Which of the following describes the positive solution to the equation below?
the solution is an irrational number.
the solution is a rational number.
the solution is greater than two but less than three.
the solution is a repeating decimal.
the solution is greater than one but less than two.
the solution is greater than zero but less than one.
choose all that apply

The solution is an irrational number ⇒ 1st answer

The solution is greater than two but less than three ⇒ 3rd answer

Step-by-step explanation:

* Lets revise some definitions

- A number is rational if we can write it as a fraction where the numerator

 and the denominator are both whole numbers

- A number is irrational if cannot be written as a ratio of two integers

- Repeating decimals are rational numbers because they can be

 represented as a ratio of two integers

* Lets solve the problem

- The equation is x² = 5

- To solve the equation take square root for both sides

∴ x = ± √5

∵ We need the positive solution

∴ x = √5

∵ √5 cannot be written as a ratio of two integers

∴ √5 is an irrational number

∴ The solution is an irrational number

- To find between which two integers √5 lies, find the two square

  numbers before and after 5

∵ 4 is a square number less then 5

∵ 9 is a square number greater than 5

∴ 4 < 5 < 9 ⇒ take square root for all

∴ √4 < √5 < √9

∵ √4 = 2 and √9 = 3

∴ √5 lies between 2 and 3 ⇒ 2 < √5 < 3

∴ The solution is greater than two but less than three

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

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step-by-step explanation: