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Home Question Bank Math Algebra Archive 2025 January 08

Algebra Questions from Jan 08,2025

Browse the Algebra Q&A Archive for Jan 08,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Solve for \( u \), where \( u \) is a real number. \[ \sqrt{u}=2 \] If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( u=\square \square \) |ll \( \begin{array}{l}4 x-5 y=-20 \\ 3 x+y=23\end{array} \) 3.) \( \left(\frac{2}{3}\right)^{x}=\frac{16}{81} \) Simplify the expression. Do not use spaces between numbers or signs. \( 12 c-c= \) Simplify the expression. Do not use spaces between numbers or signs. \( 5 x+4+9 x= \) 12. Solve the systemi of equations shown below algebraically: \[ \begin{array}{r}(x-3)^{2}+(y+2)^{2}=16 \\ 2 x+2 y=10\end{array} \] 12. Solve the system of equations shown below algebraically: \( \begin{array}{l}(x-3)^{2}+(y+2)^{2}=16 \\ 2 x+2 y=10\end{array} \) 2) In an arithmetic sequence \( T_{1}=(1-x)^{2} \) and \( T_{2}=1+x^{2} \) : a) Write down an expression for the common difference in terms of \( x \). b) Determine the value(s) of \( x \) if \( S_{10}=310 \). 3) Using your knowledge of serles: a) Prove that the surn of the fusst \( n \), odd natural numbers is \( n^{2} \). b) Prove that the sum of the first \( n \), even natural numbers is \( n^{2}+n \). 4) The sum of the first 5 terms of an arithmetic sequence is 0 and the ficth term is 8. Determine the common difference and the first term 5) In a geometric series the first term is 36 , the last term is 16 and the sum of the series is 76 . Determine the common ratio and the number of terms in the sequence. 6) The sum of the first 4 terms of an arithmetic sequence is 24 . The \( 7^{\text {th }} \) term exceeds the \( 3^{\text {rd }} \) term by 24. Determine the sum of the first 12 terms. O Copyright Kevia Smith/Eerlat Books CC 19 Estimation Gabe goes to the mall. If \( b \) is the number of items he bought, the expression \( 15.27 b+28 \) gives the amount he spent in dollars at one store. Then he spent 20 dollars at another store. Find the expression which represents the amount Gabe spent at the mall. Then estimate how much Gabe spent if he bought 5 items. What expression represents the amount in dollars that Gabe spent at the mall? \( \square \) (Simplify your answer. Use whole numbers or decimals for any numbers in the expression.) \( (-2 x-3)+(6+6 n)+(5 n+4 x) \) \( (-2 x-3)+(6+6 n)+(5 n+4 x)=\square \) (Simplify your answer.)
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