Which statement is true about the relationships between the number sets?(1 point)

Question

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.

Not all natural numbers are real numbers.
Not all natural numbers are real numbers.

Some irrational numbers are also integers.

Answer 1

Some irrational numbers are also integers.

Answer 2

Which of the following is true about 9?(1 point)
Responses

It is an integer but not a whole number.
It is an integer but not 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 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.

Answer 3

It is both an integer and a whole number.

Answer 4

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

5 1/2, 28−−√, 5.5¯¯¯, 23/4

28−−√, 5 1/2, 5.5¯¯¯, 23/4

28−−√, 5.5¯¯¯, 23/4, 5 1/2

23/4 , 5.5¯¯¯, 28−−√, 5 1/2

Answer 5

5 1/2, 5.5¯¯¯, 23/4, 28−−√

Answer 6

Which set of numbers is always irrational?(1 point)
Responses

non-terminating, non-repeating decimals
non-terminating, non-repeating decimals

positive decimals
positive decimals

repeating decimals
repeating decimals

terminating decimals

Answer 7

non-terminating, non-repeating decimals

Answer 8

he 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?

Answer 9

To find the length from one corner to an opposite corner of a square, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

In this case, the side length of the square park is 70 feet and the diagonal is 2–√ times the side length.

So, let's calculate the length of the diagonal using the provided approximation for √2, which is 1.4:

Diagonal = 2–√ * Side length
Diagonal = 2 * 1.4 * 70
Diagonal = 2.8 * 70
Diagonal = 196 feet

Therefore, the approximate length from one corner to an opposite corner of the square park is 196 feet.

Answer 10

Using rational approximations, what is an inequality statement comparing 91−−√
and 98−−√
? Enter <, >, or =.(1 point)
The inequality is: 91−−√___98−−√

Answer 11

To compare 91−−√ and 98−−√ using rational approximations, we can round each square root to the nearest integer.

Approximating the square root of 91: √91 ≈ 9.54, which we can round down to 9.
Approximating the square root of 98: √98 ≈ 9.90, which we can round up to 10.

So, the inequality is:

9 < 10

Therefore, the inequality statement comparing 91−−√ and 98−−√ is: 91−−√ < 98−−√