For the following problem, do not include a graph. \( 0 \) of \( 1 \) (a) For the parabola \( y = - 4 x ^ { 2 } + 7 x + 1 \) , find the vertex. (b) Does the vertex correspond to the highest point or the lowest point on the graph?  (a) The vertex is \( ( \frac { 7 } { 8 } , \frac { 65 } { 16 } ) \) (Simplify your answer. Type an ordered pair.) (b) Is the vertex the highest point or lowest point on the graph? Lowest point 

Soient xety deux nombres reels tels que \( : x \leq \frac{1}{2}, y \geq \frac{3}{2} \) et \( x-2 y=5 \) On pose \( A=\sqrt{x^{2}+(x-1)^{2}+2 x(x-1)} \) et \( B=\sqrt{4 y^{2}+(2 y-3)^{2}+4 y(2 y-3)} \) 1) Montrer que : \( A=\sqrt{(2 x-1)^{2}} \) et \( B=\sqrt{\left(4 y-3 t^{2}\right.} \) 4) Simplifier Ies nombres \( A \) et \( B \) 8) Determiner la valeur numérique du nombre \( A+3 \) X

Для матриць A та В знайти матриці: 1. \( \mathrm{A}+\mathrm{B} \); 2. \( 2 \mathrm{~A} ; \) 3. \( \mathrm{A}-\mathrm{B} ; \) 4. A * B \( A=\left(\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right) ; \quad B=\left(\begin{array}{ccc}-1 & 0 & 1 \\ 2 & -3 & 4\end{array}\right) \)

\( \left(I^{\text {st }}\right. \) Session 2022) If the ratio between the fourth term from the beginning to the fourth term from the end in the expansion of \( \left(\frac{a}{x}+\frac{x}{a}\right)^{2 n} \) equals \( a^{4}: x^{4} \) , then \( n=\cdots \cdots \) \( \begin{array}{llll}\text { (a) } 2 & \text { (b) } 4 & \left.\text { (where } x \in \mathbb{R}^{*}, a \in \mathbb{R}^{*}\right)\end{array} \)

In the expansion \( \left(\sqrt[3]{2}+\frac{1}{\sqrt[3]{3}}\right)^{n} \) if the ratio between the seventh term from the beginning to the seventh term from the end \( 1: 6 \), then \( n \) equals \( \begin{array}{llll}\text { (a) } 7 & \text { (b) } 8 & \text { (c) } 9 & \text { (d) } 10\end{array} \)

Solve the equation: \( \sqrt{x + 4} = 6 \)