Answer:
7,850
I’m pretty sure that’s right, I just added 25,000 and 15,250 together then subtracted the answer from 32,400 and got 7,850
You can find counterexamples to disprove this claim. We have positive integers that are perfect square numbers; when we take the square root of those numbers, we get an integer.
For example, the square root of 1 is 1, which is an integer. So if y = 1, then the denominator becomes an integer and thus we get a quotient of two integers (since x is also defined to be an integer), the definition of a rational number.
Example: x = 2, y = 1 ends up with
which is rational. This goes against the claim that
is always irrational for positive integers x and y.
Any integer y that is a perfect square will work to disprove this claim, e.g. y = 1, y = 4, y= 9, y = 16. So it is not always irrational.
Answer:
I got x = -7 I hope this helps
Answer:
Width = 18, height = 3
Or
Width = 6, height = 9
Step-by-step explanation:
Complete question
( A piece of sheet metal 24 inches wide is bent to form a gutter as shown in the picture below, if the cross sectional area is 54 square inches, find the depth of the gutter).
X = width, Y = height
X - 2y = 24........ equation i
X = 24 - 2y.......... equation ii
Area = xy
54 = xy........ equation iii
Put equation ii into equation iii
54 = (24 - 2y) * y
54 = 24y - 2y²
2y² - 24y + 54 = 0........ equation iv
Solving equation iv using quadratic methods,
Factors = (y-3), (y-9)
(Y-3)(y-9) = 0
y = 3 or y = 9
Substitute y = 3 or y = 9 into equation ii
X = 24 -2(3) = 18 or x = 24 - 2(9) = 6
If Width = 18, height = 3
Or
Width = 6, height = 9