Let the original fraction be
![\dfrac{n-1}{n}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn-1%7D%7Bn%7D)
Now let's increase both numerator and denominator by 2:
![\dfrac{n+1}{n+2}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn%2B1%7D%7Bn%2B2%7D)
This produces a 1/12 increase:
![\dfrac{n+1}{n+2}-\dfrac{n-1}{n}=\dfrac{1}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn%2B1%7D%7Bn%2B2%7D-%5Cdfrac%7Bn-1%7D%7Bn%7D%3D%5Cdfrac%7B1%7D%7B12%7D)
The left hand side can be rearranged as
![\dfrac{2}{n^2+2n}=\dfrac{1}{12}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7Bn%5E2%2B2n%7D%3D%5Cdfrac%7B1%7D%7B12%7D)
Invert both sides:
![\dfrac{n^2+2n}{2}=12 \iff n^2+2n=24](https://tex.z-dn.net/?f=%5Cdfrac%7Bn%5E2%2B2n%7D%7B2%7D%3D12%20%5Ciff%20n%5E2%2B2n%3D24)
Solve the quadratic equation:
![n^2+2n-24=0 \iff n=-6 \lor n=4](https://tex.z-dn.net/?f=n%5E2%2B2n-24%3D0%20%5Ciff%20n%3D-6%20%5Clor%20n%3D4)
So, in the first case, the original fraction is
![\dfrac{n-1}{n}=\dfrac{-6-1}{-6}=\dfrac{7}{6}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn-1%7D%7Bn%7D%3D%5Cdfrac%7B-6-1%7D%7B-6%7D%3D%5Cdfrac%7B7%7D%7B6%7D)
In the second case, we have
![\dfrac{n-1}{n}=\dfrac{4-1}{4}=\dfrac{3}{4}](https://tex.z-dn.net/?f=%5Cdfrac%7Bn-1%7D%7Bn%7D%3D%5Cdfrac%7B4-1%7D%7B4%7D%3D%5Cdfrac%7B3%7D%7B4%7D)
Answer:
QPR = 73
Step-by-step explanation:
there opposite angles so there equal, therefore we set them equal to each other
(6x+25)=(10x-7)
-4x= -32
x= 8
plug in
6(8)+25
73
Circumference = (π) x (diameter)
Circumference = 8π
(π) x (diameter) = 8π
Diameter = 8
Radius = 4
Area = π x (Radius)²
Area = π x (4)²
Area = π x (16) = <u>50.27 units²</u> (rounded)
All you have to do is insert the x and y value's, then solve.
x = -3
y = -7
(3(-3) - 2(-7)) (-3(-3) + 4(-7))
(-9 + 14) (9 + -28) (Two negatives make a positive.)
(5)(-19)
= -95
Hope this helps you! Happy thanksgiving, here's a turkey!
Answer:
The 30% of a number can be calculated multiplying that number by 0.3, so, if we call the number we don't know x, we can write this equation:
0.3x = 12
And then solve it for x::
x = 12/0.3 = 40
So now we know that the number is 40.
We can replace the 40 in the equation to get if our answer is correct or not..
30% of 40: 0.3 * 40 = 12
And then, we see it's correct