Answer:
Is irrational
Step-by-step explanation:
Let
be a rational number, and
be an irrational number. If their sum were rational, say
, then we'd have

but
is the difference between two rational numbers, and thus a rational number. But it also equals
, which is irrational by hypothesis. Since we have a contradiction, we conclude that the sum of a rational and an irrational can't be rational.
Answer:

Step-by-step explanation:
Each seven-letter word is worth 50 points.
words are then worth
.
Since Sal gets 100 points for playing the game, his points total after
words is
. If he wants to break the record, he must get, at least, 18000 points. "At least" in inequality means
(just as "at most" means
). Then the required inequality is
.
Note that the question says "18000 or more", which is why we used the
symbol. If the phrase had been "more than 18000", we would have used
.
Answer:
4,2,1
Step-by-step explanation:
Assuming you want the expression to be simplified.
We begin with the following:

Simplify the first part,

. That is 25. Now we have this:
Next, simplify

, which is 1/3, and get this:
The next part is

. Simplify the denominator,

, which is 81. Simplify the numerator, which is 1/125. Then divide 1/125 by 81, which we will keep as a fraction for simplicity's sake, but simplify it to

. Now we have:

Now simplify

, which is 0.2, or 1/5. Now we have:
Finally, simplify

. That is 1/27. We have:

Lastly, multiply them all together! Now we are done, with the product of:

That certainly did take a while to type in all the LaTex, so I really hope that helped!
Note- if anything isn't working with the LaTex, just tell me and I'll fix it! (:
Answer:
The standard form of the ellipse is
.
Step-by-step explanation:
The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:
(1)
If we know that
and
, then the coordinates of the center are, respectively:



The length of each semiaxis is, respectively:




The standard equation of the ellipse is described by the following formula:

Where:
,
- Coordinates of the center of the ellipse.
,
- Length of the orthogonal semiaxes.
If we know that
,
,
and
, then the standard form of the ellipse is:
