Question
Using rational approximations, what is an inequality statement comparing 91−−√
and 98−−√
? Enter <, >, or =.(1 point)
The inequality is: 91−−√
98−−√
and 98−−√
? Enter <, >, or =.(1 point)
The inequality is: 91−−√
98−−√
Answers
GPT 3.5
The inequality is: 91−−√ < 98−−√
Write 2,468 in expanded form.(1 point)
Responses
(2 x 1,000) + (4 x 100) + (6 x 10) + (8 x 1)
(2 x 1,000) + (4 x 100) + (6 x 10) + (8 x 1)
(4 x 100) + (6 x 10) + (8 x 1)
(4 x 100) + (6 x 10) + (8 x 1)
(8 x 1,000) + (6 x 100) + (4 x 10) + (2 x 1)
(8 x 1,000) + (6 x 100) + (4 x 10) + (2 x 1)
(2 x 1,000) + (4 x 100) + (6 x 10) + (0 x 1
Responses
(2 x 1,000) + (4 x 100) + (6 x 10) + (8 x 1)
(2 x 1,000) + (4 x 100) + (6 x 10) + (8 x 1)
(4 x 100) + (6 x 10) + (8 x 1)
(4 x 100) + (6 x 10) + (8 x 1)
(8 x 1,000) + (6 x 100) + (4 x 10) + (2 x 1)
(8 x 1,000) + (6 x 100) + (4 x 10) + (2 x 1)
(2 x 1,000) + (4 x 100) + (6 x 10) + (0 x 1
GPT 3.5
The expanded form of 2,468 is:
(2 x 1,000) + (4 x 100) + (6 x 10) + (8 x 1)
(2 x 1,000) + (4 x 100) + (6 x 10) + (8 x 1)
Express 711
as a repeating decimal. Mark the cycle of repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.
(1 point)
as a repeating decimal. Mark the cycle of repeating digits with a bar.
Note: You will find the option to add a bar above text in the Geometry (∠
) keyboard.
(1 point)
GPT 3.5
The decimal representation of 711 as a repeating decimal is 0.711 (with the 1s repeating).
Convert 0.09¯¯¯¯¯
to a rational number in simplest form.(1 point)
to a rational number in simplest form.(1 point)
GPT 3.5
To convert the repeating decimal 0.09¯¯¯¯¯ to a rational number in simplest form, we can represent it as a fraction.
Let x = 0.09¯¯¯¯¯.
Then, 100x = 9.09¯¯¯¯¯.
Subtracting the equation x = 0.09¯¯¯¯¯ from 100x = 9.09¯¯¯¯¯, we get:
99x = 9
Dividing both sides of the equation by 99, the coefficient of x, we get:
x = 9/99
Simplifying the fraction 9/99, we can divide both the numerator and the denominator by 9, resulting in:
x = 1/11
Therefore, 0.09¯¯¯¯¯ is equal to 1/11 in simplest form.
Let x = 0.09¯¯¯¯¯.
Then, 100x = 9.09¯¯¯¯¯.
Subtracting the equation x = 0.09¯¯¯¯¯ from 100x = 9.09¯¯¯¯¯, we get:
99x = 9
Dividing both sides of the equation by 99, the coefficient of x, we get:
x = 9/99
Simplifying the fraction 9/99, we can divide both the numerator and the denominator by 9, resulting in:
x = 1/11
Therefore, 0.09¯¯¯¯¯ is equal to 1/11 in simplest form.
Convert 0.7¯¯¯
to a fraction.(1 point)
The fraction equivalent of 0.7¯¯¯ is
to a fraction.(1 point)
The fraction equivalent of 0.7¯¯¯ is
GPT 3.5
To convert the repeating decimal 0.7¯¯¯ to a fraction, we can represent it as x:
x = 0.7¯¯¯
Multiplying both sides of the equation by 10, we get:
10x = 7.7¯¯¯
Subtracting the equation x = 0.7¯¯¯ from 10x = 7.7¯¯¯, we get:
9x = 7
Dividing both sides of the equation by 9, the coefficient of x, we get:
x = 7/9
Therefore, the fraction equivalent of 0.7¯¯¯ is 7/9.
x = 0.7¯¯¯
Multiplying both sides of the equation by 10, we get:
10x = 7.7¯¯¯
Subtracting the equation x = 0.7¯¯¯ from 10x = 7.7¯¯¯, we get:
9x = 7
Dividing both sides of the equation by 9, the coefficient of x, we get:
x = 7/9
Therefore, the fraction equivalent of 0.7¯¯¯ is 7/9.
Which of the following is an irrational number between 4 and 8?(1 point)
Responses
5–√
square root of 5
12−−√
square root of 12
17−−√
square root of 17
8–√
Responses
5–√
square root of 5
12−−√
square root of 12
17−−√
square root of 17
8–√
GPT 3.5
The irrational number between 4 and 8 is the square root of 5 (5−−√).
Which of the following rational numbers is not between 3–√ and 6–√
?(1 point)
Responses
1.8
1 point 8
4–√
square root of 4
1.5
1 point 5
2
?(1 point)
Responses
1.8
1 point 8
4–√
square root of 4
1.5
1 point 5
2
GPT 3.5
The rational number that is not between 3−−√ and 6−−√ is 4−−√.
Describe the relationship between integers and whole numbers. Are all integers also whole numbers? Are all whole numbers also integers? Give examples to support your answer.(4 points)
GPT 3.5
In mathematics, integers and whole numbers are related, but they are not exactly the same.
Integers are the set of positive and negative whole numbers, including zero. Therefore, all integers are whole numbers. For example, -3, 0, and 7 are integers, and they are also whole numbers.
On the other hand, whole numbers are the set of non-negative numbers, including zero. This means that all whole numbers are integers, except for negative integers. For example, 0, 7, and 12 are whole numbers, and they are also integers. However, -3 is an integer but not a whole number because it is negative.
To summarize, while all integers are also whole numbers, not all whole numbers are integers because whole numbers do not include negative values.
Integers are the set of positive and negative whole numbers, including zero. Therefore, all integers are whole numbers. For example, -3, 0, and 7 are integers, and they are also whole numbers.
On the other hand, whole numbers are the set of non-negative numbers, including zero. This means that all whole numbers are integers, except for negative integers. For example, 0, 7, and 12 are whole numbers, and they are also integers. However, -3 is an integer but not a whole number because it is negative.
To summarize, while all integers are also whole numbers, not all whole numbers are integers because whole numbers do not include negative values.