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Home Question Bank Math Archive 2025 January 10

Math Questions from Jan 10,2025

Browse the Math Q&A Archive for Jan 10,2025, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Calculate the gross profit for an item that cost the business \( \$ 6 \) and sold for \( \$ 8 \). Gross Profit = \$[?] 1) Sotre the giren systen by usiry the inverse of the coefficient mutrix. \[ \begin{array}{c} 2 x+y+3 z=2 \\ x+2 z=1 \\ y+z=4 \end{array} \] 2) Differentiate the furetion \[ f(z)=\frac{z^{4}}{4}-\frac{5}{z^{1 / 3}} \] 3) Differentia/e the futalisa \[ y=\frac{1}{x+\frac{1}{x++^{\prime}}} \] 4) Find the Marginal-cost functict if lise areraye-cos/ function "I \[ \bar{c}=2 q+\frac{10,000}{q^{2}} \] 5) A manufacturer's maryial cosl funation is \[ \frac{d c}{d q}=0.6 q+2 \] If preduction is presently set it \( q=20 \) Unils per week, how nueh nore would It cost to merease prodection to 100 Units per week? Sia dato il problema di Cauchy \( \left\{\begin{array}{l}\dot{y}=\left(y^{2}-3 y+2\right)(t-3) \\ y(0)=\frac{3}{2}\end{array}\right. \) É vero che: Scegli un'alternativa: il problema di Cauchy ha più di una soluzione locale il problema di Cauchy ha un'unica soluzione, illimitata inferiormente il problema di Cauchy Thon ha soluzione il problema di Cauchy ha un'unica soluzione, illimitata superiormente il problema di Cauchy ha un'unica soluzione, limitata s streak, so let's start a new one today. \( \begin{array}{l}\text { Find the solution to the system of equations. } \\ \text { You can use the interactive graph below to find the solution. } \\ \left\{\begin{array}{l}y=-7 x+3 \\ y=-x-3\end{array}\right. \\ \text { week } \\ \text { streak }\end{array} \) Khan Academy Donate streak, so let's start a new one today. week Level 4 (i) Find the solution to the system of equations. You can use the interactive graph below to find the solution. \[ \begin{array}{l} \left\{\begin{array}{l} -8 x+4 y=24 \\ -7 x+7 y=28 \end{array}\right. \\ x=\square \end{array} \] S start a new one today. \[ \begin{array}{l}-3 x+3 y=9 \\ \text { Estimate the solution to the system of equations. } \\ \text { You can use the interactive graph below to find the solution. } \\ 2 x-7 y=-14 \\ \text { Choose } 1 \text { answer: } \\ \text { (A) } x=-1 \frac{2}{5}, y=1 \frac{3}{5} \\ \text { (B) } x=-2 \frac{2}{5}, y=1 \frac{3}{5} \\ \text { (C) } x=-1 \frac{2}{5}, y=2 \frac{3}{5} \\ \text { (D) } x=-2 \frac{2}{5}, y=2 \frac{3}{5}\end{array} \] Given: \( D \) is the midpoint of \( \overline{A C}, \overline{B A} \cong \overline{B C} \) and \( \angle E D A \cong \angle F D C \). Prove: \( \triangle A E D \cong \triangle C F D \). Note: quadrilateral properties are not permitted in this proof. Graficar \( y=4 \operatorname{sen} 2 x \) Find the solution to the system of equations. You can use the interactive graph below to find the solution. \( \left\{\begin{array}{l}-3 x-9 y=18 \\ 4 x+3 y=12\end{array}\right. \) \( x= \) a) \( \frac{9^{-1} x^{-2} y^{2}}{\left(3 x y^{-1}\right)^{-3}} \)
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