Hey bot how would I do the work for this answer. 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 70 feet on a side?(1 point)
To find the approximate length from one corner to an opposite corner of a square park, we can use the formula given: diagonal = (2–√) * side length.
Given information:
Square side length = 70 feet
Approximate square root of 2 = 1.4
First, we can substitute the values into the formula:
diagonal = (2–√) * side length
diagonal = (2–1.4) * 70
Next, simplify the equation:
diagonal = (0.6) * 70
Finally, calculate the diagonal length:
diagonal = 42 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 42 feet.
Using a number line, what whole number and rational number to the nearest half is 30−−√
between?(1 point)
30−−√ is between
and
To determine the whole number and the rational number to the nearest half that 30−−√ is between, we need to find the two numbers that are closest to but on either side of 30−−√.
Given information:
30−−√
We can estimate the value of 30−−√:
√30 is approximately equal to 5.48 (rounded to two decimal places)
Next, we need to find the whole number and rational number to the nearest half that are on either side of 5.48 on the number line:
5.5 is the rational number to the nearest half that is greater than 5.48.
5 is the whole number to the nearest half that is less than 5.48.
Therefore, 30−−√ is between 5 and 5.5 on the number line.
Using a number line, what whole number and rational number to the nearest half is 68−−√
between?(1 point)
Responses
between 8.5 and 9
between 8.5 and 9
between 7.5 and 8
between 7.5 and 8
between 8 and 8.5
between 8 and 8.5
between 9 and 9.5
To determine the whole number and rational number to the nearest half that 68−−√ is between, we need to find the two numbers that are closest to but on either side of 68−−√.
Given information:
68−−√
First, we need to estimate the value of 68−−√:
√68 is approximately equal to 8.246 (rounded to three decimal places)
Next, we need to find the whole number and rational number to the nearest half that are on either side of 8.246 on the number line:
8 is the whole number to the nearest half that is less than 8.246.
8.5 is the rational number to the nearest half that is greater than 8.246.
Therefore, 68−−√ is between 8 and 8.5 on the number line.
Using rational approximations, what is an inequality statement comparing 91−−√
and 98−−√
? Enter <, >, or =.(1 point)
The inequality is: 91−−√
98−−√
To determine an inequality statement comparing 91−−√ and 98−−√ using rational approximations, we can round the square roots to the nearest whole number.
Given information:
Square root of 91 ≈ 9.54 (rounded to two decimal places)
Square root of 98 ≈ 9.899 (rounded to three decimal places)
Rounded values:
Square root of 91 ≈ 10
Square root of 98 ≈ 10
Since 10 is equal to 10, the inequality statement would be:
91−−√ = 98−−√
Express 711
as a repeating decimal. Mark the cycle of repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard. show the work
To express 711 as a repeating decimal, we can divide 711 by another number repeatedly until the division becomes repeating.
711 ÷ 99 = 7 with a remainder of 24
To continue the division, we add a 0 after the decimal point and divide 240 by 99.
240 ÷ 99 = 2 with a remainder of 42
Again, we add a 0 after the decimal point and divide 420 by 99.
420 ÷ 99 = 4 with a remainder of 24
Once more, we add a 0 after the decimal point and divide 240 by 99.
240 ÷ 99 = 2 with a remainder of 42
The division pattern repeats with the remainder 24 followed by 42. Therefore, the repeating decimal representation of 711 is:
7.242424...
You can mark the cycle of repeating digits by placing a bar over the numbers that repeat like this:
7.24̅
Convert 0.09¯¯¯¯¯
to a rational number in simplest form.