What are we supposed to use?
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
Answer:
Julie has 6 photos that she wants to rearrange.
Two of them are fixed at the middle position.
=> There are 4 photos left for rearranging.
=> This is the permutation with n = 4, k = 4.
=> The number of ways Julie can arrange the photos:
N = 4 x 3 x 2 x 1 = 24 ways
Hope this helps!
:)
Answer:
-3
Step-by-step explanation:
dividing a positive and a negative equals a negative so put the 4.5 in parentheses with the 1.5 and put the negative outside the parentheses. then do what's in the parentheses and add your negative which makes you get a -3
Answer:
x=45
Step-by-step explanation:
30/x = 54/81
30 = 54/81(x)
x = 30 ÷ 54/81
x=45
