Answer:
D. empty set
Step-by-step explanation:
Each of the operations X-Y and Y-X removes elements that are common to X and Y. The resulting two sets have no elements in common, so their intersection is the empty set.
_____
X -Y = {2, 5, 6}
Y -X = {3, 7, 8}
{2, 5, 6} ∩ {3, 7, 8} = { }
Answer:
3/4
Step-by-step explanation:
Average change is change in y / change in x
(y2-y1)-(x2-x1)
(3-0)/(-3-(-7))
3/4
In (-7,0)
-7 is x1, 0 is y1
In (-3,3)
-3 is x2 and 3 is y2
Firstly we need to find out how much is 7% from $124.95:
7% * 124.95 =
= 7/100 * 124 95/100 =
= 7/100 * 12495/100 =
= 87465/10000 =
= 8,7465
As far as we talk about money, we can round it to the nearest cent:
8.7465 ≈ 8.75
So we have $124.95 (original price) + $8.75 (tax) + $10 (charge for shipping).
$124.95 + $8.75 + $10 = $133.70 + $10 = $143.70
Answer: <u>Patel paid $143.70</u>.
Step-by-step explanation:
(a²-b²)(c²-d²) = a²c² - a²d² - b²c² + b²d²
(b²-d²)(c²-a²) = b²c² - a²b² - c²d² + a²d²
the sum of both is
a²c² + b²d² - a²b² - c²d² = a²(c²-b²) + d²(b²-c²) =
= a²(c²-b²) - d²(c²-b²) = (c²-b²)(a²-d²) = 2021
after a little check we find 2021 is only divisible by 43 and 47 (or 1 and 2021).
so, it is clear that our expression resembles
43×47 = 2021
that means that e.g. c²-b² = 43, and a²-d² = 47
or the other way around, it does not matter.
what squared integer numbers give a difference of 43 ? and 47 ?
squared numbers
1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256
289 324 361 400 441 484 529 576
aha ! 484 - 441 = 43
and 576 - 529 = 47
so, we get
a = sqrt(576) = 24
b = sqrt(441) = 21
c = sqrt(484) = 22
d = sqrt(529) = 23
one could also use the formula for consecutive squared numbers
(n+1)² = n² + 2n + 1
under the assumption that the 2 numbers are convective (which it turns out they are in this example) we get
(n+1)² - n² = 2n + 1 = 43
2n = 42
n = 21
n+1 = 22
and for 47
2n + 1 = 47
2n = 46
n = 23
n+1 = 24