Answer:
check this out
Step-by-step explanation:
From the information obtained from the question, two equations can be created:
Let x and z be the two numbers (parts)
![\frac{1}{z} + \frac{1}{x} = \frac{3}{10}](https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7Bz%7D%20%20%20%2B%20%20%20%5Cfrac%7B1%7D%7Bx%7D%20%20%3D%20%20%20%5Cfrac%7B3%7D%7B10%7D%20%20)
. . . . (1)
![z + x = 15](https://tex.z-dn.net/?f=z%20%20%2B%20%20%20x%20%20%3D%20%2015)
. . . . (2)
By transposing (2), make 'z' the subject of the equation
![z = 15 - x](https://tex.z-dn.net/?f=z%20%3D%2015%20-%20x)
. . . . (3)
By substituting (3) into equation (1) to find a value for x
![\frac{1}{(15 - x)} + \frac{1}{x} = \frac{3}{10}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B%2815%20-%20x%29%7D%20%2B%20%5Cfrac%7B1%7D%7Bx%7D%20%3D%20%5Cfrac%7B3%7D%7B10%7D)
![\frac{15}{( 15 - x ) ( x )} = \frac{3}{10}](https://tex.z-dn.net/?f=%20%5Cfrac%7B15%7D%7B%28%2015%20-%20x%20%29%20%28%20x%20%29%7D%20%20%3D%20%20%20%5Cfrac%7B3%7D%7B10%7D%20)
![3 ( - x^{2} + 15 x ) = 150](https://tex.z-dn.net/?f=3%20%28%20-%20x%5E%7B2%7D%20%20%2B%2015%20x%20%29%20%20%3D%20%20150)
![3 x^{2} - 45x + 150 = 0](https://tex.z-dn.net/?f=3%20x%5E%7B2%7D%20%20-%2045x%20%2B%20150%20%3D%200)
⇒
![( x - 5 ) ( x - 10 ) = 0](https://tex.z-dn.net/?f=%28%20x%20-%205%20%29%20%20%28%20x%20-%2010%20%29%20%20%3D%200)
∴ either
![( x - 5) = 0](https://tex.z-dn.net/?f=%28%20x%20-%205%29%20%3D%200)
OR
![( x - 10 ) = 0](https://tex.z-dn.net/?f=%28%20x%20-%2010%20%29%20%3D%200)
Thus x = 5 or x = 10
By substituting the values of x into (2) to find z
z + (5) = 15 OR z + (10) = 15
⇒ z = 10 OR z = 5
So, the two numbers or two parts into which fifteen is divided to yield the desired results are 5 and 10.
20% x 50 =(20 / 100) x 50 = (20 x 50) / 100 = 1000 / 100 = 10
answer is 10
Answer:
The two numbers following 1,-2,3,-4,5... are -6 and 7.
Step-by-step explanation:
index: 1 2 3 4 5 ....
value: 1 -2 3 -4 5
Let the index be n. Then the first term is a(1), the secon is a(2), and so on.
a(2) = 2*(-1)^(2-1) = 2*(-1) = -2 (correct)
a(3) = 3*(-1)^(3-1) = 3*(-1)^2 = 3 (correct)
a(4) = 4*(-1)^(4-1) = 4*(-1)^3 = -4 (correct)
So the general formula for a(n) is: a(n)=n(-1)^(n-1)
Thus,
a(5) = 5(-1)^4 = 5
a(6) = 6(-1)^5 = -6
a(7) = 7(-1)^6 = 7
The "next two numbers in the pattern" are -6 and 7. The first 7 numbers are
1,-2,3,-4,5, -6, 7