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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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18. Fill in the blank with an appropriate inequality a. If \( x<-2 \), then \( 1-\mathrm{x} \) b. If \( \frac{1}{2}\left(3 x-\frac{2}{3}\right) \leq x+5 \), then \( x+\frac{7}{3} \) c. If \( 3 x-1>5 x-3 \), then \( 3 x \) 1) \( a^{2}-4 \) \( \left. \begin{array} { l } { x ^ { 2 } - x - 6 } \\ { x ^ { 2 } - x - 72 } \\ { x ^ { 2 } + 5 x - 6 } \\ { x ^ { 2 } - 4 x - 45 } \\ { x ^ { 2 } + 3 x - 18 } \end{array} \right. \) \( \left. \begin{array} { l l } { x ^ { 2 } - 4 } & { = y ^ { 2 } - 2 ^ { 2 } } \\ { y ^ { 2 } - 1 } & { = } \\ { 25 x ^ { 2 } - 36 } & { = } \\ { 16 - 81 a ^ { 2 } } & { = } \end{array} \right. \) 4. The factors of \( 2 x^{2}-8 \) are: \( 2\left(4 x^{2}\right) \) \( 2\left(x^{2}+4\right) \) Teniendo en cuenta la expresión \( 6 \mathrm{x}-2 \mathrm{y} \leq-12 \), es correcto afirmar que se trata de una desigualdad lineal: a. estricta de dos variables. b. débil de una variable. c. debicta de una variable. La ecuación de la linea recta asociada con la desigualdad \( 3 / 2 y-5 / 2 x \geq-2 \mathrm{es} \) : a. \( \quad y=\frac{5}{3}-\frac{4}{3} x \) b. \( \quad y=-\frac{5}{3} x+\frac{4}{3} \) c. \( y=\frac{5}{3} x-\frac{4}{3} \) d. \( y=-\frac{5}{3}+\frac{4}{3} x \) Solve: \[ \frac{x-a}{x-b}+\frac{x-b}{x-a}=\frac{a}{b}+\frac{b}{a} \] stema \( \left\{\begin{array}{l}x+y=10 \\ 2 x-y=8\end{array}\right. \) La desigualdad lineal \( 15 y+2 x<-5 \) es un semiplano que: a. contiene al punto \( (-3,0) \) b. está delimitado por una línea curva. c. contiene al punto \( (0,0) \). d. se encuentra a la derecha del punto \( (0,0) \)
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