Which statement is true about the relationships between the number sets? (1 point)
• Some irrational numbers are also integers.
• Whole numbers include all positive integers and negative integers.
• All integers are also rational numbers.
• Not all natural numbers are real numbers.
All integers are also rational numbers.
Which set of numbers is always irrational? (1 point)
O non-terminating, non-repeating decimals
O repeating decimals
O positive decimals
• terminating decimals
The set of numbers that is always irrational is non-terminating, non-repeating decimals.
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 70 feet on a side? (1 point)
To find the length from one corner to an opposite corner of a square park, we can use the Pythagorean theorem. In this case, the diagonal is equal to 2 times the side length.
Given that the side length of the square park is 70 feet, we can calculate the length of the diagonal as follows:
diagonal = 2 * side length = 2 * 70 feet = 140 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 140 feet.
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 70 feet on a side? (1 point)
***?????***
I apologize for the confusion in my previous response. To find the approximate length in feet from one corner to an opposite corner of a square park, we need to use the diagonal formula.
Given that the side length of the square park is 70 feet, the diagonal would be:
diagonal = 2 * side length = 2 * 70 feet = 140 feet
Therefore, the approximate length from one corner to an opposite corner of the square park is 140 feet.
Using a number line, what whole number and rational number to the nearest half is 68 between? (1 point)
To find the whole number and rational number to the nearest half that 68 is between, we can use a number line.
Let's look at the number line below:
... | 67.5 | ---- 68 ----- | 68.5 | ...
From the number line, we can see that 68 is located exactly halfway between the two whole numbers 67 and 68. Therefore, 68 is the whole number to the nearest half.
To find the rational number to the nearest half, we can use the same number line. The number line shows that 68 is closer to 67.5 than to 68.5. Therefore, the rational number to the nearest half is 67.5.
What’s the square root of 68
The square root of 68 is approximately 8.246.
Explain how please.
To find the square root of 68, we can use various methods such as long division, prime factorization, or estimation.
One method is to use estimation by finding the perfect square that is closest to 68. Since 8^2 = 64 and 9^2 = 81, we can estimate that the square root of 68 falls between 8 and 9.
We can then refine our estimation by considering the decimal part. To do this, we can use the method of averaging. We start with a guess, let's say 8.5, and square it: 8.5^2 = 72.25. This is larger than 68, so our guess is too high.
Next, we choose a smaller number, let's say 8.2, and square it: 8.2^2 = 67.24. This is less than 68, so our guess is too low.
We can continue to refine our estimate by choosing numbers closer to 8.2 and 8.5, such as 8.3, 8.4, and so on, until we find a number whose square is very close to 68. By doing this, we find that the square root of 68 is approximately 8.246.
It's important to note that the square root of 68 is an irrational number, meaning it cannot be expressed as an exact fraction or terminating decimal. However, we can still approximate its value using methods like the one described above.
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Which statement is true about the relationships between the number sets?(1 point)
Responses
All integers are also rational numbers.
All integers are also rational numbers.
Not all natural numbers are real numbers.
Not all natural numbers are real numbers.
Some irrational numbers are also integers.
The statement "Not all natural numbers are real numbers" is true about the relationships between the number sets.
Using rational approximations, what is an inequality statement comparing v91 and v98? Enter <, >, or =. (1 point)
To compare the square root of 91 (√91) and the square root of 98 (√98) using rational approximations, we can find their decimal approximations and compare them.
√91 is approximately 9.539
√98 is approximately 9.899
Since 9.539 is less than 9.899, we can say that √91 < √98.
Express if as a repeating decimal. Mark the cycle of repealing digits with a bar.
To express the square root of 91 (√91) as a repeating decimal, we need to find its decimal approximation and identify any recurring patterns.
The square root of 91 is approximately 9.539392014169456...
To determine if there is a repeating pattern, we can continue calculating more decimal places:
9.5393920141694567818479822036781258052359009715...
From the calculations, we can see that there is no repeating pattern in the decimal representation of the square root of 91. Therefore, √91 cannot be expressed as a repeating decimal.
Convert 0.09 to a rational number in simplest form. (1 point)
To convert 0.09 to a rational number in simplest form, we need to express it as a fraction.
0.09 can be written as 9/100 because the decimal point indicates that the 9 is in the hundredths place.
Now, we can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which in this case is 9:
9/100 ÷ 9/9 = 1/11
Therefore, 0.09 as a rational number in simplest form is 1/11.