Rational function with Trig coefficients

The horizontal asymptote would be $y=1$ since the graph would approach the ratio of the leading coefficients, which is $1$ , as x approaches infinity. If we let $F(x)=1$ , then $x^2+\sin(θ)|x-7|+\cos(θ)=x^2+\cos(θ)|x+4|+\sin(θ)$ . By canceling out the $x$ and factoring, $\tan(θ)=$ $\frac{1-|x+4|}{1-|x-7|}$ . Since there is only $1$ possible asymptote, that means there is $1$ possible value for $x$ , so $|x+4|=|x-7|≠1$ and $θ=45°$ . This yields only $x+4=7-x$ as $x+4=x-7$ has no solution, so $2x=3$ and $x=1.5$ . As a result, the intersection is $(1.5,1)$ so $10(1.5)+5(1)=20$ which is the final answer.