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Home Question Bank Math Algebra Archive 2025 January 16

Algebra Questions from Jan 16,2025

Browse the Algebra Q&A Archive for Jan 16,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Which equation has the same solution as \( x^{2}+16 x-18=4 \) ? \( \begin{array}{l}\text { Answer } \\ \begin{array}{l}(x-8)^{2}=86 \\ (x-8)^{2}=-42\end{array} \\ \left.(x+8)^{2}=-8\right)^{2}=8\end{array} \) Solve the equation for all values of x by completing the square. Express your answer in simplest for \[ x^{2}+6=10 x \] Factor the expression completely. \[ x^{3} y^{5}-x^{4} y \] \( 8(5+h+2) \) \( 8(h+\square+2) \) Apply the Commutative Property of Addition and add. \( 8(h+\square) \) \( 8 \cdot h+8 \cdot \square \) Apply the Distributive Property and multiply. \( 8 \cdot h+56 \) \( 7 \cdot g - 35 = 7 ( g - \square ) \) Solve the equation for all values of x by completing the square. Express your answer in simplest forr \[ x^{2}+2 x-35=0 \] Answer Attempt 1 out of 2 Additional Solution No Solution \[ x= \] \( \square \) Submit Answer \( 14 ( r + 6 ) = 14 \cdot r + \square \) 7. \( -3 \sqrt{13}-12 \sqrt[3]{13}+6 \sqrt{13}+5 \sqrt[3]{13}= \) 2.3 Is 100 a term in the sequence? Justify your answer. The sum of the second and sixth terms of an arithmetic sequence is 4 The third term is 24 niore than the \( 11^{\text {th }} \) term. 3.1 Determine the first three terms in the sequence. 3.2 Determine a formula for the \( n^{\text {th }} \) term of the sequence. 3.3 Determine the \( 17^{\text {th }} \) term in the sequence. 3.4 Is 72 a term in the sequence? Justify your answer. Which term in the sequence \( 2 ; \frac{5}{3}, \frac{4}{3}, 1 ; \ldots \) has a value of 8 ? Consider the sequence 13,\( 11 ; 9 ; 7 ; 5 \) 11. \( x^{2}-9 x+8 \) 12.) \( x^{2}+x-42 \) \[ [x-9) \] 13. \( x^{2}-x-72 \) 14. \( x^{2}+2 x-63 \) \( -45 \) \[ \begin{array}{l} x^{2}+13 x+40 \\ x^{2}+8 x+5 x+40 \\ x(x+8)+5(x+8) \\ x+8)(x+5) \end{array} \]
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