thedudemanguyperson

You have made some good progress. BDC is a 30-60-90 triangle. This means that BD:DC:BC=1:sqrt3:2. It also means that angle CBD=60 degrees. So our answer is 45+60=105 degrees

There are no given sentences.

Note that \(\frac{dy}{dx}(log_a x)=\frac{1}{x\ln a}\). So \(\frac{dy}{dr}(log_2 r * log_4 r)=\frac{dy}{dr}(log_2 r)*\frac{dy}{dr}(log_4 r)=\frac{1}{r\ln 2}*\frac{1}{r\ln 4}=\frac{1}{r^2\ln 2\ln 4}\)

First, she gets it on sale, so \(y-0.15y=0.85y\). Then, take that 0.85y and multiply it by 1.05 (to add the sales tax). So the result is \((0.85y)(1.05)=0.8925y\).

\(a+b=82, a=4b-3\rightarrow 4b-3+b=82\rightarrow 5b-3=82\rightarrow 5b=85\rightarrow \boxed{b=17}\rightarrow \boxed{a=4*17-3=65}\)

Solution here: https://artofproblemsolving.com/community/c3h2267357_help_on_percents

Hopefully this helps.

https://imgur.com/7l9GAtE

You could let \(f(x)=ax^2+bx+c\) and solve the system, but that is messy. Alternatively, we can plot the points. This shows us that the vertex of the parabola is simply (3,2)! So our graph is shifted three to the right, and 2 up. This means that \(f(x)=(x-3)^2+2=x^2-6x+11\). 

Graph --> https://www.desmos.com/calculator/xvkbk8bhpl

\(x\equiv 3\pmod{7}, x\equiv 6\pmod{8}, x\equiv 2\pmod{5}\). You can either list or use CRT from here. You should get 262.

Let first term be a and diff be n. 8a+28n=244 and a+2n=20. Solving a=6,n=7, so 6 is our answer.