Answer:
Concept: Algebraic Analysis
![\geqslant \: \: \: \: \: \: \: \: \: \: \leqslant](https://tex.z-dn.net/?f=%20%5Cgeqslant%20%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%5Cleqslant%20)
- Those two symbols indicate one solution
![< \: \: \: \: \: \: \: >](https://tex.z-dn.net/?f=%20%3C%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%5C%3A%20%20%3E%20)
- Those symbols indicate a range of values
![x < 15 < x](https://tex.z-dn.net/?f=x%20%3C%2015%20%3C%20x)
- Indicates two bounded answers
- In an inequality there is always a solution
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:
(1/6)^2
Step-by-step explanation:
We want to find the fraction that is equivalent to 1/36.
Let us look at each of them individually:
a. ![(\frac{1}{108})^3 = \frac{1}{1259712}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B108%7D%29%5E3%20%3D%20%5Cfrac%7B1%7D%7B1259712%7D)
b. ![(\frac{1}{9})^4 = \frac{1}{6561}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B9%7D%29%5E4%20%3D%20%20%5Cfrac%7B1%7D%7B6561%7D)
c. ![(\frac{1}{6})^2 = \frac{1}{36}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B6%7D%29%5E2%20%3D%20%20%5Cfrac%7B1%7D%7B36%7D)
d. ![(\frac{1}{5})^2 = \frac{1}{25}](https://tex.z-dn.net/?f=%28%5Cfrac%7B1%7D%7B5%7D%29%5E2%20%3D%20%5Cfrac%7B1%7D%7B25%7D)
Therefore, the correct answer is c.
Answer: A negative
Step-by-step explanation:
The opposite of a negative is positive, the opposite of a positive is a negative.