Find the zeros for the given polynomial function and give the multiplicity for each zero. State whet zero. \( f(x)=x^{3}-34 x^{2}+289 x \) (Simplify your answer.) B. There are three zeros. The multiplicity of the smallest zero is (Simplify your answers.) C. There are two zeros. The multiplicity of the smallest zero is 1 . The multiplicity of the larg (Simplify your answers.) Determine the behavior of the function at each zero. Select the correct choice below and, if nece A. The graph crosses the \( x \)-axis at \( x=\square \). The graph touches the \( x \)-axis and turns around a (Type integers or decimals. Simplify your answers. Use a comma to separate answers as B. The graph touches the \( x \)-axis and turns around at all zeros. C. The graph crosses the \( x \)-axis at all zeros.

The pH at \( 25^{\circ} \mathrm{C} \) of an aqueous solution of the sodium salt of \( \alpha \)-naphthol \( \left(\mathrm{NaC}_{10} \mathrm{H}_{7} \mathrm{O}\right) \) is 11.24. Calculate the concentration of \( \mathrm{C}_{10} \mathrm{H}_{7} \mathrm{O} \) in this solution, in moles per liter. \( \mathrm{K}_{\mathrm{a}} \) for \( \mathrm{HC}_{10} \mathrm{H}_{7} \mathrm{O} \) is equal to \( 4.6 \times 10^{-10} \).

Select the correct answer from each drop-down menu. The of Earth's orbit is among the planet's unique characteristics. This characteristic allows water to exist in solid, liquid, and gas forms on Earth. Earth's distance from the nature of its orbit, allow this phenomenon to take place.

7. If \( y=18 \) when \( x=3 \), what is the value of \( k \) ? 8. If \( y=10 \) when \( x=\frac{2}{5} \), what is the equation of the variation? If \( y=100 \) when \( x=27 \), what is the value of \( k \) and the equation of the variation? If \( y=12 \) when \( x=\frac{2}{3} \), what is the value of \( k \) and the equation of variation?

What is the pH of a \( 3.81 \times 10^{-5} \mathrm{M} \) solution of the strong acid HBr ? \( \mathrm{HBr}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{Br}^{-}(\mathrm{aq})+\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq}) \) \( [\mathrm{HBr}]_{0}=3.81 \times 10^{-5} \) Submit Show Approach Show Tutor Steps

The value of \( \mathrm{K}_{\mathrm{a}} \) for nitrous acid is \( 4.50 \times 10^{-4} \). What is the value of \( \mathrm{K}_{\mathrm{b}} \), for its conjugate base, \( \mathrm{NO}_{2} \) ? Write the equation for the reaction that goes with this value of \( \mathrm{K}_{\mathrm{b}} \) for \( \mathrm{NO}_{2} \). It is not necessary to include states such as ( \( a q) \) or (l). \[ \]