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).
The height of an equilateral triangle equals 3√2 times the side length.
Given that the side length is 8 meters, we can substitute this value into the equation:
Height = 3√2 * Side length
Height = 3√2 * 8
Now, we just need to substitute the value of √2 with the given value of 74:
Height = 3 * (74) * 8
Height = 222 * 8
Height = 1776
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters is 1776 meters.
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 point)
Given that the square root of 3 is represented as 7/4, we can substitute this value into the equation:
Height = 3√2 * Side length
Height = 3 * (7/4) * 8
To simplify the equation, we can first multiply 3 and 8:
Height = 24 * (7/4)
Next, we can simplify the expression (7/4):
Height = (24 * 7) / 4
Height = 168 / 4
Height = 42
Therefore, the approximate height of an equilateral triangle with a side length of 8 meters, using 7/4 for the square root of 3, is 42 meters.
Using a number line, what whole number and rational number to the nearest half is 40−−√ between?(1 poi
To determine which whole number and rational number to the nearest half the square root of 40 lies between, we can look at the number line.
By calculating the square root of 40, we find that it is approximately 6.32456.
On the number line, we can see that 6 is the whole number right before 6.32456, and 7 is the whole number right after it.
To find the nearest half, we can divide the interval between 6 and 7 into halves:
6 ------------ 6.5 ------------ 7
Since 6.32456 is closer to 6.5 than it is to 6, the square root of 40, rounded to the nearest half, is between 6 and 6.5.
Therefore, the whole number to the nearest half is 6, and the rational number to the nearest half is 6.5.
Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.
To compare 81−−√ and 8–√8 using rational approximations, we can find their decimal approximations.
The square root of 81 is exactly 9.
The square root of 8 is approximately 2.82843.
Comparing these decimal approximations, we can see that 9 is greater than 2.82843.
Therefore, the inequality statement comparing 81−−√ and 8–√8 is:
81−−√ > 8–√8
Monique measured the widths of several stamps in her collection of world stamps. The measurements are 1 5/8in., 1 11/16in., 1 1 1 1 3/4in., and 1 1/2in. What is the width of the widest stamp?(1 point)
To find the width of the widest stamp among the given measurements, we need to compare the measurements and determine the largest one.
The given measurements are:
1 5/8in.
1 11/16in.
1 1 1 1 3/4in.
1 1/2in.
To facilitate the comparison, it can be helpful to convert all the measurements to the same denominator:
1 5/8in. = (8 + 5)/8 = 13/8in.
1 11/16in. = (16 + 11)/16 = 27/16in.
1 1 1 1 3/4in. = (4 x 16 + 3)/16 = 67/16in.
1 1/2in. = (2 + 1)/2 = 3/2in.
Now, we can determine which fraction is the largest.
Comparing the fractions, we can see that 67/16in. is the largest among them.
Therefore, the width of the widest stamp is 67/16in.
What is the circumference of a circle with a diameter of 4.5 miles? Estimate the circumference to the hundredths place using 3.14 for π
.
The circumference of a circle can be calculated using the formula C = πd, where C is the circumference and d is the diameter.
Given that the diameter is 4.5 miles, we can plug in this value into the formula:
C = 3.14 * 4.5
C = 14.13
Therefore, the circumference of the circle with a diameter of 4.5 miles is approximately 14.13 miles when rounded to the hundredths place.
Write 6,739 in expanded form.
To write 6,739 in expanded form, we break down the number by its place values.
6,739 can be written in expanded form as:
6,000 + 700 + 30 + 9
Therefore, the expanded form of 6,739 is:
6,000 + 700 + 30 + 9
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 can perform long division:
0.7272...
_______________
11 | 8.0000
-7.92
_______
80
-77
_____
30
- 22
_____
80
- 77
_____
30
- 22
_____
80
- 77
_____
30
- 22
_____
80
- 77
_____
30
- 22
_____
...
We can see that the remainder repeats as 30-22-80-77. Therefore, the decimal representation of 8/11 is 0.7272... where the cycle of repeating digits is marked by a bar above the digits: 0.72̅.
0.72 in simplest form
The number 0.72 is already in simplest form because it does not contain any common factors that can be simplified.
Convert 0.72¯¯¯¯¯ to a rational number in simplest form
To convert the repeating decimal 0.72¯¯¯¯¯ to a rational number in simplest form, we can let x = 0.727272... and write an equation to solve for x.
To do this, we can multiply both sides of the equation by 100 to get rid of the repeating decimal:
100x = 72.727272...
Next, we subtract x from both sides to eliminate the repeating decimal:
100x - x = 72.727272... - 0.727272...
99x = 72
Now, we can divide both sides by 99 to solve for x:
x = 72/99
To simplify the fraction 72/99, we can find the greatest common divisor (GCD) of the numerator and denominator, which is 9:
72/99 = (72/9) / (99/9) = 8/11
Therefore, 0.72¯¯¯¯¯ is equivalent to the rational number 8/11 in simplest form.
Which of the following is a rational number between 5 and 5 1/4?
To find a rational number between 5 and 5 1/4, we can look for a fraction that falls between these two numbers on the number line.
5 can be written as 5/1, and 5 1/4 can be written as 21/4.
To find a rational number between these two fractions, we can think of a fraction with a numerator and denominator that lie between 5 and 21/4.
One possible rational number that fits this criteria is 19/4, which can be expressed as 4 3/4.
Therefore, the rational number 4 3/4 is between 5 and 5 1/4.
What is a rational number with a denominator of 7 that is between 7–√ and 8–√. Write your answer as an improper fraction.(
To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we can take the average of these two numbers.
First, let's simplify the given numbers:
7–√ = 7 – √(7) = 7 – 2.645751 = 4.354249
8–√ = 8 – √(8) = 8 – 2.828427 = 5.171573
Now, we can find the average of these two numbers:
(4.354249 + 5.171573) / 2 = 9.525822 / 2 = 4.762911
To convert this decimal to a fraction with a denominator of 7, we multiply both the numerator and denominator of the fraction by 7:
4.762911 * 7 / 1 * 7 = 33.340377 / 7
Therefore, a rational number between 7–√ and 8–√, with a denominator of 7, is 33.340377 / 7 written as an improper fraction.
wrong
Apologies for the incorrect response. Let's try again.
To find a rational number with a denominator of 7 that falls between 7–√ and 8–√, we can look for a fraction that lies between these two radical expressions.
Let's simplify 7–√ and 8–√:
7–√ = 7 – √7
8–√ = 8 – √8 = 8 – 2√2
Now, let's find a rational number with a denominator of 7 that falls between these two expressions.
To do this, we can take the average of the two expressions:
(7 – √7 + 8 – 2√2) / 2 = (15 – √7 – 2√2) / 2
To simplify further, we can multiply the numerator and denominator by 2 to eliminate the fraction:
(2(15) – 2(√7) – 2(2√2)) / 2 = (30 – 2√7 – 4√2) / 2
Now, we can simplify the expression:
(30 / 2) – (2√7 / 2) – (4√2 / 2) = 15 – √7 – 2√2
Therefore, the rational number with a denominator of 7 that is between 7–√ and 8–√ is (15 – √7 – 2√2) / 7 written as an improper fraction.
Describe the relationship between rational numbers and whole numbers. Are all rational numbers also whole numbers? Are all whole numbers also rational numbers? Give examples to support your answer.
Rational numbers and whole numbers are related, but they are not the same.
All whole numbers are rational numbers because they can be expressed as a fraction with a denominator of 1. For example, 3, 7, and -1 are all whole numbers, and they can be written as fractions: 3/1, 7/1, and -1/1.
On the other hand, not all rational numbers are whole numbers. Rational numbers include all integers, fractions, and terminating or repeating decimals. Examples of rational numbers that are not whole numbers include 1/2, -3/4, and 2.5.
In summary, while all whole numbers are rational numbers, not all rational numbers are whole numbers. Whole numbers form a subsection within the larger category of rational numbers.