Which statement is true about the relationships between the number sets?(1 point)
Responses
All integers are also rational numbers.
All integers are also rational numbers.
Whole numbers include all positive integers and negative integers.
Whole numbers include all positive integers and negative integers.
Some irrational numbers are also integers.
Some irrational numbers are also integers.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
All integers are also rational numbers.
Which of the following is true about 9?(1 point)
Responses
It is an integer but not a rational number.
It is an integer but not a rational number.
It is both an integer and a whole number.
It is both an integer and a whole number.
It is a whole number but not an integer.
It is a whole number but not an integer.
It is an integer but not a whole numb
It is both an integer and a whole number.
Four people have found the distance in kilometers across a small bridge using different methods.
Their results are given in the table. Order the distances from least to greatest.
(1 point)
Responses
512, 28−−√, 5.5¯¯¯, 234
512, 28−−√, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 234
28−−√, 5.5¯¯¯, 234, 512
28−−√, 5.5¯¯¯, 234, 512
234 , 5.5¯¯¯, 28−−√, 512
234 , 5.5¯¯¯, 28−−√, 512
5.5¯¯¯, 28−−√, 234, 512
Four people have found the distance in kilometers across a small bridge using different methods.
Their results are given in the table. Order the distances from least to greatest.
512, 28−−√, 5.5¯¯¯, 234
512, 28−−√, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 234
28−−√, 512, 5.5¯¯¯, 234
28−−√, 5.5¯¯¯, 234, 512
28−−√, 5.5¯¯¯, 234, 512
234 , 5.5¯¯¯, 28−−√, 512
234 , 5.5¯¯¯, 28−−√, 512
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234, 5.5¯¯¯, 28−−√, 512
Which set of numbers is always irrational?(1 point)
Responses
terminating decimals
terminating decimals
non-terminating, non-repeating decimals
non-terminating, non-repeating decimals
repeating decimals
repeating decimals
positive decimals
non-terminating, non-repeating decimals
Question
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)
ft.
To find the length from one corner to an opposite corner of the square park, we can use the formula for the diagonal of a square. The diagonal of a square is equal to the side length times the square root of 2.
Given the side length of the square park is 70 feet, we can substitute this value into the formula:
Diagonal = side length * √2
Diagonal = 70 * √2
Now, we can approximate the value of √2 using 1.4:
Diagonal ≈ 70 * 1.4
Diagonal ≈ 98 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 98 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 rational number to the nearest half that 30−−√ is between, we can consider the values on a number line.
The square root of 30, 30−−√, is approximately 5.48. To find the whole number and rational number to the nearest half, we need to find the closest values to 5.48 on the number line.
The whole number to the left of 5.48 is 5, and the whole number to the right of 5.48 is 6.
To find the rational number to the nearest half, we need to determine the closer of the two halves: 5.5 and 6. To do this, we can measure the distance between 5.48 and each of the halves.
The distance between 5.48 and 5.5 is 0.02, and the distance between 5.48 and 6 is 0.52. Since 0.02 is closer to 5.5 than 6, we can conclude that the rational number to the nearest half is 5.5.
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 8 and 8.5
between 8 and 8.5
between 7.5 and 8
between 7.5 and 8
between 9 and 9.5
between 9 and 9.5
To determine the whole number and rational number to the nearest half that 68−−√ is between, we can consider the values on a number line.
The square root of 68, 68−−√, is approximately 8.25. To find the whole number and rational number to the nearest half, we need to find the closest values to 8.25 on the number line.
The whole number to the left of 8.25 is 8, and the whole number to the right of 8.25 is 9.
To find the rational number to the nearest half, we need to determine the closer of the two halves: 8 and 8.5. To do this, we can measure the distance between 8.25 and each of the halves.
The distance between 8.25 and 8 is 0.25, and the distance between 8.25 and 8.5 is 0.25 as well. Since the distances are equal, we can choose either 8 or 8.5 as the rational number to the nearest half.
Therefore, 68−−√ is between 8 and 8.5 (or 8.25) on the number line.