Answer:
Sarah is incorrect.
Step-by-step explanation:
By plugging 10 in as 'x' to the equation, we get y=21+(2*10). 2 x 10 is 20, and 20 + 21 is <em>not</em> 42 - it's 41. So, Sarah is incorrect.
.2 goes into 7 35 times.
you move the decimal in .2 to make it 2 and make 7 70; 2 goes into 7 3 times which gives you 6 on top and 10 on the bottom, 2 goes into ten 5 times so your final answer would be 35
if you've read those links already, you'd know what we're doing here.
we'll move the repeating part to the left-side of the dot, by multiplying by "1" and as many zeros as needed, or 10 at some power pretty much.
on 0.13 we need 100 to get 13.13.... and on 0.1234, we need 10000 to get 1234.1234....
![\bf 0.\overline{13}~\hspace{10em}x=0.\overline{13} \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{|lll|ll} \cline{1-3} &&\\ 100\cdot 0.\overline{13}& = & 13.\overline{13}\\ 100\cdot x&& 13 + 0.\overline{13}\\ 100x&&13+x \\&&\\ \cline{1-3} \end{array}\implies \begin{array}{llll} 100x=13+x\implies 99x=13 \\\\ x=\cfrac{13}{99} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 0.\overline{1234}~\hspace{10em}x=0.\overline{1234} \\\\[-0.35em] ~\dotfill](https://tex.z-dn.net/?f=%20%5Cbf%200.%5Coverline%7B13%7D~%5Chspace%7B10em%7Dx%3D0.%5Coverline%7B13%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill%5C%5C%5C%5C%0A%5Cbegin%7Barray%7D%7B%7Clll%7Cll%7D%0A%5Ccline%7B1-3%7D%0A%26%26%5C%5C%0A100%5Ccdot%200.%5Coverline%7B13%7D%26%20%3D%20%26%2013.%5Coverline%7B13%7D%5C%5C%0A100%5Ccdot%20x%26%26%2013%20%2B%200.%5Coverline%7B13%7D%5C%5C%0A100x%26%2613%2Bx%0A%5C%5C%26%26%5C%5C%0A%5Ccline%7B1-3%7D%0A%5Cend%7Barray%7D%5Cimplies%20%5Cbegin%7Barray%7D%7Bllll%7D%0A100x%3D13%2Bx%5Cimplies%2099x%3D13%0A%5C%5C%5C%5C%0Ax%3D%5Ccfrac%7B13%7D%7B99%7D%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A%5Crule%7B34em%7D%7B0.25pt%7D%5C%5C%5C%5C%0A0.%5Coverline%7B1234%7D~%5Chspace%7B10em%7Dx%3D0.%5Coverline%7B1234%7D%0A%5C%5C%5C%5C%5B-0.35em%5D%0A~%5Cdotfill%20)
