Answer:
see explanation
Step-by-step explanation:
Under a reflection in the x- axis
a point (x, y ) → (x, - y )
We have
(a, b ) → (a, - b ) ← reflection in the x- axis
Answer:
5 units
Step-by-step explanation:
its hard to tell but i think it dilated 5 units
Answer : Top cell = 12 ; Bottom cell = 7
Step-by-step explanation:
The rules of a diamond problem states that, one should add the two numbers (3 and 4) to get the value in the bottom cell and multiply the two numbers (3 and 4) again to get the value in the top cell.
Therefore; Top cell, 3×4= 12 Bottom cell, 3+4 = 7.
![\bf ~~~~~~~~~~~~\textit{negative exponents}\\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\\\ \textit{also recall that }a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}} \\\\ -------------------------------](https://tex.z-dn.net/?f=%5Cbf%20~~~~~~~~~~~~%5Ctextit%7Bnegative%20exponents%7D%5C%5C%5C%5C%0Aa%5E%7B-n%7D%20%5Cimplies%20%5Ccfrac%7B1%7D%7Ba%5En%7D%0A%5Cqquad%20%5Cqquad%0A%5Ccfrac%7B1%7D%7Ba%5En%7D%5Cimplies%20a%5E%7B-n%7D%0A%5Cqquad%20%5Cqquad%20%0Aa%5En%5Cimplies%20%5Ccfrac%7B1%7D%7Ba%5E%7B-n%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Ctextit%7Balso%20recall%20that%20%7Da%5E%7B%5Cfrac%7B%20n%7D%7B%20m%7D%7D%20%5Cimplies%20%20%5Csqrt%5B%20m%5D%7Ba%5E%20n%7D%20%0A%5Cqquad%20%5Cqquad%0A%5Csqrt%5B%20m%5D%7Ba%5E%20n%7D%5Cimplies%20a%5E%7B%5Cfrac%7B%20n%7D%7B%20m%7D%7D%0A%5C%5C%5C%5C%0A-------------------------------)
![\bf \cfrac{(-54)^2}{\sqrt[3]{(-54)^5}}\implies \cfrac{(-54)^2}{(-54)^{\frac{5}{3}}}\implies (-54)^2(-54)^{-\frac{5}{3}}\implies (-54)^{2-\frac{5}{3}} \\\\\\ (-54)^{\frac{6-5}{3}}\implies (-54)^{\frac{1}{3}}\implies \sqrt[3]{(-54)^1}\implies \sqrt[3]{(-54)} \\\\\\ \begin{cases} 54=2\cdot 3\cdot 3\cdot 3\\ \qquad 2\cdot 3^3 \end{cases}\implies \sqrt[3]{-1\cdot 2\cdot 3^3 }\implies 3\sqrt[3]{-2}](https://tex.z-dn.net/?f=%5Cbf%20%5Ccfrac%7B%28-54%29%5E2%7D%7B%5Csqrt%5B3%5D%7B%28-54%29%5E5%7D%7D%5Cimplies%20%5Ccfrac%7B%28-54%29%5E2%7D%7B%28-54%29%5E%7B%5Cfrac%7B5%7D%7B3%7D%7D%7D%5Cimplies%20%28-54%29%5E2%28-54%29%5E%7B-%5Cfrac%7B5%7D%7B3%7D%7D%5Cimplies%20%28-54%29%5E%7B2-%5Cfrac%7B5%7D%7B3%7D%7D%0A%5C%5C%5C%5C%5C%5C%0A%28-54%29%5E%7B%5Cfrac%7B6-5%7D%7B3%7D%7D%5Cimplies%20%28-54%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Cimplies%20%5Csqrt%5B3%5D%7B%28-54%29%5E1%7D%5Cimplies%20%5Csqrt%5B3%5D%7B%28-54%29%7D%0A%5C%5C%5C%5C%5C%5C%0A%5Cbegin%7Bcases%7D%0A54%3D2%5Ccdot%203%5Ccdot%203%5Ccdot%203%5C%5C%0A%5Cqquad%202%5Ccdot%203%5E3%0A%5Cend%7Bcases%7D%5Cimplies%20%5Csqrt%5B3%5D%7B-1%5Ccdot%202%5Ccdot%203%5E3%20%7D%5Cimplies%203%5Csqrt%5B3%5D%7B-2%7D)
![\bf -5\sqrt[3]{2x+3}=15\impliedby \textit{we first raise both sides by }^3 \\\\\\ (-5\sqrt[3]{2x+3})^3=(15)^3\implies (-5)^3(\sqrt[3]{2x+3})^3=3375 \\\\\\ (-125)(2x+3)=3375\implies 2x+3=\cfrac{3375}{-125}\implies 2x+3=-27 \\\\\\ 2x=-30\implies x=-\cfrac{30}{2}\implies x=-15](https://tex.z-dn.net/?f=%5Cbf%20-5%5Csqrt%5B3%5D%7B2x%2B3%7D%3D15%5Cimpliedby%20%5Ctextit%7Bwe%20first%20raise%20both%20sides%20by%20%7D%5E3%0A%5C%5C%5C%5C%5C%5C%0A%28-5%5Csqrt%5B3%5D%7B2x%2B3%7D%29%5E3%3D%2815%29%5E3%5Cimplies%20%28-5%29%5E3%28%5Csqrt%5B3%5D%7B2x%2B3%7D%29%5E3%3D3375%0A%5C%5C%5C%5C%5C%5C%0A%28-125%29%282x%2B3%29%3D3375%5Cimplies%202x%2B3%3D%5Ccfrac%7B3375%7D%7B-125%7D%5Cimplies%202x%2B3%3D-27%0A%5C%5C%5C%5C%5C%5C%0A2x%3D-30%5Cimplies%20x%3D-%5Ccfrac%7B30%7D%7B2%7D%5Cimplies%20x%3D-15)
