Sum/difference:
Let
This means that
Now, assume that 
is rational. The sum/difference of two rational numbers is still rational (so 5-x is rational), and the division by 3 doesn't change this. So, you have that the square root of 8 equals a rational number, which is false. The mistake must have been supposing that was rational, which proves that the sum/difference of the two given terms was irrational
Multiplication/division:
The logic is actually the same: if we multiply the two terms we get
if again we assume x to be rational, we have
But if x is rational, so is -x/15, and again we come to a contradiction: we have the square root of 8 on one side, which is irrational, and -x/15 on the other, which is rational. So, again, x must have been irrational. You can prove the same claim for the division in a totally similar fashion.
If the truck can carry 1000 apples at a time, Bananaville is 1000 miles away from Appleland and you pay one apple per mile, then it's impossible to deliver any apple to Bananaville, because on 1000 miles you'll pay 1 apple * 1000 miles = 1000 apples as a tax. So no matter if you go once, twice, three times or a hundred times there - you'll be never able to deliver any apple.
Answer: The highest number of apples you can get to Bananaville is 0.
Answer:
She gave away 12, so she still has 4.
Step-by-step explanation:
16 times .75 equals 12.
Answer: D. 13 1/2.
Step-by-step explanation:
1/2*3= 1 1/2 cups of dishwashing liquid.
4 1/2*3= 13 1/2 cups of water will be used with 1 1/2 cups of dishwashing liquid.
Answer:
vi = 25.28 m/s
Step-by-step explanation:
a = -9.4 m/s²
x = 34 m
vf = 0 m/s
vi = ?
We can apply the equation
vf² = vi² + 2*a*x
⇒ vi = √(vf² - 2*a*x)
⇒ vi = √((0 m/s)² - 2*(-9.4 m/s²)*34 m)
⇒ vi = 25.28 m/s
