Which set of numbers is always rational?(1 point)
Responses
fractions
fractions
decimals
decimals
positive numbers
positive numbers
integers
fractions and integers
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 = side length * √3/2
Given that the side length is 8 meters, we can substitute this value into the formula:
height = 8 * 74/2
Simplifying the expression:
height ≈ 8 * 37
height ≈ 296 meters
Therefore, the approximate height 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?
To find the length of the diagonal of a square, we can use the formula:
diagonal = side length * (√2)
Given that the side length is 700 feet and using the approximation 1.4 for the square root of 2, we can substitute these values into the formula:
diagonal = 700 * 1.4
Simplifying the expression:
diagonal ≈ 980 feet
Therefore, the approximate length 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?
To determine the whole number and rational number that √40 is between, let's find the two perfect square numbers that √40 is between.
√40 is between two perfect square numbers √36 = 6 and √49 = 7.
Now, let's find the rational number to the nearest half between 6 and 7. The rational number that is halfway between 6 and 7 is 6.5.
Therefore, to the nearest half, √40 is between the whole number 6 and the rational number 6.5.
Convert 0.72(repeating) to a rational number in simplest form
To convert the repeating decimal 0.72(repeating) to a rational number, we can use the concept of "x" being equal to the repeating decimal and subtracting it from the original number.
Let's multiply 0.72(repeating) by 100 to move the decimal point two places to the right:
100x = 72.72(repeating)
Now, let's subtract x from 100x to eliminate the repeating decimal:
100x - x = 72.72(repeating) - 0.72(repeating)
99x = 72
Next, let's simplify the expression by dividing both sides by 99:
x = 72/99
To further simplify the fraction, we can divide the numerator and denominator by their greatest common divisor, which is 9:
x = 8/11
Therefore, the repeating decimal 0.72(repeating) can be converted to the rational number 8/11 in simplest form.