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![\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)
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![\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)
22)
The area of ABED is 49 square units. Given AGequals9 units and ACequals10 units, what fraction of the area of ACIG is represent
ed by the shaded region?
1 answer:
Answer:
The fraction of the area of ACIG represented by the shaped region is 7/18
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
In the square ABED find the length side of the square
we know that
AB=BE=ED=AD
The area of s square is
where b is the length side of the square
we have
substitute
therefore
step 2
Find the area of ACIG
The area of rectangle ACIG is equal to
substitute the given values
step 3
Find the area of shaded rectangle DEHG
The area of rectangle DEHG is equal to
we have
substitute
step 4
Find the area of shaded rectangle BCFE
The area of rectangle BCFE is equal to
we have
substitute
step 5
sum the shaded areas
step 6
Divide the area of of the shaded region by the area of ACIG
Simplify
Divide by 5 both numerator and denominator
therefore
The fraction of the area of ACIG represented by the shaped region is 7/18
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