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Home Question Bank Math Algebra Archive 2025 January 19

Algebra Questions from Jan 19,2025

Browse the Algebra Q&A Archive for Jan 19,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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QUESTION 23 Find the equation of the line that has the given slope and passes through the given point. \( \begin{array}{l}\text { m=-4,(-3,-8) } \\ y=-4 x-20 \\ x=-4 y-20 \\ y=-4 x+20 \\ x=-4 y+20\end{array} \) \( C 1 w^{\circ} \quad 4, \overline{2} \times 3,=120 \) simpllity te Solloming: (3). \( 12^{n+1} \cdot 9^{2 n-1} \) (5) \( \frac{9^{x-1} \cdot 12^{x+1}}{27^{x} \cdot 4^{x-1}} \) (3) \( \frac{12^{n+1!} \cdot 9^{n n-1}}{36^{n} \cdot 8^{1-n}} \) (1) \( \frac{s^{x} \cdot 25^{x-1}}{5 \cdot 125^{x}} \) (9) \( \frac{3^{z x-1}-3^{x+2}}{3^{x}+3^{x+2}} \) (8). \( \frac{3^{2 n}-9^{n+1}}{72^{n}} \) (4) \( \frac{2^{2 n-1}+3 \cdot 2^{2 n-3}}{5 \cdot 40^{n-1}+4^{n+1}} \) (3) \( \frac{25^{n} \cdot 15^{n-1} \cdot 3^{n}}{125^{n} \cdot 9^{n-1}} \) Rearrange the polynomial \( x^3 + 2 - 7x^2 \) into standard form. factorise flly \( 8 p x-12 p^{2} x \) 3 [a] If \( f(x)=x^{2}-3 x, g(x)=x-3 \), find : \( f(\sqrt{2})+3 g(\sqrt{2}) \) Two submersibles, one red and one blue, started rising toward the surface at the same time. They each rose at a constant speed. The red submersible started rising from an altitude of 80 meters below the surface. After 30 seconds, it was 60 meters below the surface. The following equation gives the altitude (in meters relative to the surface) of the blue submersible as a function of time (in seconds). A \( =-90+0.6 t \) Which submersible started rising from a higher altitude? Choose 1 answer: (A) The red submersible (B) The blue submersible (C) They both started from the same altitude Which submersible rose faster? The functions \( f \) and \( g \) are defined as follows. \[ f(x)=x^{2}+5 x+8 \quad \text { and } \quad g(x)=\frac{2}{x^{2}-3} \] Find \( f(x-3) \) and \( g\left(-\frac{5}{x}\right) \) The functions \( f \) and \( g \) are defined as follows. \[ f(x)=x^{2}-2 x-6 \text { and } g(x)=\frac{5 x-1}{9 x-4} \] Find \( f(x+7) \) and \( g\left(\frac{x}{2}\right) \) The functions \( f \) and \( g \) are defined as follows. \[ f(x)=\frac{5 x+3}{6 x+7} \quad \text { and } g(x)=\sqrt{x^{2}-4 x} \] Find \( f\left(\frac{5}{x}\right) \) and \( g(x-3) \) \( \frac { 2,5 \cdot 10 ^ { n + 20 } - 5 \cdot 10 ^ { n + 40 } } { 50 \cdot 5 ^ { n + 10 } - 10 \cdot 20 ^ { n + 80 } } \)
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