You can treat it as an arithmetic sequence, so multiply the average integer value by the number of integers:
(40+12)/2 × (40 -12 +1) = 26×29 =
754You can subtract the sum of integers 1–11 (66) from the sum of integers 1–40 (820) to get the sum of integers from 12–40: 820 - 66 =
754.
You can let a graphing calculator do it. (See attached.) This method takes perhaps the least amount of thought. It, too, gets a sum of
754.
3: (X + 1) (X + 3)
= (x + 1)(x + 3)
= (x)(x) + (x)(3) + (1)(x) + (1)(3)
= X^2 + 3X + X + 3
= X^2 + 4x + 3
4:
(y + 6) (y + 4)
= (y + 6)(y + 4)
= (y)(y) + (y)(4) + (6)(y) + (6)(4)
= y^2 + 4y + 6y + 24
= y^2 + 10y + 24
5:
(z - 5) ( (z + 3)
= (z + - 5)(z + 3)
= (z)(z) + (z)(3) + ( - 5)(z) + ( - 5)(3)
= z^2 + 3z - 5z - 15
= z^2 - 2z - 15
6:
(a + 8) (a -3)
= (a + 8)(a + - 3)
= (a)(a) + (a)( - 3) + (8)(a) + (8)( - 3)
= a^2 - 3a + 8a - 24
= a^2 + 5a - 24
7:
(g - 7) ( g - 2)
= (g + - 7)(g + - 2)
= (g)(g) + (g)( - 2) + ( - 7)(g) + ( - 7)( - 2)
= g^2 - 2g - 7g + 14
= g^2 - 9g + 14
8:
(n - 6) (n - 4)
(n + - 6)( n + - 4)
= (n)(n) + (n)( - 4) + ( - 6)( n) + (- 6)( - 4)
= n^2 - 4n - 6n + 24
= n^2 - 10n + 24
9:
(3m + 1) ( m + 9)
= (3m + 1)(m + 9)
= (3m)(m) + (3m)(9) + (1)(m) + (1)(9)
= 3m^2 + 27m + m + 9
= 3m^2 + 28m + 9
10:
(2p - 4) ( 3p + 2)
= (2p + - 4)(3p + 2)
= (2p)(3p) + (2p)(2) + ( - 4)(3p) + (- 4)(2)
= 6p^2 + 4p - 12p - 8
= 6p^2 - 8p - 8
11:
(6 - 5s) (2 - s)
= (6 + - 5s)(2 + - s)
= (6)(2) + (6)( - s) + ( - 5s)(2) + (- 5s)( - s)
= 12 - 6s - 10s + 5s^2
= 5s^2 - 16s + 12
Hope that helps!!!! wowzah….my brain is tired now.....have a good day...
We know, Area of a Hexagon = 3√3a² / 2
A = 3√3 /2 * 10²
A = 3√3 * 100/2
A ≈ 259.81 m²
In short, Your Answer would be: 259.81 m²
Hope this helps!
The transformation starts with T-1, 1(x, y) and ends with RO, 90° (counter-clockwise).
To find the original point, we work backwards.
We start with RO, -90° (clockwise):
which gives
We then do the reverse of T-1, 1(x, y), which is T1, -1(x, y):
which gives
so the answer is
.