To find the circumference of a circle with a diameter of 1/2 inch, we can use the formula C = πd, where C is the circumference and d is the diameter.
Given that the diameter is 1/2 inch and using the approximation pi ≈ 3.14, we can substitute these values into the formula to find the circumference.
C = 3.14 × (1/2)
C = 3.14/2
C ≈ 1.57
Therefore, the approximate circumference of a circle with a diameter of 1/2 inch is 1.57 inches.
The circumference of a circle equals pi times the diameter. Using 3.14 to approximate pi, what is the approximate circumference in inches of a circle with a diameter of 1/2 in.?
39 answers
9/4 is close to the square root of what integer?
To find the square root of an integer close to 9/4, we can simply square integers until we get close to 9/4.
Let's start with the square of 1:
1^2 = 1
Next, let's try the square of 2:
2^2 = 4
The square of 2 is the closest to 9/4 since it is 4 and 9/4 is equal to 2.25. So, 9/4 is close to the square root of 4.
Let's start with the square of 1:
1^2 = 1
Next, let's try the square of 2:
2^2 = 4
The square of 2 is the closest to 9/4 since it is 4 and 9/4 is equal to 2.25. So, 9/4 is close to the square root of 4.
Categorize each statement as true or false(4 points)
True False
√11 is between 3 and 4, √33 is greater that 6, √60 is less that 8 √18 is between 5 and 6
True False
√11 is between 3 and 4, √33 is greater that 6, √60 is less that 8 √18 is between 5 and 6
True False
√11 is between 3 and 4 √33 is greater than 6
√60 is less than 8 √18 is between 5 and 6
√11 is between 3 and 4 √33 is greater than 6
√60 is less than 8 √18 is between 5 and 6
Categorize each statement as true or false(4 points)
True
False
√11 is between 3 and 4,
√33 is greater that 6,
√60 is less that 8
√18 is between 5 and 6
True
False
√11 is between 3 and 4,
√33 is greater that 6,
√60 is less that 8
√18 is between 5 and 6
True
False
True
False
False
True
False
3√5
is a rational number because it's a fraction
true or false?
is a rational number because it's a fraction
true or false?
False
What could the possible irrational number be as identified by the dot
\/
|---------|---
5 6
(1 point)
6.9
6.9
6–√
square root of 6
40−−√
square root of 40
60/10
\/
|---------|---
5 6
(1 point)
6.9
6.9
6–√
square root of 6
40−−√
square root of 40
60/10
The possible irrational number as identified by the dot in that range would likely be the square root of 6, represented as 6–√.
Identify which condition is necessary for a number to be a rational. (1 point)
Responses
It must be able to be expressed as an integer divided by a nonzero integer
It must be able to be expressed as an integer divided by a nonzero integer
It must not be negative
It must not be negative
It must be a fraction
It must be a fraction
It must not be an endless decimal
Responses
It must be able to be expressed as an integer divided by a nonzero integer
It must be able to be expressed as an integer divided by a nonzero integer
It must not be negative
It must not be negative
It must be a fraction
It must be a fraction
It must not be an endless decimal
The correct response is:
It must be able to be expressed as an integer divided by a nonzero integer
It must be able to be expressed as an integer divided by a nonzero integer
Which of the following is irrational?(1 point)
Responses
3.636363636363636...
3.636363636363636...
52.781654292
52.781654292
5√7
the fraction with numerator square root of 5 and denominator 7
−7837
Responses
3.636363636363636...
3.636363636363636...
52.781654292
52.781654292
5√7
the fraction with numerator square root of 5 and denominator 7
−7837
The irrational number among the options is 5√7, which is the number represented as the square root of 5 divided by 7.
Which of the following is irrational?(1 point)
Responses
3.636363636363636...
3.636363636363636...
52.781654292
52.781654292
5√7
the fraction with numerator square root of 5 and denominator 7
−78/37
Responses
3.636363636363636...
3.636363636363636...
52.781654292
52.781654292
5√7
the fraction with numerator square root of 5 and denominator 7
−78/37
The irrational number among the options is 5√7, which is the number represented as the square root of 5 divided by 7.
Using a number line, what is the approximate number value of 103−−−√? Provide your answer in decimal form, rounded to the nearest hundredth.(1 point)
103−−−√ is approximately
103−−−√ is approximately
To approximate the value of √103, we can use a number line or a calculator. Rounding to the nearest hundredth, we find that √103 is approximately 10.15.
Using a number line, what whole number and rational number to the nearest half is 10−−√ between?(1 point)
10−−√ is between _ and _ .
10−−√ is between _ and _ .
To determine the whole number and rational number to the nearest half that 10−−√ is between, we can use a number line or a calculator to estimate the value.
By calculating or approximating the square root of 10, we find that it is approximately 3.16.
So, 10−−√ is between the whole number 3 and the rational number 3.5.
By calculating or approximating the square root of 10, we find that it is approximately 3.16.
So, 10−−√ is between the whole number 3 and the rational number 3.5.
Using a number line, what whole number and rational number to the nearest half is 97−−√ between?(1 point)
97−−√ is between _ and _ .
97−−√ is between _ and _ .
To determine the whole number and rational number to the nearest half that 97−−√ is between, we can use a number line or a calculator to estimate the value.
By calculating or approximating the square root of 97, we find that it is approximately 9.85.
So, 97−−√ is between the whole number 9 and the rational number 9.5.
By calculating or approximating the square root of 97, we find that it is approximately 9.85.
So, 97−−√ is between the whole number 9 and the rational number 9.5.
wrong
Apologies for the incorrect response.
To determine the whole number and rational number to the nearest half that 97−−√ is between, we can use a number line or a calculator to estimate the value.
By calculating or approximating the square root of 97, we find that it is approximately 9.85.
So, 97−−√ is between the whole number 9 and the rational number 9.5.
To determine the whole number and rational number to the nearest half that 97−−√ is between, we can use a number line or a calculator to estimate the value.
By calculating or approximating the square root of 97, we find that it is approximately 9.85.
So, 97−−√ is between the whole number 9 and the rational number 9.5.
Using rational approximations, what is an inequality statement comparing 21−−√ and 17−−√? Enter <, >, or =.
The inequality is: 21−−√ _ 17−−√.
The inequality is: 21−−√ _ 17−−√.
To compare 21−−√ and 17−−√ using rational approximations, we can round each square root to a rational number.
Approximating 21−−√ as 4.58 and 17−−√ as 4.12, we can conclude that 21−−√ is greater than 17−−√.
Therefore, the inequality is: 21−−√ > 17−−√.
Approximating 21−−√ as 4.58 and 17−−√ as 4.12, we can conclude that 21−−√ is greater than 17−−√.
Therefore, the inequality is: 21−−√ > 17−−√.
Using rational approximations, what is an inequality statement comparing π and 8−−√? Enter <, >, or =.
The inequality is: π _ 8−−√.
The inequality is: π _ 8−−√.
To compare π and 8−−√ using rational approximations, we can substitute the value of π as approximately 3.14 and approximate 8−−√ as 2.83.
Comparing these values, we see that π is greater than 8−−√.
Therefore, the inequality is: π > 8−−√.
Comparing these values, we see that π is greater than 8−−√.
Therefore, the inequality is: π > 8−−√.
Using a number line, what is the approximate value of 19−−√?
4.5
4.5
4.38
4.38
4.13
4.13
4.25
4.25
4.5
4.5
4.38
4.38
4.13
4.13
4.25
4.25
To determine the approximate value of 19−−√ using a number line, we can estimate its position.
By approximating the square root of 19, we find that it is approximately 4.36.
Based on this approximation, the value of 19−−√ is closest to 4.36.
Therefore, the option closest to the approximate value of 19−−√ on the number line is 4.38.
By approximating the square root of 19, we find that it is approximately 4.36.
Based on this approximation, the value of 19−−√ is closest to 4.36.
Therefore, the option closest to the approximate value of 19−−√ on the number line is 4.38.
Using a number line, what whole number and rational number to the nearest half is 105−−−√ between?
between 11 and 11.5
between 11 and 11.5
between 10 and 10.5
between 10 and 10.5
between 10.5 and 11
between 10.5 and 11
between 9.5 and 10
between 11 and 11.5
between 11 and 11.5
between 10 and 10.5
between 10 and 10.5
between 10.5 and 11
between 10.5 and 11
between 9.5 and 10
To determine the whole number and rational number to the nearest half that 105−−−√ is between, we can use a number line or a calculator to estimate the value.
By approximating the square root of 105, we find that it is approximately 10.24.
So, 105−−−√ is between the whole number 10 and the rational number 10.5.
Therefore, the correct answer is: between 10 and 10.5.
By approximating the square root of 105, we find that it is approximately 10.24.
So, 105−−−√ is between the whole number 10 and the rational number 10.5.
Therefore, the correct answer is: between 10 and 10.5.
Using rational approximations, what statement is true?
48−−√>36−−√
start root 48 end root greater than start root 36 end root
49−−√>7
start root 49 end root greater than 7
48−−√<36−−√
start root 48 end root less than start root 36 end root
49−−√<7
48−−√>36−−√
start root 48 end root greater than start root 36 end root
49−−√>7
start root 49 end root greater than 7
48−−√<36−−√
start root 48 end root less than start root 36 end root
49−−√<7
To compare the values 48−−√ and 36−−√ using rational approximations, we can round each square root to a rational number.
Approximating 48−−√ as 6.93 and 36−−√ as 6, we see that 48−−√ is greater than 36−−√.
Therefore, the statement that is true is: 48−−√ > 36−−√.
Approximating 48−−√ as 6.93 and 36−−√ as 6, we see that 48−−√ is greater than 36−−√.
Therefore, the statement that is true is: 48−−√ > 36−−√.
Using rational approximations, what statement is true?
71−−√>61−−√
start root 71 end root greater than start root 61 end root
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
81−−√<9
start root 81 end root less than 9
81−−√>9
71−−√>61−−√
start root 71 end root greater than start root 61 end root
71 −−−√<61−−√
start root 71 end root less than start root 61 end root
81−−√<9
start root 81 end root less than 9
81−−√>9
To compare the values 71−−√ and 61−−√ using rational approximations, we can round each square root to a rational number.
Approximating 71−−√ as 8.4 and 61−−√ as 7.8, we see that 71−−√ is greater than 61−−√.
Therefore, the statement that is true is: 71−−√ > 61−−√.
Approximating 71−−√ as 8.4 and 61−−√ as 7.8, we see that 71−−√ is greater than 61−−√.
Therefore, the statement that is true is: 71−−√ > 61−−√.
Using rational approximations, what statement is true?
12 −−−√ >π
start root 12 end root greater than pi
16−−√>4
start root 16 end root greater than 4
12 −−−√<π
start root 12 end root less than pi
16 −−−√<4
12 −−−√ >π
start root 12 end root greater than pi
16−−√>4
start root 16 end root greater than 4
12 −−−√<π
start root 12 end root less than pi
16 −−−√<4
To compare the values of 12−−−√ and π using rational approximations, we can round each square root and the value of π to rational numbers.
Approximating 12−−−√ as 3.46 and π as 3.14, we see that 12−−−√ is greater than π.
Therefore, the statement that is true is: 12−−−√ > π.
Approximating 12−−−√ as 3.46 and π as 3.14, we see that 12−−−√ is greater than π.
Therefore, the statement that is true is: 12−−−√ > π.
9 answers