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Home Question Bank Math Algebra Archive 2025 February 18

Algebra Questions from Feb 18,2025

Browse the Algebra Q&A Archive for Feb 18,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Suppose that the polynomial function \( f \) is defined as follows. \[ f(x)=(x+2)^{3}(x-6)(x+13)(x-2) \] List each zero of \( f \) according to its multiplicity in the categories below. If there is more than one answer for a multiplicity, separate them with commas. If there Zero(s) of multiplicity one: Zero(s) of multiplicity two: Zero(s) of multiplicity three: 4. What is \( x^{\wedge} 2+x^{\wedge} 2 \) ? A. \( x^{\wedge} 4 \) B. \( 2 x^{\wedge} 2 \) C. \( x^{\wedge} 2 \) D. \( 2 x^{\wedge} 4 \) Solve for a Specific Variable (Quadratics) 3. Below is the equation for the volume of cylinder. Solve the equation for \( r \). \( V=\pi r^{2} h \) Factor the following binomial. (using the difference of square method) \[ 4 x^{2}-4 \] \( ([?] x+\square)(\square x-\square) \) clu Solve for \( x \) and \( y \) simulteineously (1) \( 4 x-2 y=6 \) and \( 2 y+3 x=8 \) (2) \( 3^{x+y}=27 \) and \( 2^{y}=4^{x+1} \) 1tcu Selve for \( x \) and \( y \operatorname{simuitancously} \) (1) \( 2 x-y=17 \) and \( 4 y+3 x=9 \) (2) \( 2 x-4 y=6 \) and \( 3 x-5 y=10 \) (3) \( 2 x+y=8 \) and \( 2 y+3 x=2 \) (4) \( x+3 y=5 \) and \( 2 x-6 y+2=0 \) (5) \( x+y=12 \) and \( 4 x+2 y=6 y+4 \) 93-100 - Diga si la ecuación dada es verdadera para todos los va- lores de las variables. (No considere ningún valor que haga que el denominador sea cero.) \( \begin{array}{ll}\text { 93. } \frac{16+a}{16}=1+\frac{a}{16} & \text { 94. } \frac{b}{b-c}=1-\frac{b}{c} \\ \text { 95. } \frac{2}{4+x}=\frac{1}{2}+\frac{2}{x} & \text { 96. } \frac{x+1}{y+1}=\frac{x}{y} \\ \text { 97. } \frac{x}{x+y}=\frac{1}{1+y} & \text { 98. } 2\left(\frac{a}{b}\right)=\frac{2 a}{2 b} \\ \text { 99. } \frac{-a}{b}=-\frac{a}{b} & \text { 100. } \frac{1+x+x^{2}}{x}=\frac{1}{x}+1+x\end{array} \) Factor the following binomial. \[ 16-25 x^{2} \] \( ([?]+x)(\square-\quad x) \) Solving a word problem ualng a quadralle copuatlon wilh Iratlonal rools A model rocket is launched with an initial upward velocity of \( 65 \mathrm{~m} / \mathrm{m} \). The rocket's height, \[ h=65 t-5 t^{2} \] Find all values of \( t \) for which the rocket's height is 25 meters. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.) Factor the following binomial. \[ 1-x^{2} \] \( ([?]+\quad x)(\square-x) \) 1) The sum of \( x \) and 2 \( \qquad \) 2) \( \quad \) d divided by 8 \( \qquad \) 3) The product of 9 and \( m \) \( \qquad \) 4) Subtract 5 from c \( \qquad \) 5) Combine \( y \) and 7 \( \qquad \) 6) Three-sevenths of \( h \) \( \qquad \) 7) 3 multiplied by d \( \qquad \) 8) One-quarter added to \( n \) \( \qquad \) 9) b decreased by 10 \( \qquad \) 10) One-half of \( k \) \( \qquad \)
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