Fill in the blanks. Consider the equation \( \sqrt{7 x+1}=x-2 \). Squaring the left side and simplifying results in \( \ldots \) squaring the right side and simplifying resul Consider the equation \( \sqrt{7 x+1}=x-2 \). Squaring the left side and simplifying results in \( \sqrt{7} x+\sqrt{1} \). Squaring the right side and simplifying res

4. Let \( V \) be a vector space, and \( f: V \rightarrow R, g: V \rightarrow R \) two linear mappings. Let \( F: V \rightarrow R^{2} \) be the mapping defined by \( F(v)=(f(v), g(v)) \). Show that \( F \) is linear.

\( 1< \) The point at which a company's profits equal zero is called the company's break-even point. Let \( R \) represent a company's revenue, let \( C \) represent the company's costs, and let \( x \) represent the number of units produced and sold each day \( R(x)=300 x \) \( C(x)=160.5 x+69,750 \) (a) Find the firm's break-even point; that is, find \( x \) so that \( R=C \) (b) Find the values of \( x \) such that \( R(x)>C(x) \). This represents the number of units that the company must sell to eam a profit.

Calcula el valor de \( q \) \( \frac{3}{5}=\frac{q}{10} \) \( q=\square \)

Suppose that the quantity supplied \( S \) and quantity demanded \( D \) of \( T \)-shirts at a concert are given by the following functions where \( p \) is the price. \[ \begin{array}{l}S(p)=-350+40 p \\ D(p)=1150-60 p\end{array} \] Answer parts (a) through (c). (a) Find the equilibrium price for the \( T \)-shirts at this concert. The equilibrium price is \( \$ \square \) (Round to the nearest dollar as needed.)

\( \frac{\frac{\frac{\frac{3}{2a-3}+2}{-6}}{2a-4}-4}{} \)