Calcola l'area di un trapezio avente la base mag- giore, la base minore e l'altezza lunghe rispettiva- mente \( 26 \mathrm{~cm}, 12 \mathrm{~cm} \) e 15 cm . \( \left[285 \mathrm{~cm}^{2}\right] \)

Determine if the following lines are parallel, perpendicular, or neither \[ \begin{array}{l}y=\frac{8 x}{7}-1 \\ -x+3 y=1\end{array} \]

What results when a plane is parallel to the axis of a double-napped cone and passes through the vertex? point parabola two intersecting lines a single line

BCD un carré et \( G= \) bary \( \{(A, 2) ;(B,-1) ;(C, 2) ;(D ; 1)\} \) oient \( I= \) bary \( \{(A, 2) ;(B,-1)\} \) et \( J= \) bary \( \{(C, 2) ;(D ; 1)\} \); Montrer que \( 2 \overrightarrow{G A}-\overrightarrow{G B}=\overrightarrow{G I} \) et \( 2 \overrightarrow{G C}+\overrightarrow{G D}=3 \overrightarrow{G j} \) En déduire que \( G=\operatorname{bary\{ }(I, 1) ;(1,3)\} \) Construire I et \( J \) puis \( G \) a) Vérifier que: \( \forall M \in(P): 2 \overrightarrow{M A}-\overrightarrow{M B}+2 \overrightarrow{M C}+\overrightarrow{M D}=4 \overrightarrow{M G} \) b) Déterminer l'ensemble des points M du plan \( (P) \) tel que : \[ \|2 \overrightarrow{M A}-\overrightarrow{M B}+2 \overrightarrow{M C}+\overrightarrow{M D}\|=4\|2 \overrightarrow{M A}-\overrightarrow{M B}\| \]

Angles 3 and 5 are \( \square \) and \( m \angle 5 \) is \( (2 x+11)^{\circ} \).

EXERCISE 15.1 (in the figure, seg OP \( \perp \mathrm{seg} S T \). Chord LM \( \| \) chord ST. O is the centre of the circle. \( \mathrm{ON}=6 \mathrm{~cm}, \mathrm{LM}=16 \mathrm{~cm} \). Find the length of the longest chord that can be drawn in the circle. (2018) \( \begin{array}{llll}\text { (1) } 32 \mathrm{~cm} & \text { (2) } 20 \mathrm{~cm} & \text { (3) } 12 \mathrm{~cm} & \text { (4) } 22 \mathrm{~cm}\end{array} \)