Which statement is true about the relationships between the number sets?(1 point)
Responses
Whole numbers include all natural numbers and 0.
Not all natural numbers are real numbers.
All rational numbers are also integers.
Some irrational numbers are also integers.
The statement "It is both an integer and a whole number" is true about -9.
The statement "Whole numbers include all natural numbers and 0" is true.
Which of the following is true about −9?(1 point)
Responses
It is both an integer and a whole number.
It is a whole number but not an integer.
It is an integer but not a whole number.
It is an integer but not a rational number.
A sign in a gas station advertises gas at the rate of $3.39 9 over 10 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?
To write the price strictly as a decimal, we need to remove the fraction. To do so, we divide 9 by 10: $$\frac{9}{10} = 0.9$$
The gas is advertised at the rate of $3.39 + 0.9 per gallon.
To find the total cost, we add the whole dollar amount with the decimal amount: $$3.39 + 0.9 = 4.29$$
Therefore, a gallon of gas costs $4.29 when written strictly as a decimal.
Which set of numbers is always rational?(1 point)
Responses
decimals
integers
fractions
positive numbers
The set of numbers that is always rational is fractions.
The height of an equilateral triangle equals √3 over 2 times the side length. Using 7 over 4 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?(1 point)
To find the approximate height of the equilateral triangle, we can substitute the given values into the formula.
Height of an equilateral triangle = (√3/2) * side length
Substituting √3 = 7/4 and side length = 8:
Height = (7/4) * 8/2
= 7 * 8 / 4 * 2
= 56 / 8
= 7
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 7 meters.
To determine which statement is true about the relationships between the number sets, we need to understand the definitions of each set.
1. Whole numbers: Whole numbers include all the natural numbers (positive integers) including zero. So the statement "Whole numbers include all natural numbers and 0" is true.
2. Natural numbers: Natural numbers are the positive integers (1, 2, 3, ...). Real numbers include all the numbers on the number line, both positive and negative, including fractions and irrational numbers. Therefore, the statement "Not all natural numbers are real numbers" is true.
3. Rational numbers: Rational numbers are any numbers that can be expressed as a fraction of two integers. This includes integers (whole numbers and their negatives). So the statement "All rational numbers are also integers" is false because some rational numbers are not integers.
4. Irrational numbers: Irrational numbers are the numbers that cannot be expressed as a fraction of two integers. They include numbers like π and √2. Since irrational numbers are not integers, the statement "Some irrational numbers are also integers" is false.
Based on the explanations provided, the true statement about the relationships between the number sets is:
"Whole numbers include all natural numbers and 0."