@Bot GPT 3.5 Which set of numbers is always rational?(1 point)
Responses
fractions
fractions
integers
integers
decimals
decimals
positive numbers
fractions
The height of an equilateral triangle equals 3√2 times the side length. Using 74 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point)
To find the height of an equilateral triangle, we can use the formula:
height = √3/2 * side length
Given that the side length is 8 meters, we can substitute this value into the formula:
height = (√3/2) * 8
To approximate the value, we can use 74 for the square root of 3:
height = (74/2) * 8
= 37 * 8
= 296 meters (approximate)
Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is 296 meters.
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?(1 point)
To find the length of the diagonal of a square, we can use the formula:
diagonal = (2 - √2) * side length
Given that the side length is 700 feet, we can substitute this value into the formula:
diagonal = (2 - √2) * 700
To approximate the value, we can use 1.4 for the square root of 2:
diagonal = (2 - 1.4) * 700
= (0.6) * 700
= 420 feet (approximate)
Therefore, the approximate length from one corner to an opposite corner of the square park that is 700 feet on a side is 420 feet.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between
and
To determine the whole number and rational number to the nearest half that 40 - √2 is between, we can approximate the value of √2 to the nearest decimal.
√2 is approximately 1.41.
Since 1.41 is closer to 1.5 than 1, the whole number to the nearest half that 40 - √2 is between is 40 - 1.5 = 38.5.
The rational number to the nearest half that 40 - √2 is between is 40 - 1 = 39.
Therefore, 40 - √2 is between 38.5 and 39.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 8.5 and 9
between 8.5 and 9
between 8 and 8.5
between 8 and 8.5
between 7 and 7.5
between 7 and 7.5
between 7.5 and 8
To find the whole number and rational number to the nearest half that 58 - √2 is between, we need to approximate the value of √2 to the nearest decimal.
√2 is approximately 1.41.
Since 1.41 is closer to 1.5 than 1, we can subtract it from 58 to find the whole number:
58 - 1.5 = 56.5
So the whole number to the nearest half that 58 - √2 is between is 56.5.
The rational number to the nearest half that 58 - √2 is between is 58 - 1 = 57.
Therefore, 58 - √2 is between 56.5 and 57.
wrong, Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 8.5 and 9
between 8.5 and 9
between 8 and 8.5
between 8 and 8.5
between 7 and 7.5
between 7 and 7.5
between 7.5 and 8