1 and 5/9 are rational numbers. The second is already a fraction and the first one, 1, is a natural number, but all the natural numbers can be written as the result of a fraction. For example: 1=6/6.

About the last number, I don't know if it's written correctly. That should be pi maybe, that is 3.14159.... In that case it's an irrational number.

Irrational numbers are all those real numbers that are not rational.

In general you have that:

ℕ ⊂ ℤ ⊂ ℚ ⊂ ℝ

ℕ. Natural numbers. It's the "smallest" one.

ℤ. Integers. Made with positive and negative natural numbers. Includes the natural numbers then.

ℚ. Rational numbers. Everything that can be written as a fraction. Includes both ℕ and ℤ.

ℝ. Real numbers. Any kind of number, fraction or not.

7 0

3 years ago

Delaney would like to make a 5 lb nut mixture that is 60% peanuts and 40% almonds. She has several pounds of peanuts and several

Alchen [17]

Answer:

a) The system that models the situation is:

p + 0.2m = 3

p + m = 5

b) The solution of the system is:

m = 2.5

p = 2.5

Step-by-step explanat:

It is desired to obtain 5 pounds of a mixture containing 40% peanuts and 60% almonds.

It has a mixture of 20% peanuts and 80% almonds.

p: number of pounds of peanuts

m = amount of mixture

The equation that represents the amount of peanut and mixture that is needed is:

p + m = 5 pounds

m = 5-p (i)

The amount of peanut in total that the mixture should have is:

p + 0.2m = 0.6 (5)

p + 0.2m = 3 (ii)

a) The system that models the situation is:

p + 0.2m = 3

p + m = 5

Now we substitute (i) in (ii) and clear p.

p + 0.2 (5-p) = 3

p-0.2p = 2

p = 2.5 pounds

Now we find m

m = 5 - 2.5

m = 2.5 pounds

b) The solution of the system is:

m = 2.5

p = 2.5

7 0

3 years ago