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.
To convert the repeating decimal 0.09¯¯¯¯¯ to a rational number in simplest form, we can use the method of repeated decimal as a fraction.
Let x = 0.09¯¯¯¯¯
We can multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 9.99¯¯¯¯¯
Now, we subtract the original equation from the multiplied equation to eliminate the repeating decimal:
100x - x = 9.99¯¯¯¯¯ - 0.09¯¯¯¯¯
99x = 9.90
Next, we divide both sides of the equation by 99 to solve for x:
x = 9.90 / 99
x = 0.1
Therefore, the rational number in simplest form for the repeating decimal 0.09¯¯¯¯¯ is 0.1.
The fraction equivalent of 0.7¯¯¯ is
To find the fraction equivalent of the repeating decimal 0.7¯¯¯, we can set x = 0.7¯¯¯ and subtract x from 10x to eliminate the repeating decimal.
Let x = 0.7¯¯¯
Multiply both sides by 10 to eliminate the repeating decimal:
10x = 7.7¯¯¯
Now subtract the original equation from the multiplied equation:
10x - x = 7.7¯¯¯ - 0.7¯¯¯
9x = 7
Divide both sides by 9 to solve for x:
x = 7 / 9
Therefore, the fraction equivalent of the repeating decimal 0.7¯¯¯ is 7/9.
Which of the following is an irrational number between 4 and 8?(1 point)
Responses
17−−√
square root of 17
5–√
square root of 5
12−−√
square root of 12
8–√
To determine which of the options is an irrational number between 4 and 8, we can calculate the square roots of each option and check if they fall within the given range.
Given Options:
- √17 (square root of 17)
- √5 (square root of 5)
- √12 (square root of 12)
- 8−√
Calculating the square roots:
- √17 ≈ 4.12
- √5 ≈ 2.24
- √12 ≈ 3.46
- 8−√ ≈ 7.59
Based on the calculations, the option that represents an irrational number between 4 and 8 is √17 (square root of 17), since it falls within the given range.
Which of the following rational numbers is not between 3–√ and 6–√
?(1 point)
Responses
1.8
1 point 8
4–√
square root of 4
1.5
1 point 5
2
To determine which of the given rational numbers is not between 3–√ and 6–√, we can compare the values of each number to the square roots.
Given Options:
- 1.8
- 4–√ (square root of 4)
- 1.5
- 2
Calculating the square roots:
- 3–√ ≈ 1.732 (rounded to three decimal places)
- 6–√ ≈ 2.449 (rounded to three decimal places)
Comparing the values:
- 1.8 is between 3–√ and 6–√.
- 4–√ is equal to 2 and falls between 3–√ and 6–√.
- 1.5 is between 3–√ and 6–√.
- 2 is between 3–√ and 6–√.
Based on the comparisons, none of the given options are not between 3–√ and 6–√. All of the options fall within the range mentioned.
Describe the relationship between integers and whole numbers. Are all integers also whole numbers? Are all whole numbers also integers? Give examples to support your answer.
The relationship between integers and whole numbers is that all integers are also whole numbers, but not all whole numbers are integers.
Integers are numbers that include all positive whole numbers, negative whole numbers, and zero. Examples of integers include -3, 0, and 5. These numbers can be represented on a number line including negative numbers, zero, and positive numbers.
On the other hand, whole numbers are non-negative numbers which include all positive integers and zero. Examples of whole numbers include 0, 1, and 6. These numbers are represented on a number line with no negative values.
From this, we can understand that all integers, which include both negative numbers and zero, are also whole numbers. However, whole numbers do not include negative integers. Therefore, not all whole numbers are integers.