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Hogar Banco de preguntas Matemáticas Álgebra Archive 2024 December 31

Algebra Questions from Dec 31,2024

Browse the Algebra Q&A Archive for Dec 31,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Evaluate the following expression at \( x=-6 \). \( 5 x-8 \) Select the correct answer below: -42 -41 -39 -38 -34 Simplify the given expression: \[ -3 \times\left[75 \div(9-4)^{2}\right]^{2} \] (C) 200 V \( \begin{array}{ll}\text { (D) } 240 \mathrm{~V} & \text { 1. } 272 \text {; two real solutions } \\ \text { 36. Match each equation on the left with its discriminant and description of its } \\ \text { A. } x^{2}-3 x+6=0 & \text { 2. }-136 \text {; two imaginary solutions } \\ \begin{array}{ll}\text { B. } 8 x^{2}-4 x-8=0 & \text { 3. }-15 \text {; two imaginary solutions } \\ \text { C. } 6 x^{2}-12 x+2=-4 & \text { 4. } 0 \text {; one real solution } \\ \text { D. } 7 x^{2}-2 x-5=-10 & \end{array}\end{array}> \) If \( L \) and \( \frac{3}{L} \) are the two roots of the equation : \( a x^{2}+b x+12=0 \), then \( a=\ldots \ldots \) \( \begin{array}{llll}\text { (a) } 3 & \text { (b) } 4 & \text { (c) } 6 & \text { (d) } 12\end{array} \) 32. Caleb and a friend are throwing snowbals at a red bucket on a hill. The flight of a snowball can be modeled by the equation \( y=-0.02 x^{2}+x+4 \), where \( x \) is the horizontal distance and \( y \) is the height of the snowball in feet. The hill's slope can be modeled by the equation \( y=0.3 x-7.2 \). What is the approximate location where the red bucket should be placed? Justify your answer. 30. HTEM A sea lion dives off a rock into the ocean. Its path can be modeled by a quadratic equation lion's path: \( y=-0.5 x^{2}-x+6 \) where \( x \) is its horizontal distance traveled in feet and \( y \) is its elevation in feet with respect to the water. At the same time, a fish is swimming towards the surface on a path modeled by \( y=4 x-30 \). Where will the paths of the sea lion and fish mect? lustify your answer. 30. STEM A sea lion dives off a rock into the ocean. It path can be modeled by a quadratic equation where \( x \) is its horizontal distance traveled in feet and \( y \) is its elevation in feet with respect to the water. At the same time, a fish is swimming towards the surface on a path modeled by \( y=4 x-30 \). Where will the paths of the sea lion and fish meet? Justify your answer. (h) If \( \frac{x}{y}=2 \) and \( \frac{y}{z}=3 \), find the value of \( \frac{x+y}{y+z} \), 28. \( \begin{array}{l}y=3 x^{2}-2 x \\ 3 x-2 y=4\end{array} \) 26. \( \begin{array}{l}y=x^{2}+2 x \\ 2 x-y=-4\end{array} \)
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