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.
All rational numbers are also integers.
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.
It is both an integer and a whole number.
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)
A gallon costs $3.39910, writing the price strictly as a decimal.
Which set of numbers is always rational?(1 point)
Responses
integers
integers
positive numbers
positive numbers
fractions
fractions
decimals
fractions
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)
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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
so what is the answer?
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.
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)
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
the answer?
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.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 point)
40−−√ is between
and
.
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.
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
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.
so its between?
Apologies for the confusion in my response. To clarify, 58−−√ is between 7 and 7.5 on the number line.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√
8–√8.
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.
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
(6×1,000)+(7×100)+(3×10)+(9×1)
Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
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.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
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.
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
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.
so its option 4?
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.