Which set of numbers is always rational?(1 point)
Responses
decimals
decimals
integers
integers
fractions
fractions
positive numbers
positive numbers
The set of numbers that is always rational is 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)
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To find the height of an equilateral triangle, you can multiply the side length by the square root of 3 divided by 2.
Given that the square root of 3 is approximately 74, we can substitute this value into the formula:
Height = side length * (√3 / 2)
Height ≈ 8 * (74 / 2)
Height ≈ 8 * 37
Height ≈ 296
Therefore, the approximate height in meters of an 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, you can multiply the side length by the square root of 2.
Given that the square root of 2 is approximately 1.4, we can substitute this value into the formula:
Diagonal = side length * √2
Diagonal ≈ 700 * 1.4
Diagonal ≈ 980
Therefore, the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side is 980 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−−√ is between, we first need to find the whole number and the nearest half that 40−−√ is approximately equal to.
To find the whole number, we can round down 40−√ to the nearest whole number.
40−√ is approximately equal to 6.324555...
Rounded down, this becomes 6.
To find the nearest half, we can round the decimal portion of 40−√ to the nearest half.
The decimal portion is 0.324555...
Rounded to the nearest half, this becomes 0.5 since it is closer to 0.5 than to 0.
Therefore, 40−−√ is between the whole number 6 and the rational number 6.5.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
between 7.5 and 8
between 7.5 and 8
between 8.5 and 9
between 8.5 and 9
between 7 and 7.5
between 7 and 7.5
between 8 and 8.5
To determine the whole number and rational number to the nearest half that 58−−√ is between, we first need to find the whole number and the nearest half that 58−−√ is approximately equal to.
To find the whole number, we can round down 58−√ to the nearest whole number.
58−√ is approximately equal to 7.615...
Rounded down, this becomes 7.
To find the nearest half, we can round the decimal portion of 58−√ to the nearest half.
The decimal portion is 0.615...
Rounded to the nearest half, this becomes 0.5 since it is closer to 0.5 than to 0.
Therefore, 58−−√ is between the whole number 7 and the rational number 7.5.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√
8–√8.