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Home Question Bank Math Algebra Archive 2024 December 28

Algebra Questions from Dec 28,2024

Browse the Algebra Q&A Archive for Dec 28,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Si las raíces de una ecuación cuadrática son \( 3 / 2 \) y -5 , entonce es: Simplify the radical expression: \( \sqrt{50x^2} \) Part-II: Fill in the blank space by short answer only (1pt each) 5. What is the negation of; Every student in this class likes mathematics. 6. The GCF and LCM of two numbers are 3 and 180 respectively. If one of the numbers is 12, then the second number is. What does the exponent in an expression indicate? Determine the value(s) of k for which the equation \( \frac{1}{\mathrm{k}}=\mathrm{x}^{2}-\mathrm{x}+1 \) where \( \mathrm{k} \neq 0 \) has real roots. Sbuve that \( (2 \sqrt{2})^{5}=32 \sqrt{2} \) ExERCICE 3 Inéquation Résoudre dans \( \mathbb{R} \) les inéquations suivantes : \( \begin{array}{lll}\text { 1) } x^{2}+3 x-4 \leqslant 0 & \text { 2) } 7 x-3 \leqslant 2 x^{2} & \text { 3) } \frac{5 x^{2}-3 x}{x^{2}+4 x+3} \geqslant 0\end{array} \) EXERCICE 1 - 1 (3 points) Forme canonique et variation Soit la fonction trinôme \( f \) suivante : \( f(x)=2 x^{2}+12 x+53 \). 1) Déterminer la forme canonique de \( f(x) \). 2) En déduire les variations de \( f \) et dresser le tableau de variation de \( f \). 3) D'après le tableau de variation de \( f \), la parabole représentant \( f \) coupe-t-elle l'axe des abscisses? Pourquoi? h) \( \left\{\begin{array}{l}x+y+z=50 \\ 2 x=y+1 \\ 2 x=5 z\end{array}\right. \) 95 If \( \frac{\log x}{\log 3}+\frac{\log x}{\log 9}+\frac{\log x}{\log 27}=22 \), then \( x=\ldots \ldots \ldots \ldots \ldots \) \( \begin{array}{llll}\text { (a) } 3^{2} & \text { (b) } 3^{9} & \text { (c) } 3^{12} & \text { (d) } 3^{27}\end{array} \)
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