The answer is as follows:
There are 2 pints in a quart.
There are 2 quarts in a half gallon.
There are 2 half gallons in a gallon.
Therefore, we can conclude that there are 10 quarts of orange juice.
- 1 1/10 + (-1 2/5)
- 1 1/10 + (-1 4/5)
-2 5/10
-2 1/2
Answer: The inverse of the linear function f(x)=2x+1 is f^(-1) (x) = (1/2)x-1/2
Solution
f(x)=2x+1
y=f(x)
y=2x+1
Isolating x: Subtracting 1 both sides of the equation:
y-1=2x+1-1
y-1=2x
Multiplying both sides of the equation by 1/2:
(1/2)(y-1)=(1/2)2x
(1/2)y-1/2=x
x=(1/2)y-1/2
Changing "x" by "f^(-1) (x)" and "y" by "x":
f^(-1) (x) = (1/2)x-1/2
U + 4/5 = 2 and 1/3
Subtract 4/5 from each side of the equation:
U = (2 and 1/3) - (4/5)
Now it's just problem in plain old adding and subtracting fractions,
just like the ones you've done many times before.
First let's change (2 and 1/3) to a fraction: 2 and 1/3 = 7/3
So you have to find the value of (7/3) - (4/5) .
In order to add or subtract fractions, they need to have a common denominator.
The least common multiple of 3 and 5 is 15, so that's a good choice.
7/3 = 35/15
4/5 = 12/15
Now the problem is: (35/15) - (12/15).
That's 23/15 . . . . . the same thing as <u>1 and 8/15</u> .
That's the value of ' U '. What an ugly number !
That is the definition of a irrational number, A rational number must be able to be written as a ratio of 2 integers. The denominator cannot be 0, because that would make the number undefined
