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Home Question Bank Math Algebra Archive 2025 January 01

Algebra Questions from Jan 01,2025

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

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\( f \alpha \) and \( \beta \) are the roots of the quadratic quation \( a x^{2}+b x+c=0 \), find in term: f \( \alpha \) and \( \beta \), the roots of the equation \( c x^{2}+b x+a=0 \). \[ x=\frac{-b \pm \sqrt{b^{2}-4 a r}}{2 a} \] A continuación utiliza el método de completar cuadrados para resolver las sigulentes ecuaciones cuadráticas. \[ \begin{array}{l} \text { 1. } 3 a^{2}-10 a=-1 \\ \text { 3. } x^{2}+16 x=57 \\ 3 a^{2}-100+1=0 \\ a=3 b=10 c=1 \\ \begin{array}{l} x=-(-10) \pm \sqrt{-10)^{2}-4(3)(1)} \\ 2 . z^{2}+10 z=56 \quad 2(3) \quad 4 . m+14 m=32 \end{array} \\ a=1 \\ x=-16 \\ x=16{ }^{t} \end{array} \] (4) \( 2 x^{2}+3 x^{2}=2 \) The equation \( 3 x^{2}+3 k x+k=0 \) where \( k \) is ion-zero constant, has roots \( \alpha \) and \( \beta \). find the quadratic equation whose oots are \( \frac{\alpha^{2}}{\beta\left(\alpha^{3}+\beta^{3}+k^{3}\right)} \) and \( \frac{\beta^{2}}{\alpha\left(\alpha^{3}+\beta^{3}+k^{3}\right)} \) Select all equations that have graphs with the same \( y \) intercept. 1 2 3 4 \( y=3 x-8 \) \( y=3 x-9 \) \( y=3 x+8 \) \( y=5 x-8 \) \( y=2 x-8 \) \( y=\frac{1}{3} z-8 \) Solve the 3-part Open Sentence. * \( \begin{array}{l}20>5 x+15>5 \\ \text { Mark only one oval. } \\ \text { No Real Number Solutions } \\ \text { All Real Number Solutions } \\ x>4 \\ 1>x>-2 \\ 1<x<-2\end{array} \) 21. A fitness club charges \( \$ 25 \) per month as well as a one-time \( \$ 80 \) fee of al new members. Which equation represents the cost in dollars, \( c \), for a nen member who prepays for \( m \) months? A \( c=105 m \) B. \( c=m+105 \) C. \( c=80 m+25 \) D. \( c=25 m+80 \) 4) The Logan family is renting a beach house from Aqua Coast Beach Rentals. Mr. Logan called the rental agency ahead of time to get the total cost for 9 days. The rental agent explained that since the family plans to stay during the off-season, there will be a one-time discount of \( \$ 25 \) applied to their rental cost. The Logans will pay \( \$ 920 \) in all. W)) Which equation can you use to find \( d \), how much the agency charges per day? \( 9(d-25)=920 \) \( 9 d-25=920 \) Solve for x using the quadratic formula in the equation: \( 3x^{2} - 6x + 2 = 0 \) 5. Soive the 3 part Open Sentance \[ \begin{array}{l}11=3 x-7=29 \\ \text { Mark only one oval. } \\ \text { No Real Number Solutions } \\ \text { All Real Number Solutions } \\ x=72 \\ x=6,12 \\ x=1.33,7.33\end{array} \]
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