The two legs of a right triangle measure 23.5 and 27.9. Solve the triangle.

Solve each equation. First, multiply the binomials. To solve $(x-6)(2 x-3)=(x+2)(x+9)$, see below.

$$\begin{aligned} (x-6)(2 x-3) &=(x+2)(x+9) \\ 2 x^2-15 x+18 &=x^2+11 x+18 \\ x^2-26 x &=0 \\ x(x-26) &=0 \\ x=0 \text { or } x-26 &=0 \\ x &=26 \end{aligned}$$

$$(x+6)(x-6)=(2 x-9)(x+4)$$

Balance the following equations, and then write the net ionic equation

(a) $\mathrm{Zn}(\mathrm{s})+\mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{H}_2$ (g) $+\mathrm{ZnCl}_2$ (aq)

(b) $\mathrm{Mg}(\mathrm{OH})_2$ (s) $+\mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{MgCl}_2$ (aq) $+\mathrm{H}_2 \mathrm{O}(\ell)$

(c) $\mathrm{HNO}_3(\mathrm{aq})+\mathrm{CaCO}_3(\mathrm{~s}) \rightarrow \mathrm{Ca}\left(\mathrm{NO}_3\right)_2(\mathrm{aq})+\mathrm{H}_2 \mathrm{O}(\ell)+\mathrm{CO}_2(\mathrm{~g})$

(d) $\left(\mathrm{NH}_4\right)_2 \mathrm{~S}(\mathrm{aq})+\mathrm{FeCl}_3(\mathrm{aq}) \rightarrow \mathrm{NH}_4 \mathrm{Cl}(\mathrm{aq})+\mathrm{Fe}_2 \mathrm{~S}_3(\mathrm{~s})$

A pole 24 feet high has a shadow eight feet long. A nearby pole is 72 feet tall. How long is its shadow?

Identify the spectator ions in the complete ionic equation.

$$\begin{aligned} 2 \mathrm{~K}^{+}(a q)+\mathrm{S}^{2-}(a q)+\mathrm{Pb}^{2+}(a q)+2 \mathrm{NO}_3^{-}(a q) \longrightarrow \\ & \operatorname{PbS}(s)+2 \mathrm{~K}^{+}(a q)+2 \mathrm{NO}_3^{-}(a q) \end{aligned}$$

Two students find the probability of rolling two number cubes and getting a sum less than 6. Which student is correct? Explain the error.

Use a calculator to approximate the degree measure (to 1 decimal place) or radian measure (to 4 decimal places) of the angle $\theta$ subject to the given condition:

$\cos \theta=-\frac{2}{13}$ and $180^{\circ}<\theta<270^{\circ}$

After you have written your critical review, answer the following questions.

How do you think writing your critical review strengthened your understanding of the story?

Plot each of the given points in a coordinate plane. R(7, -2)

Complete the anticipation guide below by writing an $\mathbf{A}$ (agree) or a $\mathbf{D}$ (disagree) next to each statement below.

• Criminals can never be heroes.
• You should be willing to sacrifice your life to save the person you love.
• People in authority are always right.

Subtract. a. $\frac { 9 } { 13 } - \frac { 11 } { 13 }$, b. −57.49 − (−35.7), c. $7 \frac { 3 } { 10 } - \left( - 4 \frac { 1 } { 5 } \right)$, d. −319.12 − 88.16

For recurrent tonsillitis, what is sometimes performed?

a. splenectomy

b. tonsillectomy

c. lymph node biopsy

d. lymphoma

e. splenomegaly

Write complete ionic and net ionic equations for each of the following reactions. A. $\mathrm{K}_{2} \mathrm{S}(\mathrm{aq})+\mathrm{CoCl}_{2}(\mathrm{aq}) \rightarrow 2 \mathrm{KCl}(\mathrm{aq})+\mathrm{CoS}(\mathrm{s})$ B.

$$\begin{array}{c}{\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})+\mathrm{CaCO}_{3}(\mathrm{s}) \rightarrow} \\ {\mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{CO}_{2}(\mathrm{g})+\mathrm{CaSO}_{4}(\mathrm{s})}\end{array}$$

C.

$$\begin{aligned} 2 \mathrm{HClO}(\mathrm{aq})+& \mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq}) \rightarrow \\ 2 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})+\mathrm{Ca}(\mathrm{ClO})_{2}(\mathrm{aq}) \end{aligned}$$

Convert each degree measure to radians. $5^{\circ}$ (to the nearest hundredth)