For Geometric Progression
#1 = a = 5
#2 = ar = x
#3 = ar^2 = y
#4 = ar^3 = 40
We need to find 'r'
To do this ,divide #4 by #1 , hence
ar^3 / a = 40 / 5
Hence r^3 = 8 (Notice the 'a' cancels down to leave 'r^3'
Cube root both sides
Hence r = 2
When r = 2
#2 = ar = 5 X 2 = 10 = x
#3 = ar%2 - 5 x 2^2 = 5 x 4 = 20 = y
So the geometric progression is 5,x,y,40 = 5,10,20,40
In a GP each term is the previous term multiplied by a constant.
Let the common difference be r, then:
x = 5r
y = xr = 5rr = 5r²
40 = yr = 5r²r = 5r³
→ 5r³ = 40
→ r³ = 8
→ r = 2
→ x = 5 × 2 = 10
→ y = 10 × 2 = 20
x2 + 13x + 40 = x2 + 5x + 8x + 40 = x(x + 5) + 8(x + 5) = (x + 8)(x + 5)
1*40 2*20 5*8
the answer to 8 x 5 is 40
1 x 40 = 40 2 x 20 = 40 4 x 10 = 40 5 x 8 = 40
40/2 x 5 = 20 x 5 = 100
The geometric mean is a positive number x such that x/5 = 25/x. Thus, x2 = 125, so x = 5*sqrt(5).
√1 x √25 = 1 x 5 = 5
√5 x √6 = 2.23606797749979 x 2.44948974278318 = 5.47722557505166
-x^2 -13x -40 = -(x^2 + 13x + 40) = -(x + 5)*(x + 8)-x^2 -13x -40 = -(x^2 + 13x + 40) = -(x + 5)*(x + 8)-x^2 -13x -40 = -(x^2 + 13x + 40) = -(x + 5)*(x + 8)-x^2 -13x -40 = -(x^2 + 13x + 40) = -(x + 5)*(x + 8)
40 = 5(x-10) 40 = 5x - 50 5x = 40 + 50 x = 90 / 5 x = 18 to check : 40 = (?) 5 (18 - 10) 40 = 5 (8) 40 = 40
x2 + 13x + 40 = x2 + 5x + 8x + 40 = x(x + 5) + 8(x + 5) = (x + 8)(x + 5)
1, 2, 4, 5, 8, 10, 20, 40: 1 x 40, 2 x 20, 4 x 10, 5 x 8Also, 2 x 2 x 2 x 5 = 40
5/8 x 40 = 25
13
1*40 2*20 5*8
the answer to 8 x 5 is 40
The prime factorization of 40 is 23 x 5.The prime factorization of 65 is 5 x 13.The greatest common factor of 40 and 65 is 5.