If 9 of the sparrows is 45% of the birds in the backyard, 9/x = 45/100.
Cross multiply to get 9 * 100 = 45x; simplified is 900 = 45x or 20.
This means that there are 20 birds in the backyard. You can check this by dividing 9/20 which equals 45%
1. H+S=40
2. 19H+25S=922
From 1,
19H+19S=760
Subtract this from 2 to eliminate H,
19H+25S-19H-19S=922-760
6S=162
Solve for S, then use either equation to solve for H.
64 78 80 80 80 81 81 82 83 89 90 Not ecaxt but close, it should help atleast, everything is right except mean
A(4,2), B(2,8)
AC: y=x-2
Point point form for a line through (a,b) and (c,d) is (c-a)(y-b)=(d-b)(x-a)
AB is (2 - 4)(y - 2) = (8-2)(x-4)
-2(y - 2)=6(x-4)
y - 2 = -3(x-4)
y = -3x + 14
BC is perpendicular through B, so slope 1/3 and we calculate the constant as y-(1/3)x:
y = (1/3) x + (8 - (1/3)(2) ) = (1/3) x + 22/3
a)Answer: BC is y = (1/3) x + 22/3
C is the meet of AC and BC,
x - 2 = (1/3) x + 22/3
3x - 6 = x + 22
2x = 28
x = 14
y = x-2 = 12
Check: y = (1/3)x + 22/3 = (14+22)/3 = 36/3 = 12 good
C(14,12)
The remaining corner is D. We have A-B=D-C or
D = A+C-B+C = (4,2)+(14,12)-(2,8) = (16, 6)
b)Answer: B(2,8) [given, but asked for] C(14,12), D(16,6)
To expand (3 - 2x)^6 use the binomial theorem:
(x + y)^ n = C(n,0) x^ny^0 + C(n,1)x^(n-1) y + C(n,2)x^(n-2) y^2 + ...+ C(n,n+1)xy^(n-1) + C(n,n)x^0y^n
So, for x = 3, y = -2x , and n = 6 you get:
(3 - 2x) ^6 = C(6,0)(3)^6 + C(6,1)(3)^5 (-2x) + C(6,2) (3)^4 (-2x)^3 + C(6,3) (3^3) (-2x)^4 + C(6,4)(3)^2 (-2x)^4 + C(6,5) (3) (-2x)^5 + C(6,6) (-2x)^6
So, the sixth term is C(6,5)(3)(-2x)^5 = 6! / [5! (6-5)! ] * 3 * (-2)^5 x^5 = - 6*3*32 = - 576 x^5.
The coefficient of that term is - 576.
Answer: - 576
