Express the equation of the given line in standard form. Then find the distance from the given point $P\left(x_1, y_1\right)$ to that line. Round answers to the nearest hundredth.

The line is perpendicular to the line $2 y=3 x-4$ and passes through the origin; $P(2,-5)$.

Solve each polynomial equation. If a solution occurs more than once, state its multiplicity.

$$x^3+x^2-9 x-9=0$$

Express each quadratic function in the form $f(x)=a(x-h)^2+k$. Then use transformations of the graph of $f(x)=x^2$ to graph each function.

$$f(x)=-2 x^2-5$$

Solve.

$$-\frac{42}{y}=\frac{y-25}{3}$$

Determine the symmetries of each equation. Then use the properties of symmetry to graph each equation.

$$x y^2-1$$

Show that $P(1,1), Q(5,4), R(9,1)$, and $S(5,-2)$ are the vertices of a rhombus.

Express the equation of the given line in the form $A x+B y+C=0$. Then find the distance from the given point $P\left(x_1, y_1\right)$ to that line. Round answers to the nearest hundredth.

$$x=3 ; P(5,7)$$

Solve each quadratic equation by an appropriate method.

$$x^2-10 x+70=0$$

Determine the equation of the line satisfying the given conditions:

Passes through the point $(-2,-4)$ and has slope of $-2$

Show that $P(-3,2), Q(-2,-1), R(0,3)$, and $S(-1,6)$ are vertices of a parallelogram.

Factor completely: $25 x^2+50 x y+25 y^2$

For each point, determine another point that satisfies the specified symmetry.

$(-3,9) ; y$-axis

Express the equation of the given line in the form $A x+B y+C=0$. Then find the distance from the given point $P\left(x_1, y_1\right)$ to that line. Round answers to the nearest hundredth.

$y$-axis; $P(-5,-7)$

Solve each polynomial equation. If a solution occurs more than once, state its multiplicity.

$$-2 x^5+24 x^4-70 x^3=0$$