Algebra Questions from Jan 26,2025

Browse the Algebra Q&A Archive for Jan 26,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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6) \( \left(4 x^{3}-6 y^{2}\right)^{7} \) 1. Let \( R \) be a relation from \( \{11,12,13\} \) and \( \{8,10,12\} \) defined by \( y=x-3 \), then the relation \( R^{-1} \) is: A. \( \{(11,8),(13,10)\} \) B. \( \{(\mathbf{8}, 11),(\mathbf{9}, 12),(\mathbf{1 0 , 1 1 )}\} \) C. \( \{(8,11),(10,13)\} \) D. none Find the Range of the following function. 1. \( f(x)=3 x+5 \), where: a. \( x=1 \) b. \( x=-3 \) c. \( \mathrm{x}=0 \) 2. \( f(x)=-5 x-9 \) where: a. \( \mathrm{x}=3 \) b. \( x=-6 \) c. \( \mathrm{x}=2 \) 3. \( f(x)=4 x^{2}+13 \) where: a. \( x=-5 \) b. \( x=9 \) 4. \( f(x)=x^{2}-9 x+3 \quad \) where: a. \( x=-1 \) b. \( x=0 \) 4. What is the solution to the equation \( -0.2(x-20)=44-x \) ? \( \begin{array}{ll}\text { (A) } x=-90 & \text { (C) } x=50 \\ \text { (B) } x=-50 & \text { (D) } x=90\end{array} \) Find the value of \( a \) that makes the equation true for all values of \( x \cdot\left(\frac{32}{2}\right)^{-2 x}=a^{x} \) \( a=\frac{1}{16} \) \( a=\frac{1}{256} \) \( a=256 \) \( a=16 \) \( a \) nsider the quadratic number pattern: \( 45 ;-122 ;-101 ; \ldots \) Write down the value of \( T_{4} \). 4. The function \( L(d)=2 d^{4}-21 d^{3}+38 d^{2}+21 d+ \) 6600 represents the total number of likes Simon's rideo had received \( d \) days after he posted it online. After what whole number of days did his video get 12,320 likes? Garrett has one dollar less than three times as much money as Liz has. Together they have \( \$ 179 \). How much money does Garrett have? 30. The function \( S(m)=m^{3}-18 m^{2}+72 m+100 \) represents the number of skateboards sold each month at a store where \( m \) is the whole number of months after releasing a new model. How many months after the model was released were 181 skateboards sold? Question Solve the following quadratic inequality. Give your answer in interval notation.
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