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Home Question Bank Math Algebra Archive 2024 December 28

Algebra Questions from Dec 28,2024

Browse the Algebra Q&A Archive for Dec 28,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( 4 ( ( \frac { \sqrt { 3 } } { 2 } x - \frac { 1 } { 2 } y ) ^ { 2 } ) + ( 2 \sqrt { 3 } ( \frac { \sqrt { 3 } } { 2 } x - \frac { 1 } { 2 } y ) ( \frac { 1 } { 2 } x + \frac { \sqrt { 3 } } { 2 } y ) ) + 2 ( ( \frac { 1 } { 2 } x + \frac { \sqrt { 3 } } { 2 } y ) ^ { 2 } ) + 10 \sqrt { 3 } ( \frac { \sqrt { 3 } } { 2 } x - \frac { 1 } { 2 } y ) + 10 ( \frac { 1 } { 2 } x + \frac { \sqrt { 3 } } { 2 } y ) = 5 \) If a function \( f(x) = 3x + 2 \), what is its inverse function? \( 4 ( ( \frac { \sqrt { 3 } } { 2 } x - \frac { 1 } { 2 } y ) ^ { 2 } ) + ( 2 \sqrt { 3 } ( \frac { \sqrt { 3 } } { 2 } x - \frac { 1 } { 2 } y ) ( \frac { 1 } { 2 } x + \frac { \sqrt { 3 } } { 2 } y ) ) + 2 ( ( \frac { 1 } { 2 } x + \frac { \sqrt { 3 } } { 2 } y ) ^ { 2 } ) + 10 \sqrt { 3 } ( \frac { \sqrt { 3 } } { 2 } x - \frac { 1 } { 2 } y ) + 10 ( \frac { 1 } { 2 } x + \frac { \sqrt { 3 } } { 2 } y ) = 5 \) Divide \( x^{3}+2 x^{2}-5 x+12 \) by \( (x+3) \) Reduciendo la siguiente expresión \( \sqrt{\frac{20^{x+1}}{4^{x+2}+2^{2 x+2}}} \) 3.) The function \( g \) is related to one of the parent functions \( g(x)=-(x-2)^{\wedge} 3 \) a.) Identify the parent function \( f \). b.) Use function notation to write \( g \) in terms of \( f \). [a] Find the S.S. of the equation in \( \mathbb{R}:\left(x^{2}+4\right)\left(x^{2}-9\right)=0 \) 2.) The function \( g \) is related to one of the parent functions \( g(x)=x 2-3 \) The parent function is: \( f(x)=x^{\wedge} 2 \) Use function notation to write \( g \) in terms of \( f \). Aplica la propiedad del cociente de potencias a esta expresión: \( \frac{y^{5}}{y^{-2}} \). 1.) The function \( g \) is related to one of the parent functions \[ g(x)=x^{\wedge} 2+6 \] The parent function \( f \) is: \( f(x)=x^{\wedge} 2 \) Use function notation to write \( g \) in terms of \( f \).
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