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)
Answer: f(x) increases:(x less than or equal to sign 3)
Step-by-step explanation:
Since your equation is in vertex formula, it is more simple to find the vertex first and then go from there.
Since you have in the parenthesis (x-3) and you have the +12 on the outside, we can conclude that the vertex is (3,12) and that it is faces down because of the negative symbol in front of the vertical stretch of 3 on the outside of the parenthesis.
From there when you draw the graph it should look like an upside down U shape with the highest point being (3,12) because that that is your vertex and 12 is your max.
The axis of symmetry would be 3.
The graph would increase at x is less than or equal to 3 and x would decrease at x is greater than or equal to 3.
Answer:
cos(O) = 39 / 89
Step-by-step explanation:
Given:
ΔOPQ, where
∠Q=90°
PO = 89
OQ = 39
QP = 80
cosine of ∠O?
cos(O) = Adjacent / Hypotenuse
cos(O) = 39 / 89
5 dimes = 50 cents
2 nickels = 10 cents
you have 60 cents
