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Hogar Banco de preguntas Matemáticas Archive 2025 February 24

Math Questions from Feb 24,2025

Browse the Math Q&A Archive for Feb 24,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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If \( f(x)=5 x^{6}+4 x^{5}+2 \), then what is the remainder when \( f(x) \) is divided by \( x+1 \) ? Answer Attempt 1 out of 2 A region is defined by the functions \( y = e^{-x} \) for \( x \geq 0 \) and \( y = 0 \). What is the volume generated when this region is revolved around the line \( y = 1 \)? (i) \( 8+4 \times 2-10+3 \times 2 \) \( \left. \begin{array} { l } { f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - x + 10 } \\ { f ( 2 K + 3 ) } \end{array} \right. \) Consider the following three systems of linear equations. \[ \begin{array}{c} \text { System A } \\ \left\{\begin{array} { c } { \text { System B } } \\ { - 3 x + 4 y = - 1 5 [ A 1 ] } \\ { - 2 x + 5 y = - 1 7 [ A 2 ] } \end{array} \left\{\begin{array} { c } { 6 x - 8 y = 3 0 \quad [ B 1 ] } \\ { - 2 x + 5 y = - 1 7 [ B 2 ] } \end{array} \left\{\begin{array}{cc} 7 y=-21 \end{array} \quad[C 1]\right.\right.\right. \\ -2 x+5 y=-17[C 2] \end{array} \] Answer the questions below. For each, choose the transformation and then fill in the blank with the correct number. The arrow ( \( \rightarrow \) ) means the expression on the left becomes the expression on the right. (a) How do we transform System A into System B? \( \square \) \( \times \) Equation [A1] \( \rightarrow \) Equation [B1] \( \square \) \( \times \) Equation [A2] \( \rightarrow \) Equation [B2] \( \square \) \( \times \) Equation [A1] + Equation [A2] \( \rightarrow \) Equation [B2] \( \square \) \( \times \) Equation [A2] + Equation [A1] \( \rightarrow \) Equation [B1] (b) How do we transform System B into System C? \( \square \) \( \times \) Equation [B1] \( \rightarrow \) Equation [C1] \( \square \) \( \times \) Equation [B2] \( \rightarrow \) Equation [C2] \( \square \) \( \times \) Equation \( [\mathrm{B} 1]+ \) Equation \( [\mathrm{B} 2] \rightarrow \) Equation [C2] \( \square \) \( \times \) Equation \( [B 2]+ \) Equation \( [B 1] \rightarrow \) Equation \( [C 1] \) 1.1. Study the list of numbers below and ar Write down (answers may be repeated): 1.1.1. Natural number(s). 1.1.2. Whole number(s). 1.1.3. Rational number(s). 1.1.4. Integer(s). 1.5. Irrational number(s). 1.6. Prime number(s). 2. Determine the HCF and LCM of 46 a Solve for \( a \) and \( b \) if \( \left(a^{2}-4\right)\left(b^{2}-2\right)=0 \) 10 Angelica mixes a fruit drink using mango juice and orange juice in the ratio \( 3: 5 \). Sanjay mixes a fruit drink using mango juice and orange juice in the ratio 5:11. a What fraction of each fruit drink is orange juice? b Whose fruit drink, Angelica's or Sanjay's, has the higher proportion of orange juice? Show all your working. Justify your choice. Dati i punti \( A\left(3 ; 2 k^{2}-1\right) \) e \( B(-5 ; 6) \) determinare il valore del parametro \( k \) affinché la retta \( A B \) abbia coefficiente angolare uguale a -4 \[ \text{Find } 2011^2 - 2010^2 \text{?} \]
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