive.
3. **Option C: \(\frac{2873}{29}\)**
- Dividing numerator by denominator:
\[
\frac{2873}{29} = 99.069 \quad (\text{not equivalent to } \frac{1508}{221})
\]
4. **Option D: \(\frac{58}{17}\)**
- Dividing numerator by denominator:
\[
\frac{58}{17} \approx 3.41176 \quad (\text{not equivalent to } \frac{1508}{221})
\]
### Summary:
From this analysis, none of the options A, B, C, or D are equivalent to \(\frac{1508}{221}\).
To clarify the calculations, we can check the approximate decimal value of \(\frac{1508}{221}\):
- It can be calculated as:
\[
1508 \div 221 \approx 6.818 \quad \text{(which is the result we obtained)}
\]
Since none of the options are equal to this value, it seems there is no correct choice among the options provided. If you need further assistance or a different context, feel free to ask!