Asked by ahahahahahahahaha
Which set of numbers is always rational?(1 point)
Responses
positive numbers
positive numbers
negative numbers
negative numbers
integers
integers
decimals
Responses
positive numbers
positive numbers
negative numbers
negative numbers
integers
integers
decimals
Answers
Answered by
ahahahahahahahaha
The height of an equilateral triangle equals √3/2
times the side length. Using 7/4
for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters
times the side length. Using 7/4
for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters
Answered by
ahahahahahahahaha
The diagonal of a square equals √2
times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side
times the side length. Using 1.4 for the square root of 2, what is the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side
Answered by
ahahahahahahahaha
Using a number line, what whole number and rational number to the nearest half is √40
between
between
Answered by
ahahahahahahahaha
Using a number line, what whole number and rational number to the nearest half is √58
between
between
Answered by
GPT-4o mini
The set of numbers that is always rational is **integers**.
Integers are whole numbers that can be positive, negative, or zero, and they can be expressed as fractions with a denominator of 1 (e.g., 3 can be expressed as 3/1).
Positive numbers, negative numbers, and decimals can include rational and irrational numbers, whereas integers are always rational.
Integers are whole numbers that can be positive, negative, or zero, and they can be expressed as fractions with a denominator of 1 (e.g., 3 can be expressed as 3/1).
Positive numbers, negative numbers, and decimals can include rational and irrational numbers, whereas integers are always rational.
Answered by
GPT-4o mini
To find the height of an equilateral triangle, we can use the formula:
\[
\text{Height} = \frac{\sqrt{3}}{2} \times \text{Side length}
\]
Given that the side length is 8 meters and using \( \sqrt{3} \approx \frac{7}{4} \), we can substitute these values into the formula:
1. First, substitute the value for the square root of 3:
\[
\text{Height} \approx \frac{7}{4} \times \frac{1}{2} \times 8
\]
2. Simplifying this step by step:
\[
\text{Height} \approx \frac{7}{4} \times 4
\]
3. The 4's cancel out:
\[
\text{Height} \approx 7 \text{ meters}
\]
So, the approximate height of the equilateral triangle with a side length of 8 meters is **7 meters**.
\[
\text{Height} = \frac{\sqrt{3}}{2} \times \text{Side length}
\]
Given that the side length is 8 meters and using \( \sqrt{3} \approx \frac{7}{4} \), we can substitute these values into the formula:
1. First, substitute the value for the square root of 3:
\[
\text{Height} \approx \frac{7}{4} \times \frac{1}{2} \times 8
\]
2. Simplifying this step by step:
\[
\text{Height} \approx \frac{7}{4} \times 4
\]
3. The 4's cancel out:
\[
\text{Height} \approx 7 \text{ meters}
\]
So, the approximate height of the equilateral triangle with a side length of 8 meters is **7 meters**.
Answered by
GPT-4o mini
To find the diagonal of a square, we can use the formula:
\[
\text{Diagonal} = \sqrt{2} \times \text{Side length}
\]
Given that the side length of the square park is 700 feet and using \( \sqrt{2} \approx 1.4 \), we can substitute these values into the formula:
1. Substitute the values:
\[
\text{Diagonal} \approx 1.4 \times 700
\]
2. Calculate the diagonal:
\[
\text{Diagonal} \approx 1.4 \times 700 = 980 \text{ feet}
\]
Therefore, the approximate length from one corner to the opposite corner of the square park is **980 feet**.
\[
\text{Diagonal} = \sqrt{2} \times \text{Side length}
\]
Given that the side length of the square park is 700 feet and using \( \sqrt{2} \approx 1.4 \), we can substitute these values into the formula:
1. Substitute the values:
\[
\text{Diagonal} \approx 1.4 \times 700
\]
2. Calculate the diagonal:
\[
\text{Diagonal} \approx 1.4 \times 700 = 980 \text{ feet}
\]
Therefore, the approximate length from one corner to the opposite corner of the square park is **980 feet**.
Answered by
GPT-4o mini
To find between which whole number and rational number (to the nearest half) the value of \( \sqrt{40} \) lies, we first need to compute \( \sqrt{40} \).
1. Simplifying \( \sqrt{40} \):
\[
\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}
\]
Next, we can approximate \( \sqrt{10} \). The value of \( \sqrt{10} \) is approximately 3.162. Thus,
\[
\sqrt{40} \approx 2 \times 3.162 = 6.324
\]
2. Now, we will determine the whole number and the nearest half. The whole number parts surrounding 6.324 are:
- The largest whole number less than 6.324 is **6**.
- The smallest whole number greater than 6.324 is **7**.
3. To find the nearest half, we compare 6.324 to .0 and .5:
- It is closer to 6.5 than to 6.0.
**Conclusion**:
- The whole number is **6**.
- The rational number to the nearest half is **6.5**.
Therefore, \( \sqrt{40} \) is between **6** and **6.5**.
1. Simplifying \( \sqrt{40} \):
\[
\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10} = 2\sqrt{10}
\]
Next, we can approximate \( \sqrt{10} \). The value of \( \sqrt{10} \) is approximately 3.162. Thus,
\[
\sqrt{40} \approx 2 \times 3.162 = 6.324
\]
2. Now, we will determine the whole number and the nearest half. The whole number parts surrounding 6.324 are:
- The largest whole number less than 6.324 is **6**.
- The smallest whole number greater than 6.324 is **7**.
3. To find the nearest half, we compare 6.324 to .0 and .5:
- It is closer to 6.5 than to 6.0.
**Conclusion**:
- The whole number is **6**.
- The rational number to the nearest half is **6.5**.
Therefore, \( \sqrt{40} \) is between **6** and **6.5**.
Answered by
GPT-4o mini
To find between which whole number and rational number (to the nearest half) \( \sqrt{58} \) lies, we can start by calculating \( \sqrt{58} \).
1. **Estimate \( \sqrt{58} \)**:
We know that:
- \( \sqrt{49} = 7 \)
- \( \sqrt{64} = 8 \)
Since \( 58 \) is between \( 49 \) and \( 64 \), we can conclude that:
\[
7 < \sqrt{58} < 8
\]
2. **Calculate \( \sqrt{58} \) more accurately**:
Using a calculator, we find:
\[
\sqrt{58} \approx 7.6158
\]
3. **Determine the whole number and rational number to the nearest half**:
- The largest whole number less than \( 7.6158 \) is **7**.
- The smallest whole number greater than \( 7.6158 \) is **8**.
To find the nearest half:
- \( 7.6158 \) is closer to \( 7.5 \) than to \( 8.0 \).
**Conclusion**:
- The whole number is **7**.
- The rational number to the nearest half is **7.5**.
Thus, \( \sqrt{58} \) is between **7** and **7.5**.
1. **Estimate \( \sqrt{58} \)**:
We know that:
- \( \sqrt{49} = 7 \)
- \( \sqrt{64} = 8 \)
Since \( 58 \) is between \( 49 \) and \( 64 \), we can conclude that:
\[
7 < \sqrt{58} < 8
\]
2. **Calculate \( \sqrt{58} \) more accurately**:
Using a calculator, we find:
\[
\sqrt{58} \approx 7.6158
\]
3. **Determine the whole number and rational number to the nearest half**:
- The largest whole number less than \( 7.6158 \) is **7**.
- The smallest whole number greater than \( 7.6158 \) is **8**.
To find the nearest half:
- \( 7.6158 \) is closer to \( 7.5 \) than to \( 8.0 \).
**Conclusion**:
- The whole number is **7**.
- The rational number to the nearest half is **7.5**.
Thus, \( \sqrt{58} \) is between **7** and **7.5**.
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