The Number System Unit Test
I need help with these i have the first answer bt idk the rest
2. Which of the following is true about −9?(1 point)
A.It is a whole number but not an integer.
B.It is an integer but not a rational number.
C.It is an integer but not a whole number.
D.It is both an integer and a whole number.
3.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)
5.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)
6.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)
7.Using a number line, what whole number and rational number to the nearest half is 40−−√ between?
8.Using a number line, what whole number and rational number to the nearest half is 58−−√ between?(1 point)
Responses
A.between 8.5 and 9
B.between 7.5 and 8
C.between 7 and 7.5
D.between 8 and 8.5
Describe the relationship between integers and whole numbers. Are all integers also whole numbers? Are all whole numbers also integers? Give examples to support your answer.
can an actual person give the correct answers in written form!!!!!???????!!!?!!?!?
Here are the answers to the questions:
2. D. It is both an integer and a whole number.
3. $3.39910
5. The height of the equilateral triangle equals 3√2 times the side length. Given that 74 is approximately the square root of 3, we can calculate the height:
Height = 3√2 * Side length
Height = 3 * 74 * 8
Height = 222 * 8
Height = 1776
Therefore, the approximate height in meters of an equilateral triangle with a side length of 8 meters is 1776 meters.
6. The diagonal of the square equals 2–√ times the side length. Given that 1.4 is approximately the square root of 2, we can calculate the diagonal:
Diagonal = 2–√ * Side length
Diagonal = 1.4 * 700
Diagonal = 980
Therefore, the approximate length in feet from one corner to an opposite corner of the square park that is 700 feet on a side is 980 feet.
7. To find the whole number and rational number to the nearest half that is between 40−−√, we can use a number line:
- Since 7^2 = 49 and 8^2 = 64, we know that 40 is between the square roots of 49 and 64.
- Therefore, the whole number to the nearest half is 7.5 and the rational number to the nearest half is 7.
So, the whole number and rational number to the nearest half that is between 40−−√ is 7.5 and 7.
8. To find the whole number and rational number to the nearest half that is between 58−−√, we can use a number line:
- Since 7^2 = 49 and 8^2 = 64, we know that 58 is closer to the square root of 64.
- Therefore, the whole number to the nearest half is 8 and the rational number to the nearest half is 8.
So, the whole number and rational number to the nearest half that is between 58−−√ is 8 and 8.
thank you for the help i have a few more questions
9.Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8? Enter <, >, or =.(1 point)
The inequality is: 81−−√
8–√8.
10.Express 811 as a repeating decimal. Mark the cycle of repeating digits with a bar.(1 point)
12.Convert 0.72¯¯¯¯¯ to a rational number in simplest form.(1 point)
13.Which of the following is a rational number between 5 and 514?(1 point)
513
5 Start Fraction 1 over 3 end fraction
525
5 Start Fraction 2 over 5 end fraction
26−−√
start root 26 end root
517
14.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)
Here are the answers to your additional questions:
9. To compare 81−−√ and 8–√8 using rational approximations, we can find their decimal approximations:
- √81 ≈ 9
- √8 ≈ 2.8284 (using a calculator)
Now we can compare them:
9 > 2.8284
Therefore, the inequality statement comparing 81−−√ and 8–√8 is 81−−√ > 8–√8.
10. To express 811 as a repeating decimal, we can divide 8 by 11:
8 ÷ 11 = 0.727272...
So, 811 expressed as a repeating decimal is 0.727272... (the 27 repeats).
12. To convert 0.72¯¯¯¯¯ to a rational number in simplest form, we can let x = 0.72¯¯¯¯¯ and multiply both sides by 100 (since there are two digits repeating):
100x = 72.727272...
Now subtract x from 100x to eliminate the repeating part:
100x - x = 72.727272... - 0.72¯¯¯¯¯
99x = 72
Divide both sides by 99 to solve for x:
x = 72/99
The fraction 72/99 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 9:
72/99 = 8/11
Therefore, 0.72¯¯¯¯¯ is equal to 8/11 in simplest form.
13. To find a rational number between 5 and 514, we can use the fact that any number can be represented as a fraction with a denominator of 1. We can find a rational number between them by taking the average:
(5 + 514)/2 = 519/2
Therefore, the rational number between 5 and 514 is 519/2.
14. To find a rational number with a denominator of 7 that is between 7–√ and 8–√, we can use rational approximations:
- 7–√ ≈ 2.6458
- 8–√ ≈ 2.8284
We can find a rational number by taking their averages:
(2.6458 + 2.8284)/2 ≈ 2.7371
Converting this decimal to a fraction, we get:
2.7371 ≈ 27371/10000
Simplifying this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 1:
27371/10000
Therefore, a rational number with a denominator of 7 that is between 7–√ and 8–√ is 27371/10000.
for 9 i meant 81 not 8
Apologies for the misunderstanding.
9. To compare 81−−√ and 8–√8 using rational approximations, we can find their decimal approximations:
- √81 = 9
- √8 ≈ 2.8284 (using a calculator)
Now we can compare them:
9 > 2.8284
Therefore, the inequality statement comparing 81−−√ and 8–√8 is 81−−√ > 8–√8.