Which of the following is true about −9?(1 point)
Responses
It is an integer but not a whole number.
It is an integer but not a whole number.
It is both an integer and a whole number.
It is both an integer and a whole number.
It is an integer but not a rational number.
It is an integer but not a rational number.
It is a whole number but not an integer.
The correct answer is: It is both an integer and a whole number.
What is a number that is a whole number but not a natural number?
A number that is a whole number but not a natural number is zero (0). Natural numbers start from 1 onwards, so they do not include zero. However, zero is still considered a whole number because it is not a fraction or a decimal.
A sign in a gas station advertises gas at the rate of $3.39 9/10 per gallon. How many dollars does a gallon cost, writing the price strictly as a decimal?
Which set of numbers is always rational?(1 point)
Responses
decimals
decimals
integers
integers
positive numbers
positive numbers
fractions
The correct answer is: fractions.
Fractions are always rational numbers because they can be expressed as the quotient of two integers.
The height of an equilateral triangle equals 3√/2 times the side length. Using 7/4 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
To find the height of an equilateral triangle, you can use the formula height = (sqrt(3)/2) * side length.
Given that we will use 7/4 as the approximation for the square root of 3, we can substitute it into the formula:
height = (7/4)(8) = 14 meters.
Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is 14 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?
To find the length of the diagonal of a square, you can use the formula diagonal = (2 - √2) * side length.
Given that we will use 1.4 as the approximation for the square root of 2, we can substitute it into the formula:
diagonal = (2 - 1.4)(700) = 0.6 * 700 = 420 feet.
Therefore, the approximate length from one corner to an opposite corner of the square park with a side length of 700 feet 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
To determine the whole number and rational number to the nearest half that 40-√ is between, we can estimate the square root of 40.
The square root of 40 is approximately 6.32.
To find the whole number and rational number to the nearest half that is between 6 and 7, we look at the number line:
5.5, 6, 6.5, 7
Since 6.32 is closer to 6.5, the whole number and rational number to the nearest half that 40-√ is between are 6 and 6.5.
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 need to find approximate decimal values for each term.
81-√ is approximately equal to 9, since the square root of 81 is 9.
8-√8 is approximately equal to 4.83, since the square root of 8 is approximately 2.83, and subtracting this value from 8 gives us 4.17.
Comparing the values, we have:
9 > 4.83
Therefore, the inequality statement comparing 81-√ and 8-√8 is: 81-√ > 8-√8.
Using rational approximations, what is an inequality statement comparing 81−−√ and88–√? Enter <, >, or =.(1 point)
The inequality is: 81−−√
88-√.
To compare 81-√ and 88-√ using rational approximations, we need to find approximate decimal values for each term.
81-√ is approximately equal to 9, since the square root of 81 is 9.
88-√ is approximately equal to 9.38, since the square root of 88 is approximately 9.38.
Comparing the values, we have:
9 < 9.38
Therefore, the inequality statement comparing 81-√ and 88-√ is: 81-√ < 88-√.
Express 8/11 as a repeating decimal. Mark the cycle of repeating digits with a bar
To express 8/11 as a repeating decimal, we perform long division:
0.727272...
The digits 72 repeat infinitely, so we can place a bar over them to indicate the repeating cycle. Therefore, 8/11 is equal to 0.72¯¯¯.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form
To convert 0.72¯¯¯ to a rational number in simplest form, we can set x = 0.72¯¯¯ and multiply both sides of the equation by 100 to eliminate the repeating decimal:
100x = 72.7272...
Now, let's subtract the original equation from the multiplied equation to eliminate the repeating decimal:
100x - x = 72.7272... - 0.7272...
Simplifying this equation gives us:
99x = 72
Now, we can solve for x by dividing both sides of the equation by 99:
x = 72/99
To simplify the fraction 72/99, we can divide both the numerator and denominator by their greatest common divisor, which is 9:
72 ÷ 9 = 8
99 ÷ 9 = 11
Therefore, 0.72¯¯¯ is equal to the rational number 8/11 in simplest form.
To write the price strictly as a decimal, we need to convert the fraction 9/10 to a decimal.
To do this, we divide 9 by 10:
9 ÷ 10 = 0.9
Therefore, the fraction 9/10 can be represented as the decimal 0.9.
So, the cost of a gallon of gas is $3.39 + $0.9 = $3.39 + $0.90 = $4.29.
Therefore, a gallon of gas costs $4.29.