Which statement is true about the relationships between the number sets?(1 point)
Responses
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.
All integers are also rational numbers.
All integers are also rational numbers.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
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 both an integer and a whole number.
It is both an integer and a whole number.
It is an integer but not a rational number.
It is an integer but not a rational number.
It is a whole number but not an integer.
It is a whole number but not an integer.
It is both an integer and a whole number.
Which set of numbers is always irrational?(1 point)
Responses
non-terminating, non-repeating decimals
non-terminating, non-repeating decimals
terminating decimals
terminating decimals
repeating decimals
repeating decimals
positive decimals
non-terminating, non-repeating decimals
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)
The length of the diagonal can be found by multiplying the side length of the square by 2–√.
Given that the side length of the square park is 70 feet, we can approximate 2–√ as 2 - 1.4 = 0.6
Therefore, the approximate length of the diagonal is 70 feet * 0.6 = 42 feet.
Using rational approximations, what is an inequality statement comparing 91−−√
and 98−−√
? Enter <, >, or =.(1 point)
The inequality is: 91−−√
98−−√
To determine which statement is true about the relationships between the number sets, we can analyze each option.
1. Whole numbers include all positive integers and negative integers.
To verify this statement, we need to understand the definitions of whole numbers, positive integers, and negative integers.
- Whole numbers: These are the set of numbers that include zero (0) and all positive integers without any fractions or decimal parts.
- Positive integers: These are the set of numbers greater than zero (1, 2, 3, ...).
- Negative integers: These are the set of numbers less than zero (-1, -2, -3, ...).
By comparing these definitions, we can conclude that the statement is true because whole numbers encompass both positive and negative integers.
2. Some irrational numbers are also integers.
To evaluate this statement, let's understand the definitions involved.
- Irrational numbers: These are numbers that cannot be expressed as a fraction or ratio of two integers. They have an infinite number of non-repeating decimal places.
- Integers: These are the set of positive and negative whole numbers (including zero).
From these definitions, we can conclude that the statement is false. Irrational numbers and integers are two distinct sets of numbers; there is no overlap between them.
3. All integers are also rational numbers.
To determine the validity of this statement, let's examine the definitions.
- Integers: These are the set of positive and negative whole numbers (including zero).
- Rational numbers: These are numbers that can be expressed as a fraction or ratio of two integers.
By comparing these definitions, we can confirm that the statement is true. All integers can be expressed as a ratio of two integers, making them a subset of rational numbers.
4. Not all natural numbers are real numbers.
To assess this statement, we need explanations for natural numbers and real numbers.
- Natural numbers: These are the set of counting numbers (1, 2, 3, ...).
- Real numbers: These include all rational and irrational numbers, covering all possible numbers on the number line.
By comparing these definitions, we can ascertain that the statement is true. Real numbers encompass both natural numbers and many other numbers like fractions, decimals, irrational numbers, etc.
In conclusion, the statement "Whole numbers include all positive integers and negative integers" is true, as stated in option 1.