3. (*) Dado los vectores \( \vec{a}=\left(1,2 x_{1}, 3\right) \), \( \vec{b}=\left(-1,3 x_{2},-2 x_{1}\right), \vec{c}=\left(2,2,-3 x_{2}\right) \) los valores de \( x_{1} \quad y x_{2} \) para los cuales se cumple que \( 2 \vec{a}-3 \vec{b}+\vec{c}=(7,15,21) \) es respectivamente: a. \( (2,-1) \) b. \( (-1,2) \) c. \( (2,-3) \) d. \( (-3,1) \)

Solve for \( x \) in the logarithmic equation \( 10^{\log \left(10^{24}\right)}=10^{x} \). (1 point) \( \begin{array}{l}x=10^{24} \\ x=24^{10} \\ x=24 \\ x=10\end{array} \)

\( 1 \leftarrow \quad \begin{array}{l}\text { A company finds it can produce } 25 \text { heaters for } \$ 6550 \text {, while producing } 30 \text { heaters costs } \$ 7800 \text {. Express the cost, } \\ \text { as a linear function of the number of heaters, } x \text {. Determine the cost to produce } 40 \text { heaters. } \\ \text { Express the cost, } y \text {, as a linear function of the number of heaters, } x \text {. } \\ y=\square \\ \text { (Simplify your answer.) } \\ \text { The cost to produce } 40 \text { heaters is } \$ \square\end{array} \).

Find the slope and \( y \)-intercept of the graph of the equation. \[ y=\frac{2}{5} x-1 \] Slope \( =\square \) (Enter a fully reduced fraction.) The y-intercept is \( \square \). (Simplify your answer. Type an ordered pair.)

Solve for \( m \) \[ \begin{array}{l}-8-5 m=-3 m+6 \\ m=\square \\ \text { Submit }\end{array} \]

A line that includes the points \( (-8, v) \) and \( (-6,-10) \) has a slope of -8 . What is the value of \( v \) ?