Which set of numbers is always rational?(1 point)
Responses
integers
integers
positive numbers
positive numbers
decimals
decimals
fractions
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?
The height of an equilateral triangle can be found by multiplying the side length by √3/2.
Given that the side length is 8 meters, we can calculate the height as follows:
Height = 8 * (√3/2)
Height = 8 * (74/2) (Using 74 for √3)
Height = 8 * 37
Height = 296 meters
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 296 meters.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?
To find the whole number and rational number to the nearest half that is between 40−−√, we can start by approximating the value of 40−−√:
√40 is approximately equal to 6.32 (rounded to two decimal places).
So, 40−−√ is approximately equal to 6.32.
To find the whole number and rational number to the nearest half, we can look for the two consecutive half values that 6.32 falls between on the number line.
6 is the whole number between 6.32 and 7.
Now, we can find the rational number to the nearest half:
6 (whole number) + 0.5 (half) = 6.5
Therefore, the whole number and rational number to the nearest half that is between 40−−√ is 6 and 6.5.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.
To compare 81–√ and 8–√8 using rational approximations, we can find their decimal approximations:
81–√ ≈ 9 (since √81 = 9)
8–√8 ≈ 8–√2 ≈ 8–1.41 ≈ 6.59 (approximating √2 as 1.41)
Since 9 is greater than 6.59, the inequality statement comparing 81–√ and 8–√8 is:
81–√ > 8–√8