Algebra Questions from Nov 11,2024

Browse the Algebra Q&A Archive for Nov 11,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Find the term that does not contain \( x \) in the expansion of \( \left(8 x+\frac{1}{2 x}\right)^{8} \) Choose the correct answer for the question: Solve the equation. Write the solution set with the exact values given in terms of common or natural logarithms. Also give approximate solutions to 4 decimal places. \( e^{2 t}-4 e^{t}-32=0 \) There are 3 consecutive integers that add up to 39. What is the value of the least integer (C) Find AB: I) If \( A=\left[\begin{array}{cc}2 & -4 \\ 3 & 2\end{array}\right] \quad \& \quad B=\left[\begin{array}{cc}4 & 0 \\ -1 & 3\end{array}\right] \) A confectioner sells two types of nut mixtures. The standard-mixture package contains 100 g of cashews and 200 g of peanuts and generate a profit of R15.00 per package. The deluxe-mixture package contains 150 g of cashews and 50 g of peanuts and generates a profit of R20.00 per package. The confectioner has 15 kg of cashews and 20 kg of peanuts available. Based on past sales, he needs to have at least as many standard as deluxe packages available. (i) How many bags of each mixture should he package to maximize his profit? (ii) What is the maximum profit? Choose the correct answer for the question: a. \( \begin{array}{ll}\text { (i) } 90 \text { bags of standard and } 40 \text { bags of deluxe mixture } & \text { (ii) Maximum profit is } \\ \text { R2 } 2150.00\end{array} \) (i) 90 bags of standard and 70 bags of deluxe mixture (ii) Maximum profit is R2750.00 There are 4 consecutive odd integers with a sum of -112 . What are the integers? \( \begin{array}{ll}\text { 5. } & (2 x-4)^{2}=8 y-16 \\ \text { 6. } & x^{2}+8 x-y+6=0 \\ \text { 7. } & y^{2}+x-3 y+4=0 \\ \text { 8. } & 2 x-y^{2}-6 y+1=0 \\ \text { 9. } & x^{2}+3 x+3 y-1=0 \\ \text { 10. } & 2 x^{2}-8 x-4 y+3=0 \\ \text { 11. } & 2 x+4 y^{2}+8 y-5=0 \\ \text { 12. } & 4 x^{2}-12 x+12 y+7=0 \\ \text { 13. } & 3 x^{2}-6 x-9 y+4=0 \\ \text { 14. } & y^{2}+10 x-5=0\end{array} \) Which expression is equivalent to \( -8(x+3)-5 x+7 ? \) A. \( 13 x+31 \) B. \( -3 x+10 \) C. \( -13 x-17 \) D. \( -3 x+10 \) (3) Calcule a valor dex para \( 5 x-3>x+1 \) \( 2 x+8 \geqslant 3(x-6) \) Three consecutive integers have a sum of -87 . What is the value of the least integer
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