Question
What is a rational number with a denominator of 7 that is between sqr 7and sqr 8. Write your answer as an improper fraction.
Answers
Answer
Using a number line, what whole number and rational number to the nearest half is √ 58 between?
A.between 8.5 and 9
B. between 7.5 and 8
C. between 7 and 7.5
D. between 8 and 8.5
A.between 8.5 and 9
B. between 7.5 and 8
C. between 7 and 7.5
D. between 8 and 8.5
Answer
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?
Answer
are you sure it's not 7
Answer
A sign in a gas station advertises gas at the rate of $3.39 9/10 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?
Answered by
GPT 3.5
To find a rational number with a denominator of 7 between √7 and √8, we need to find a number whose square root is between these two values.
First, let's express √7 and √8 as fractions:
√7 ≈ 2.6457513110645907
√8 ≈ 2.8284271247461903
We can see that the whole number part of both square roots is 2. Therefore, any rational number with a denominator of 7 between these two square roots will have a whole number part of 2.
Next, we want to find the fractional part of the rational number. Since 7 is the denominator, we need a number that is between 2.6457513110645907 and 2.8284271247461903 when expressed as a fraction with a denominator of 7.
The fraction that lies between these two values is 4/7. Adding this fraction to the whole number 2 gives us the rational number:
2 + 4/7 = 14/7 + 4/7 = 18/7
Therefore, the rational number with a denominator of 7 between √7 and √8 is 18/7.
First, let's express √7 and √8 as fractions:
√7 ≈ 2.6457513110645907
√8 ≈ 2.8284271247461903
We can see that the whole number part of both square roots is 2. Therefore, any rational number with a denominator of 7 between these two square roots will have a whole number part of 2.
Next, we want to find the fractional part of the rational number. Since 7 is the denominator, we need a number that is between 2.6457513110645907 and 2.8284271247461903 when expressed as a fraction with a denominator of 7.
The fraction that lies between these two values is 4/7. Adding this fraction to the whole number 2 gives us the rational number:
2 + 4/7 = 14/7 + 4/7 = 18/7
Therefore, the rational number with a denominator of 7 between √7 and √8 is 18/7.
Answered by
GPT 3.5
To find the whole number and rational number to the nearest half that √58 is between, we can calculate the approximate decimal value of √58.
√58 ≈ 7.616
To determine the nearest half, we look at the decimal portion of this approximation. Since 0.616 is closer to 0.5 than 0, √58 is closest to the decimal value 7.5.
Now we want to find the whole numbers that √58 is between. We can determine this by looking at the whole number parts of our approximations.
7 < √58 < 8
Therefore, √58 is between the whole numbers 7 and 8, and the rational number to the nearest half is 7.5.
Therefore, the correct answer is B. between 7.5 and 8.
√58 ≈ 7.616
To determine the nearest half, we look at the decimal portion of this approximation. Since 0.616 is closer to 0.5 than 0, √58 is closest to the decimal value 7.5.
Now we want to find the whole numbers that √58 is between. We can determine this by looking at the whole number parts of our approximations.
7 < √58 < 8
Therefore, √58 is between the whole numbers 7 and 8, and the rational number to the nearest half is 7.5.
Therefore, the correct answer is B. between 7.5 and 8.
Answered by
GPT 3.5
Given that the square root of 3 is approximately 7/4, we can substitute this value into the formula for the height of an equilateral triangle to find the approximate height.
Height = (√3/2) * (side length)
Substituting (√3/2) = 7/4:
Height = (7/4) * 8 = 7 * 8 / 4 = 56 / 4 = 14
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 14 meters.
Height = (√3/2) * (side length)
Substituting (√3/2) = 7/4:
Height = (7/4) * 8 = 7 * 8 / 4 = 56 / 4 = 14
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 14 meters.
Answered by
GPT 3.5
I apologize for the mistake in my previous response. You are correct; the height of an equilateral triangle with a side length of 8 meters, using 7/4 for the square root of 3, would be 7 meters.
Thank you for catching that error, and I apologize for any confusion caused.
Thank you for catching that error, and I apologize for any confusion caused.
Answered by
GPT 3.5
To write the price strictly as a decimal, we can convert the fraction part (9/10) to a decimal.
9/10 = 0.9
The price of gas, strictly as a decimal, is $3.39 + 0.9, which is $3.39 + $0.90.
Adding the whole numbers and the decimal parts, we get:
$3.39 + $0.90 = $4.29
Therefore, a gallon of gas costs $4.29 as a decimal.
9/10 = 0.9
The price of gas, strictly as a decimal, is $3.39 + 0.9, which is $3.39 + $0.90.
Adding the whole numbers and the decimal parts, we get:
$3.39 + $0.90 = $4.29
Therefore, a gallon of gas costs $4.29 as a decimal.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.