Asked by Denki

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

All rational numbers are also integers.
All rational numbers are also integers.

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

Some irrational numbers are also integers.
Some irrational numbers are also integers.

Whole numbers include all natural numbers and 0.
Whole numbers include all natural numbers and 0.
Answered by Denki
Which of the following is true about −9?(1 point)
Responses

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

It is an integer but not a whole number.
Answered by Denki
A sign in a gas station advertises gas at the rate of $3.39910 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?(1 point)
Answered by Denki
Which set of numbers is always rational?(1 point)
Responses

integers
integers

positive numbers
positive numbers

fractions
fractions

decimals
Answered by Denki
The height of an equilateral triangle equals 3√2 times the side length. Using 74 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)
$$
Answered by Denki
so what is the answer?
Answered by Denki
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 700 feet on a side?(1 point)
Answered by Denki
the answer?
Answered by Denki
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between
and
.
Answered by Denki
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses

between 7.5 and 8
between 7.5 and 8

between 8 and 8.5
between 8 and 8.5

between 7 and 7.5
between 7 and 7.5

between 8.5 and 9
Answered by Denki
so its between?
Answered by Denki
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√
8–√8.
Answered by Denki
Write 6,739 in expanded form.(1 point)
Responses

(6×1,000)+(7×100)+(3×10)+(0×1)
left parenthesis 6 times 1,000 right parenthesis plus left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 0 times 1 right parenthesis

(9×1,000)+(3×100)+(7×10)+(6×1)
left parenthesis 9 times 1,000 right parenthesis plus left parenthesis 3 times 100 right parenthesis plus left parenthesis 7 times 10 right parenthesis plus left parenthesis 6 times 1 right parenthesis

(7×100)+(3×10)+(9×1)
left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 9 times 1 right parenthesis

(6×1,000)+(7×100)+(3×10)+(9×1)
left parenthesis 6 times 1,000 right parenthesis plus left parenthesis 7 times 100 right parenthesis plus left parenthesis 3 times 10 right parenthesis plus left parenthesis 9 times 1 right parenthesis
Answered by Denki
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
Answered by Denki
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
Answered by Denki
Which of the following is a rational number between 5 and 514?(1 point)
Responses

26−−√
start root 26 end root

517
5 Start Fraction 1 over 7 end fraction

525
5 Start Fraction 2 over 5 end fraction

513
5 Start Fraction 1 over 3 end fraction
Answered by Denki
so its option 4?
Answered by GPT 3.5
All rational numbers are also integers.
Answered by GPT 3.5
It is both an integer and a whole number.
Answered by GPT 3.5
A gallon costs $3.39910, writing the price strictly as a decimal.
Answered by GPT 3.5
fractions
Answered by GPT 3.5
The height of an equilateral triangle equals 3√2 times the side length. Using 74 for the square root of 3, the approximate height in meters of an equilateral triangle with a side length of 8 meters can be calculated as:

Height = 3√2 * Side Length
Height = 3 * 74 * 2 * 8 / 100
Height = 1.776 meters
Answered by GPT 3.5
The approximate height of an equilateral triangle with a side length of 8 meters, using 74 for the square root of 3, is 1.776 meters.
Answered by GPT 3.5
The diagonal of a square equals 2−√ times the side length. Using 1.4 for the square root of 2, the approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side can be calculated as:

Diagonal = (2−√) * Side Length
Diagonal = (2−1.4) * 700
Diagonal = 0.6 * 700
Diagonal = 420 feet
Answered by GPT 3.5
Apologies for the confusion. The approximate length in feet from one corner to an opposite corner of a square park that is 700 feet on a side, using 1.4 for the square root of 2, is 420 feet.
Answered by GPT 3.5
To find the whole number and rational number to the nearest half that 40−−√ is between, we can use a number line.

Since the square root of 40 is approximately 6.325, we can determine the numbers to the nearest half by looking at the numbers between 6 and 7 on the number line.

So, 40−−√ is between 6 and 7 on the number line.

Therefore, the whole number to the nearest half is 6, and the rational number to the nearest half is 6.5.
Answered by GPT 3.5
To find the whole number and rational number to the nearest half that 58−−√ is between, we can use a number line.

Since the square root of 58 is approximately 7.615, we can determine the numbers to the nearest half by looking at the numbers between 7 and 8 on the number line.

So, 58−−√ is between 7 and 8 on the number line.

Therefore, the whole number to the nearest half is 7, and the rational number to the nearest half is 7.5.
Answered by GPT 3.5
Apologies for the confusion in my response. To clarify, 58−−√ is between 7 and 7.5 on the number line.
Answered by GPT 3.5
To compare 81−−√ and 8–√8 using rational approximations, we can calculate their approximate decimal values and make an inequality statement.

81−−√ is approximately equal to 9. 8–√8 is approximately equal to 8.828.

So, the inequality statement is: 81−−√ > 8–√8.
Answered by GPT 3.5
(6×1,000)+(7×100)+(3×10)+(9×1)
Answered by GPT 3.5
To express 811 as a repeating decimal, we can divide 811 by the denominator 999. This is because dividing by 999 creates a repeating decimal with a cycle of 3 digits (the length of the numerator 811).

811 ÷ 999 = 0.811811811...

So, the expression of 811 as a repeating decimal is 0.811̅, with the cycle of repeating digits marked by the bar over 811.
Answered by GPT 3.5
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can rewrite it as a fraction.

Let x = 0.72¯¯¯¯¯

Multiplying both sides of the equation by 1000 (to move the decimal point three places to the right) gives:

1000x = 720.72¯¯¯¯¯

Subtracting the equation x = 0.72¯¯¯¯¯ from 1000x = 720.72¯¯¯¯¯ gives:

999x = 720

Dividing both sides of the equation by 999 gives:

x = 720/999

Therefore, 0.72¯¯¯¯¯ as a rational number in simplest form is 720/999.
Answered by GPT 3.5
A rational number is any number that can be expressed as a fraction, where the numerator and denominator are both integers.

Among the given options, the rational number between 5 and 514 is 513, which can be expressed as 5 1/3 or 5⅓.
Answered by GPT 3.5
Apologies for the confusion in my previous response. No, the correct option is not 513.

Among the given options, the rational number between 5 and 514 is 517. It is a whole number, which makes it a rational number.