You have to check which of the following expressions is the rational exponent expression of third root of 4n, or mathematically,
Consider all cases:
A. ![(4n)^3=4^3\cdot n^3=64n^3\neq\sqrt[3]{4n} .](https://tex.z-dn.net/?f=%20%284n%29%5E3%3D4%5E3%5Ccdot%20n%5E3%3D64n%5E3%5Cneq%5Csqrt%5B3%5D%7B4n%7D%20.%20%20)
B. ![3n^4\neq \sqrt[3]{4n} .](https://tex.z-dn.net/?f=%203n%5E4%5Cneq%20%5Csqrt%5B3%5D%7B4n%7D%20.%20%20)
C. quantity of 4n to the one third power is
(by the definition of rational power).
D. 4 times n to the one third power is ![4\cdot n^{\frac{1}{3} }=4\sqrt[3]{n}\neq \sqrt[3]{4n} .](https://tex.z-dn.net/?f=%204%5Ccdot%20n%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%3D4%5Csqrt%5B3%5D%7Bn%7D%5Cneq%20%5Csqrt%5B3%5D%7B4n%7D%20.%20%20)
Answer: correct choice is C.
Answer:
1. Saturday
2(a) 10,944
2(b) 32700
3. (16,24)
Step-by-step explanation:
Answer:
34 apples
Step-by-step explanation:
To answer: try setting up each of the equations for Annie and Eva.
Annie: 2(bag) + 5
Eva: 1(bag) + 11
Those two equations equal each other. So set that up:
2(bag) + 5 = 1(bag) + 11
Now solve for the size of the bag.
2(bag) - 1(bag) = 11 - 5
1(bag) = 6 apples
Now substitute 6 back into either equation to determine number of apples.
Annie: 2(6) + 5 = 12+5=17
They each have 17, so there are 34 apples in total.
Check the picture below.
now, we're making an assumption that, the two blue shaded region are equal in shape, and thus if that's so, that area above the 14 is 6 and below it is also 6, 14 + 6 + 6 = 26.
so hmm if we simply get the area of the trapezoid and subtract the area of the yellow triangle and the area of the cyan triangle, what's leftover is what we didn't subtract, namely the shaded region.
![\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h~~=height\\ a,b=\stackrel{parallel~sides}{bases~\hfill }\\[-0.5em] \hrulefill\\ h=15\\ a=14\\ b=26 \end{cases}\implies A=\cfrac{15(14+26)}{2}\implies A=300 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\Large Areas}}{\stackrel{trapezoid}{300}~~ - ~~\stackrel{yellow~triangle}{\cfrac{1}{2}(26)(9)}~~ - ~~\stackrel{cyan~triangle}{\cfrac{1}{2}(15)(6)}} \\\\\\ 300~~ - ~~117~~ - ~~45\implies 138\qquad \textit{blue shaded area}](https://tex.z-dn.net/?f=%5Ctextit%7Barea%20of%20a%20trapezoid%7D%5C%5C%5C%5C%20A%3D%5Ccfrac%7Bh%28a%2Bb%29%7D%7B2%7D~~%20%5Cbegin%7Bcases%7D%20h~~%3Dheight%5C%5C%20a%2Cb%3D%5Cstackrel%7Bparallel~sides%7D%7Bbases~%5Chfill%20%7D%5C%5C%5B-0.5em%5D%20%5Chrulefill%5C%5C%20h%3D15%5C%5C%20a%3D14%5C%5C%20b%3D26%20%5Cend%7Bcases%7D%5Cimplies%20A%3D%5Ccfrac%7B15%2814%2B26%29%7D%7B2%7D%5Cimplies%20A%3D300%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7B%5CLarge%20Areas%7D%7D%7B%5Cstackrel%7Btrapezoid%7D%7B300%7D~~%20-%20~~%5Cstackrel%7Byellow~triangle%7D%7B%5Ccfrac%7B1%7D%7B2%7D%2826%29%289%29%7D~~%20-%20~~%5Cstackrel%7Bcyan~triangle%7D%7B%5Ccfrac%7B1%7D%7B2%7D%2815%29%286%29%7D%7D%20%5C%5C%5C%5C%5C%5C%20300~~%20-%20~~117~~%20-%20~~45%5Cimplies%20138%5Cqquad%20%5Ctextit%7Bblue%20shaded%20area%7D)