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Home Question Bank Math Algebra Archive 2025 January 18

Algebra Questions from Jan 18,2025

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

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Escribe la ecuación de una recta que pasa por el punto \((2, 3)\) y tiene una pendiente de \(4\). Nicole and Randy are having an origami competition. Nicole has already made 50 cranes and can make 9 per hour. Randy has already made 85 cranes and can make 4 per hour. At what number of hours will they have made the same amount of cranes, and how many cranes is that?? \( x-y=3 \) and \( x^{2}-x y=2 y^{2}+7 \) IMU Question 3 It has been found the generally the time, \( t \), taken to a puzzle varies directly with the number of pieces, \( n \), and inversely with the number of people, \( p \), working on it. If it takes 4 people 36 minutes to solve and 180 piece puzzle, how long will it take 6 people to solve a 420 piece puzzle? IMU Question 3 It has been found the generally the time, \( t \), taken to a puzzle varies directly with the number of pieces, \( n \), and inversely with the number of people, \( p \), working on it. If it takes 4 people 36 minutes to solve and 180 piece puzzle, how long will it take 6 people to solve a 420 piece puzzle? IMU Question 3 It has been found the generally the time, \( t \), taken to a puzzle varies directly with the number of pieces, \( n \), and inversely with the number of people, \( p \), working on it. If it takes 4 people 36 minutes to solve and 180 piece puzzle, how long will it take 6 people to solve a 420 piece puzzle? for \( x \) if \( 2 x^{2}-4 x=36-\frac{270}{3 x^{2}-6 x} \) \( 4 x^{2}-y^{2}=171 \) and \( 2 x-y=9 \) EXERCISE 2 Consider the following functions: \( \begin{array}{lll}\text { (a) } f(x)=2 x+4 & \text { (b) } f(x)=3 x-6 & \text { (c) } f(x)=\frac{1}{2} x+3 \\ \text { (d) } f(x)=4 x-1 & \text { (e) } f(x)=-2 x & \text { (f) } f(x)=2 x-5\end{array} \) \( \begin{array}{ll}\text { (1) For each function determine } f^{-1} \text {, the inverse function in the form } f^{-1}(x)=\ldots \ldots \\ \text { (2) Hence draw neat sketch graphs of both functions on the same set of axes. } \\ \text { (3) Draw the line of symmetry on the same set of axes as the two graphs. } \\ \text { (4) Determine the coordinates of the point of intersection of both graphs and } \\ \text { then indicate this point on the diagram. }\end{array} \) EXERCISE 2 Consider the following functions: \( \begin{array}{lll}\text { (a) } f(x)=2 x+4 & \text { (b) } f(x)=3 x-6 & \text { (c) } f(x)=\frac{1}{2} x+3 \\ \text { (d) } f(x)=4 x-1 & \text { (e) } f(x)=-2 x & \text { (f) } f(x)=2 x-5\end{array} \) \( \begin{array}{ll}\text { (1) For each function determine } f^{-1} \text {, the inverse function in the form } f^{-1}(x)=\ldots \ldots . \\ \text { (2) Hence draw neat sketch graphs of both functions on the same set of axes. } \\ \text { (3) Draw the line of symmetry on the same set of axes as the two graphs. } \\ \text { (4) Determine the coordinates of the point of intersection of both graphs and } \\ \text { then indicate this point on the diagram. }\end{array} \)
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