Which statement is true about the relationships between the number sets?(1 point)Responses Not all natural numbers are real numbers.Not all natural numbers are real numbers.Whole numbers include all natural numbers and 0.Whole numbers include all natural numbers and 0.Some irrational numbers are also integers.Some irrational numbers are also integers.All rational numbers are also integers.
Whole numbers include all natural numbers and 0.
Question
Which of the following is true about −9?(1 point)
Responses
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 an integer but not a whole number.
It is a whole number but not an integer.
It is a whole number but not an integer.
It is both an integer and 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)
$
The decimal representation of the gas price is $3.39910.
Which set of numbers is always rational?(1 point)
Responses
integers
integers
decimals
decimals
fractions
fractions
positive numbers
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?
Given that the height of an equilateral triangle is equal to 3√2 times the side length, and the square root of 3 is approximately 74, we can calculate the approximate height as follows:
Height = 3√2 * side length
Approximating √2 as 1.414, and substituting the values:
Height = 3 * 1.414 * 8
Height = 33.936 meters
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 33.936 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?
Given that the diagonal of a square is equal to 2–√ times the side length, and √2 is approximately 1.4, we can calculate the approximate length as follows:
Diagonal = 2–√ * side length
Approximating 2–√ as 2 - 1.4 = 0.6, and substituting the values:
Diagonal = 0.6 * 700
Diagonal = 420 feet
Therefore, the approximate length from one corner to an opposite corner of a square park that is 700 feet on a side 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 determine the whole number and rational number that the square root of 40 is between, we can use a number line.
Consider that the square root of 40 is approximately 6.324555.
To the nearest half, the whole number and rational number that the square root of 40 is between are:
5.5 and 6.
Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
To determine the whole number and rational number that the square root of 58 is between, we can use a number line.
Consider that the square root of 58 is approximately 7.61577.
To the nearest half, the whole number and rational number that the square root of 58 is between are:
7.5 and 8.
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 simplify both expressions:
81√ can be approximated as 9 because 9 * 9 = 81.
8−√8 can be approximated as 2.828 because 2.828 * 2.828 ≈ 8.
Therefore, we have: 9 > 2.828
The inequality statement comparing 81√ and 8−√8 is 9 > 2.828.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: √81
√88.
To compare √81 and √88 using rational approximations, we can simplify both expressions:
√81 can be simplified as 9 because 9 * 9 = 81.
√88 can be approximated as 9.38 because 9.38 * 9.38 ≈ 88.
Therefore, we have: 9 = 9.38
The inequality statement comparing √81 and √88 is √81 = √88.
Express 811 as a repeating decimal.
To express 811 as a repeating decimal, we can divide 811 by 9 using long division:
_________
9 | 811.00
- 72
---
111
- 99
------
120
- 99
------
210
- 198
------
120
- 99
------
210
- 198
------
120
- 99
------
210
After performing the long division, we can see that the decimal representation of 811 is a repeating decimal: 811 = 90.111...
Therefore, 811 can be expressed as a repeating decimal as 90.111...
Express 8/11 as a repeating decimal.
To express 8/11 as a repeating decimal, we perform long division:
0.7272...
__________
11 | 8.0000
- 7
-------
10
- 9
-----
10
- 9
-----
10
- 9
-----
10
- 9
-----
10
- 9
-----
10
- 9
-----
10
- 9
-----
...
The division continues indefinitely, with the remainder always being 10. Therefore, the decimal representation of 8/11 is a repeating decimal:
8/11 = 0.7272...
Thus, the fraction 8/11 can be expressed as a repeating decimal as 0.7272...
Convert 0.72¯¯¯¯¯ to a rational number in simplest form.
To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can set it up as a fraction and solve for the numerator.
Let x = 0.7272...
10x = 7.2727... (multiplying both sides by 10 to shift the decimal)
100x = 72.7272... (multiplying both sides by 100 to shift the decimal)
Subtracting the two equations:
100x - 10x = 72.7272... - 7.2727...
90x = 65
Dividing both sides by 90:
x = 65/90
The fraction 65/90 can be simplified further by dividing both numerator and denominator by their greatest common divisor, which is 5:
65/90 = 13/18
Therefore, the rational number equivalent to 0.72¯¯¯¯¯ in simplest form is 13/18.
Which of the following is a rational number between 5 and 514?(1 point)
Responses
525
5 Start Fraction 2 over 5 end fraction
26−−√
start root 26 end root
513
5 Start Fraction 1 over 3 end fraction
517
The rational number between 5 and 514 is 5 Start Fraction 2 over 5 end fraction.
What is a rational number with a denominator of 7 that is between 7–√ and 8–√ . Write your answer as an improper fraction.(1 point)
To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we can convert the given square roots into rational numbers with denominators of 7.
7–√ can be written as 7/√7 * √7 = 7√7 / 7 = √7.
8–√ can be written as 8/√7 * √7 = 8√7 / 7.
To find a rational number between √7 and 8√7 / 7, we can take their average:
(√7 + 8√7 / 7) / 2 = (2√7 + 8√7) / 14 = 10√7 / 14 = 5√7 / 7.
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 5√7 / 7, written as an improper fraction.