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Home Question Bank Math Algebra Archive 2024 December 24

Algebra Questions from Dec 24,2024

Browse the Algebra Q&A Archive for Dec 24,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Для матриць A та В знайти матриці: 1. \( \mathrm{A}+\mathrm{B} \); 2. \( 2 \mathrm{~A} ; \) 3. \( \mathrm{A}-\mathrm{B} ; \) 4. A * B \( A=\left(\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6\end{array}\right) ; \quad B=\left(\begin{array}{ccc}-1 & 0 & 1 \\ 2 & -3 & 4\end{array}\right) \) Exercice 1 1) Compléter avec l'un des symboles : \( \epsilon ; \notin ; \subset \) ou \( \notin \) \( \{0 ;-7 ; 12\} \ldots \ldots \mathbb{N}^{*} ; \frac{5 \pi-\pi}{2 \pi-\pi} \ldots . \mathbb{Q} ;\left\{-1 ; \frac{18}{6} ; \sqrt{36} ;-7\right\} \ldots . \mathbb{Z} ; \frac{7}{3} \ldots \ldots \) ID 2) donner l'écriture scientifique : \( A=\frac{4 \times 300^{2} \times\left(2 \times 10^{-6}\right)^{-2}}{(0.01)^{-3}} \) Solve the equation: \( \sqrt{x + 4} = 6 \) 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 \( \left(I^{\text {st }}\right. \) 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 \( \begin{array}{llll}\text { (a) } 7 & \text { (b) } 8 & \text { (c) } 9 & \text { (d) } 10\end{array} \) Determine the values of \( x \) and \( y \), in the equation: \( \frac{x-1}{3+i}+\frac{y-1}{3-i}=i \). Solve the following equations: i) \( 2^{2 x+1}=3^{2 x-5} \quad \) ii) \( \log _{2} x-\log _{2} y=2 \) \( \log _{2}(x-2 y)=3 \) In a senior secondary school, 80 students play hockey or football. The number that plays football is 5 more than twice the number that play hockey. If 15 students play both games and every student in the schoo plays at least one game, find the number of students that play football. Solve for \( f \) in the proportion. \[ \begin{array}{l}\frac{8}{13}=\frac{f}{15.6} \\ f=\square\end{array} \] Solve for \( a \) in the proportion. \[ \begin{array}{l}\frac{19}{a}=\frac{9.5}{6} \\ a=\square\end{array} \] [b] If \( x=\sqrt{3}+\sqrt{2}, y=\frac{1}{\sqrt{3}+\sqrt{2}} \), find the value of: \( x^{2}-y^{2} \)
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