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.
Good morning,
Answer:
<h2>5+(-4) > -4 + (-7)</h2>
Step-by-step explanation:
5+(-4) = 5 - 4 = 1
-4 + (-7) = -(4+7) = -11
since 1 > -11 then 5+(-4) > -4 + (-7)
:)
No, it never can be a right triangle.
First, all the angles of an equilateral triangle is 60 degrees because all angles are the same and all the angles add up to 180:
180/3 = 60.
So if it is a right angle it needs one angle 90 degrees which an equilateral triangle can't have,
Since we have two ordered pairs, we can find the slope by plugging them into (y2-y1)/(x2-x1) which translates to (3-(-6))/(-4-(-1))=9/-3=-3
Since the slope is -3, we have the equation y=-3x+b, but we don't know b. So we plug in values for x and y and solve for b.
-6=-3(-1)+b
-6=3+b
-9=b
So the y-intercept is -9 and the full equation is y=-3x-9 which means A is the only correct answer.
Hope this helped!
To solve this problem just do the following,
x+9=-12
-9 -9
x=-21
Check
-21+9=-12 = True
Hope this helps!=)
