The factorial ! just means we multiply by every natural number less that the value so
6! =6×5×4×3×2×1= 720
for permutations we use the formula n!/(n-r)!
so we have 8!/(8-5)!=8!/3!=8×7×6×5×4
for combinations s we have n!/(n-r)!r!
so we have 12!/(12-4)!4!=12!/8!4!=12×11×10×9/4×3×2=11×10×9/2=99×5
let's firstly convert the mixed fractions to improper fractions and then divide.
![\bf \stackrel{mixed}{17\frac{13}{18}}\implies \cfrac{17\cdot 18 +13}{18}\implies \stackrel{improper}{\cfrac{319}{18}}~\hfill \stackrel{mixed}{2\frac{7}{9}}\implies \cfrac{2\cdot 9+7}{9}\implies \stackrel{improper}{\cfrac{25}{9}} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%5Cbf%20%5Cstackrel%7Bmixed%7D%7B17%5Cfrac%7B13%7D%7B18%7D%7D%5Cimplies%20%5Ccfrac%7B17%5Ccdot%2018%20%2B13%7D%7B18%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B319%7D%7B18%7D%7D~%5Chfill%20%5Cstackrel%7Bmixed%7D%7B2%5Cfrac%7B7%7D%7B9%7D%7D%5Cimplies%20%5Ccfrac%7B2%5Ccdot%209%2B7%7D%7B9%7D%5Cimplies%20%5Cstackrel%7Bimproper%7D%7B%5Ccfrac%7B25%7D%7B9%7D%7D%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill)
![\bf \cfrac{319}{18}\div \cfrac{25}{9}\implies \cfrac{319}{\underset{2}{~~\begin{matrix} 18 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{\stackrel{1}{~~\begin{matrix} 9 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{25}\implies \cfrac{319}{50}\implies 6\frac{19}{50}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B319%7D%7B18%7D%5Cdiv%20%5Ccfrac%7B25%7D%7B9%7D%5Cimplies%20%5Ccfrac%7B319%7D%7B%5Cunderset%7B2%7D%7B~~%5Cbegin%7Bmatrix%7D%2018%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7D%5Ccdot%20%5Ccfrac%7B%5Cstackrel%7B1%7D%7B~~%5Cbegin%7Bmatrix%7D%209%20%5C%5C%5B-0.7em%5D%5Ccline%7B1-1%7D%5C%5C%5B-5pt%5D%5Cend%7Bmatrix%7D~~%7D%7D%7B25%7D%5Cimplies%20%5Ccfrac%7B319%7D%7B50%7D%5Cimplies%206%5Cfrac%7B19%7D%7B50%7D)
Answer: (x + 3)(x - 4)
Step-by-Step Solution:
We need to Factorize the given Quadratic Polynomial by using Splitting the Middle Term Method.
= x^2 - x - 12
= x^2 - 4x + 3x - 12
= x(x - 4) + 3(x - 4)
=> (x + 3)(x - 4)
Answer:
d
Step-by-step explanation:
180-149= 31.
31+ 122= 153
180-153= 27
a= 27