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Home Question Bank Math Algebra Archive 2025 February 01

Algebra Questions from Feb 01,2025

Browse the Algebra Q&A Archive for Feb 01,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Simplify the algebraic expression by combining like (or similar) terms. \[ x-y^{2}+2+4 y^{2}+2 x+4 \] 13. The admission fee at a carnival is \( \$ 5 \) for children and \( \$ 8 \) for adults. On Friday, 1,250 people attended the carnival and \( \$ 7,300 \) was collected. This situation can be represented with the system \( 5 x+8 y=7,300 \) and \( x+y=1,250 \), where \( x \) represents the number of children that attended the carnival and \( y \) represents the number of adults that attended the carnival. Find the number of children and the number of adults that attended the carnival on Friday. Given the equation \( y = -\frac{1}{2}x + 4 \), plot the corresponding line on a graph. Utilice tanto la propiedad de la suma como la de multiplicación de las desigualdades para resolver la siguiente desigualdad y grafique la solución en una recta numérica. \[ 2 x-4<4 \] Si \( x+\frac{1}{x}=6 \) Calcular \( E=x^{2}+x^{-2} \) a) 34 b) 36 c) 38 d) 40 Select the correct answer. Determine which equation has the same solutions as the given equation. \[ \begin{array}{l}x^{2}=10 x=11=0 \\ \text { A. }(x-5)^{2}=36 \\ \text { B. }(x-10)^{2}=36 \\ \text { C. }(x-10)^{2}=21 \\ \text { D. }(x-5)^{2}=21\end{array} \] Consider the equations below. \[ \begin{array}{ll}\text { A. } y=-2 x^{2}-8 x \\ \text { B. } y=2(x+6)(x-2) \\ \text { C. } y=-2 x^{2}-8 x+16\end{array} \] Use the equations to complete the following statements. Equation \( v \) D. \( y=2(x+4)^{2}-2 \) \( \begin{array}{l}\text { reveals its extreme value without needing to be altered. The extreme value of this equation has a } \square \text { at the }\end{array} \) 18 Select the correct answer. Which equation could be solved using this application of the quadratic formula? \( x=\frac{-8 \pm \sqrt{8^{2}-4(3)(-2)}}{2(3)} \) A. \( -2 x^{2}-8=10 x-3 \) B. \( 3 x^{2}-8 x-10=4 \) C. \( 3 x^{2}+8 x-10=-8 \) D. \( -2 x^{2}+8 x-3=4 \) 17 Select the correct answer. What are the solutions to the equation \( x^{2}-1=399 \) ? A. \( x=20 \) and \( x=-20 \) B. \( x=200 \) and \( x=-200 \) C. \( x=400 \) and \( x=-400 \) D. \( x=\sqrt{398} \) and \( x=-\sqrt{398} \) D. Simplify the algebraic expression by combining like (or similar) terms. \[ 3 x+7 y-9 x x^{\prime}+2, \]
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