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Home Question Bank Math Algebra Archive 2025 January 13

Algebra Questions from Jan 13,2025

Browse the Algebra Q&A Archive for Jan 13,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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39. \( (a+b)(2 a+3 b)(2 x-y) \) ote: These questions are similar to the test questions from Unit 5 . 1. Write the equation of a line in \( y=m x+b \) form that would be perpendicular to a line whose equation is \( y=-\frac{1}{3} x+8 \) and pass through the point \( (0,5) \). (b) Solve. \[ y^{2}-4=0 \] The solution set is \( \{\square\} \). \( \square, \square, \ldots \frac{\square}{\square} \) Simplify the expression using the Quotient of Powers Property: \( \frac{x^{5}}{x^{2}} \) (a) Factor. \[ y^{2}-4=\square \] \( \square \) Given the function \( f(x) = 3x^{1/2} + 5 \), find its inverse. Determine whether the equation is written in the correct form to apply the zero product rule directly. If the equation is not in the correct form, explain what is wrong. \( 6 p^{2}+20 p+6=0 \) Part: \( 0 / 2 \) Part 1 of 2 s-8: s: 2x-5 are the first threc terms of an arithmetic sequence. (1) Determine the value of \( x \). (2) Deternine the feneral te (3) Determine the value of the \( 115^{\circ} \) term. \( x+1 ; 2 x ; 5 x+5 ; \ldots \) is an arithmetic sequence (2) Deternine the general (1) Determine the value of \( x \). What condition(s) is(are) necessary to solve an equation by using the zero product rule? Choose the correct answer. The equation must be set equal to 0 . The polynomial must be factored. The equation must be set equal to 0 , and the polynomial must be factored. 4. Consider the sequence \( 12,10,8,6, \ldots \) \( \begin{array}{ll}\text { (i) What is the term-to-term rule for this sequence? } \\ \text { (ii) If } T_{n}=\square n \pm \text { a number, what number goes in the box? } \\ \text { (iii) Use this to find an expression for } T_{n} \\ \text { (iv) Find } T_{10} \text { of the sequence. } \\ \text { (v) Which term of the sequence is }-14 \text { ? } \\ \text { 5. Find an expression for the } n \text {th term of these sequences: } \\ \begin{array}{ll}\text { (i) }-3,0,3,6,9, \ldots & \text { (ii) } 20,15,10,5, \ldots\end{array}\end{array} \)
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