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Home Question Bank Math Algebra Archive 2024 November 14

Algebra Questions from Nov 14,2024

Browse the Algebra Q&A Archive for Nov 14,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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\( \left. \begin{array} { l } { f ( x ) = - 2 x - 9 } \\ { g ( x ) = f ( x ) + 10 } \end{array} \right. \) Find the greatest common factor of the terms of the polynomial. \[ 36 u^{8} v^{3}-48 u^{8} v^{2}+12 u^{7} v^{7} \] Write your answer as a constant times a product of single variables raised to exponents. A person has \( \$ 31,000 \) invested in stock A and stock B. Stock A currently sells for \( \$ 30 \) a share and stock B sells for \( \$ 70 \) a share. If stock B triples in value and stock A goes up \( 50 \% \), his stock will be worth \( \$ 88,500 \). How many shares of each stock does he own? Find the greatest common factor of the terms of the polynomial. \[ 7 r^{10}+12 r^{7} s+4 r^{4}-10 s^{7} \] Write your answer as a constant times a product of single variables raised to exponents. valuate the expression below when \( y=3 \). If heeded, answer as a fraction or a decimal. \[ \frac{y \cdot 5}{y+2} \] Find the greatest common factor. \[ 2 b^{10}, 4 b^{10}, 42 b^{10}, 36 b^{10} \] Write your answer as a constant times a product of single variables raised to exponents. If 20 lb of rice and 10 lb of potatoes cost \( \$ 16.60 \), and 30 lb of rice and 12 lb of potatoes cost \( \$ 23.52 \), how much will 10 lb of rice and 50 lb of potatoes cost? Let \( x \) be the cost of 1 lb of rice and \( y \) be the cost of 1 lb of potatoes. Set up two linear equations from the given information using \( x \) and \( y \) as the variables. \( \square=16.60 \) \( \square=23.52 \) (Do not factor. Use integers or decimals for any numbers in the equations.) Factor by grouping (sometimes called the ac-method) \( 3 x^{2}+20 x+33 \) Evaluate the expression below when \( n=6 \). If needed, answer as a fraction or a decimal. \[ n^{3}-3 n+12 \] Find the greatest common factor of the terms of the polynomial. \[ 14 f^{3}+28 f \] Write your answer as a constant times a product of single variables raised to exponents.
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