Mei Mei signed up for a streaming music service that costs \( \$ 6 \) per month. The service allows Mei Mei to listen to unlimited music, but if she wants to download songs for offline listening, the service charges \$o.50 per song. How much total money would Mei Mei have to pay in a month in which she downloaded 35 songs? How much would she have to pay if she downloaded \( s \) songs? Answer Attempti out of a Cost with 35 songs:

Given \( h(x)=\sqrt{3 x+3} \), find \( h(15 \cdot 1) \). Your answer should be \( v \)

a) \( 25 x^{2}+100 y^{2}-100=0 \)

8.) Line \( l \) passing through the points \( (-3,-5) \) and \( (0,-5) \) Line \( n \) passing through the points \( (0,5) \) and \( (4,9) \) 8.) Circ

II) Por partes a) \( \int(3 x-1) e^{5 x-1} d x \) b) \( \int 3 x \operatorname{sen}(x+2) d x \) c) \( \int x^{-2} \ln 2 x d x \)

1- Montrer que : \( \exists!\alpha \in] \frac{-1}{2} ; 0\left[/ \sqrt{\alpha+1}=\frac{-2 \alpha}{\alpha+1}\right. \) 2- On considère la fonction \( h \) de la variable réel \( x \) définie sur \( \mathbb{R} \) par: \( h(x)=x^{3}-x^{2}+3 x+1 \). a- Vérifier que : \( h(\alpha)=0 \). b- Montrer que \( \alpha \) est la seule et unique solution de l'équation: \( h(x)=0 \). c- Montrer que \( h \) admet une fonction réciproque \( h^{-1} \) définie sur un intervalle \( J \) que l'on précisera. d- Montrer que : \( \left(\forall x \in \mathbb{R}^{-}\right)\left(h^{-1}(x)<0\right) \)