Question

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.
Answer
What is a number that is a whole number but not a natural number?
Answer
A sign in a gas station advertises gas at the rate of $3.39 9/10 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?
Answer
Which set of numbers is always rational?(1 point)
Responses

decimals
decimals

integers
integers

positive numbers
positive numbers

fractions
Answer
The height of an equilateral triangle equals 3√/2 times the side length. Using 7/4 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
Answer
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?
Answer
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between
Answer
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√
8–√8.
Answer
Using rational approximations, what is an inequality statement comparing 81−−√ and88–√? Enter <, >, or =.(1 point)
The inequality is: 81−−√
88-√.
Answer
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar
Answer
Convert 0.72¯¯¯¯¯ to a rational number in simplest form
Answered by GPT 3.5
The correct answer is: It is both an integer and a whole number.
Answered by GPT 3.5
A number that is a whole number but not a natural number is zero (0). Natural numbers start from 1 onwards, so they do not include zero. However, zero is still considered a whole number because it is not a fraction or a decimal.
Answered by GPT 3.5
To write the price strictly as a decimal, we need to convert the fraction 9/10 to a decimal.

To do this, we divide 9 by 10:

9 ÷ 10 = 0.9

Therefore, the fraction 9/10 can be represented as the decimal 0.9.

So, the cost of a gallon of gas is $3.39 + $0.9 = $3.39 + $0.90 = $4.29.

Therefore, a gallon of gas costs $4.29.
Answered by GPT 3.5
The correct answer is: fractions.

Fractions are always rational numbers because they can be expressed as the quotient of two integers.
Answered by GPT 3.5
To find the height of an equilateral triangle, you can use the formula height = (sqrt(3)/2) * side length.

Given that we will use 7/4 as the approximation for the square root of 3, we can substitute it into the formula:

height = (7/4)(8) = 14 meters.

Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is 14 meters.
Answered by GPT 3.5
To find the length of the diagonal of a square, you can use the formula diagonal = (2 - √2) * side length.

Given that we will use 1.4 as the approximation for the square root of 2, we can substitute it into the formula:

diagonal = (2 - 1.4)(700) = 0.6 * 700 = 420 feet.

Therefore, the approximate length from one corner to an opposite corner of the square park with a side length of 700 feet is 420 feet.
Answered by GPT 3.5
To determine the whole number and rational number to the nearest half that 40-√ is between, we can estimate the square root of 40.

The square root of 40 is approximately 6.32.

To find the whole number and rational number to the nearest half that is between 6 and 7, we look at the number line:

5.5, 6, 6.5, 7

Since 6.32 is closer to 6.5, the whole number and rational number to the nearest half that 40-√ is between are 6 and 6.5.
Answered by GPT 3.5
To compare 81-√ and 8-√8 using rational approximations, we need to find approximate decimal values for each term.

81-√ is approximately equal to 9, since the square root of 81 is 9.

8-√8 is approximately equal to 4.83, since the square root of 8 is approximately 2.83, and subtracting this value from 8 gives us 4.17.

Comparing the values, we have:

9 > 4.83

Therefore, the inequality statement comparing 81-√ and 8-√8 is: 81-√ > 8-√8.
Answered by GPT 3.5
To compare 81-√ and 88-√ using rational approximations, we need to find approximate decimal values for each term.

81-√ is approximately equal to 9, since the square root of 81 is 9.

88-√ is approximately equal to 9.38, since the square root of 88 is approximately 9.38.

Comparing the values, we have:

9 < 9.38

Therefore, the inequality statement comparing 81-√ and 88-√ is: 81-√ < 88-√.
Answered by GPT 3.5
To express 8/11 as a repeating decimal, we perform long division:

0.727272...

The digits 72 repeat infinitely, so we can place a bar over them to indicate the repeating cycle. Therefore, 8/11 is equal to 0.72¯¯¯.
Answered by GPT 3.5
To convert 0.72¯¯¯ to a rational number in simplest form, we can set x = 0.72¯¯¯ and multiply both sides of the equation by 100 to eliminate the repeating decimal:

100x = 72.7272...

Now, let's subtract the original equation from the multiplied equation to eliminate the repeating decimal:

100x - x = 72.7272... - 0.7272...

Simplifying this equation gives us:

99x = 72

Now, we can solve for x by dividing both sides of the equation by 99:

x = 72/99

To simplify the fraction 72/99, we can divide both the numerator and denominator by their greatest common divisor, which is 9:

72 ÷ 9 = 8
99 ÷ 9 = 11

Therefore, 0.72¯¯¯ is equal to the rational number 8/11 in simplest form.