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Home Question Bank Math Algebra Archive 2025 January 01

Algebra Questions from Jan 01,2025

Browse the Algebra Q&A Archive for Jan 01,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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What is the equation of the line with slope -7 which goes through the poin \( (2,5) \) ? Give your answer in slope-intercept form \( y=m x+b \). 10. \( 2\left(p^{t}\right)^{s} \) 11. \( \frac{1}{\left(\frac{1}{a}\right)^{-1}} \) 12. \( \frac{k^{0}}{k^{-1}} \) 13. \( \frac{-2}{-2^{-a}} \) Find the \( y \)-intercept of the following line. \[ y=-3 x-4 \] Give your answer as an ordered pair \( (a, b) \) For what range of values of \( x \) is \( 3 x^{2}+5 x \) -28 negative? Find the slope of the following line: \[ y=-7 x-6 \] \[ 6=8 x-2 \] Enter your answer as a simplified improper fraction, if necessary. Do not include " \( x \) Simplify the following: 1. \( 4 \times 4^{2 a} \times 4^{2} \times 4^{a} \) 2. \( \frac{3^{2}}{2^{-3}} \) 3. \( \left(3 p^{5}\right)^{2} \) 4. \( \frac{k^{2} k^{3 x-4}}{k^{x}} \) 5. \( \left(5^{z-1}\right)^{2}+5^{z} \) 6. \( \left(\frac{1}{4}\right)^{0} \) 7. \( \left(x^{2}\right)^{5} \) 8. \( \left(\frac{a}{b}\right)^{-2} \) 9. \( (m+n)^{-1} \) 10. \( 2\left(p^{t}\right)^{s} \) Determine if the following equation is an identity equation, a conditional equation, or an inconsis \[ 6 x+6 x-6=2-5 \] Select the correct answer below: Identity equation Conditional equation Inconsistent equation Content attribution Simplify the following: \( \begin{array}{ll}\text { 1. } 4 \times 4^{2 a} \times 4^{2} \times 4^{a} & \text { 14. } \frac{-h}{(-h)^{-3}} \\ \text { 2. } \frac{3^{2}}{2^{-3}} & \text { 15. }\left(\frac{a^{2} b^{3}}{c^{3} d}\right)^{2} \\ \text { 3. }\left(3 p^{5}\right)^{2} & \text { 16. } 10^{7}\left(7^{0}\right) \times 10^{-6}(-6)^{0}-6 \\ \text { 4. } \frac{k^{2} k^{3 x-4}}{k^{x}} & \text { 17. } m^{3} n^{2} \div n m^{2} \times \frac{m n}{2} \\ \text { 5. }\left(5^{z-1}\right)^{2}+5^{z} & \text { 18. }\left(2^{-2}-5^{-1}\right)^{-2} \\ \text { 6. }\left(\frac{1}{4}\right)^{0} & \text { 19. }\left(y^{2}\right)^{-3} \div\left(\frac{x^{2}}{y^{3}}\right)^{-1} \\ \text { 7. }\left(x^{2}\right)^{5} & \text { 20. } \frac{2^{c-5}}{2^{c-8}} \\ \text { 8. }\left(\frac{a}{b}\right)^{-2} & \text { 21. } \frac{2^{9 a} \times 4^{6 a} \times 2^{2}}{85 a} \\ \text { 9. }(m+n)^{-1} & \text { 22. } \frac{20 t^{5} p^{10}}{10 t^{4} p^{9}} \\ \text { 10. } 2\left(p^{t}\right)^{s} & \text { 23. }\left(\frac{q^{-3 s} y^{-4 a-1}}{q^{-3 s}}\right)^{2} \\ \text { 11. } \frac{1}{\left(\frac{1}{a}\right)^{-1}} & \text { 12. } \frac{k^{0}}{k^{-1}}\end{array} \) Solve the following equation for \( x \) : \[ -4(x-5)+1=-1+3(x+6) \]
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