Solve the equation. Approximate the result to three decimal places. $2 \log _{3} 4 x=15$

Tell which is better to buy between 8.2 oz of toothpaste for $2.99 and 6.4 oz of toothpaste for$2.49.

Find the indicated square roots. $\pm \sqrt{\frac{92}{207}}$

Write the companion matrix C$_p$ for p(t)=6-5t+t$^2$, and then find the characteristic polynomial of C$_p$.

Use a calculator to find the approximate value. Express your result in radians. $\tan ^{-1}(22.8)$

Decide whether each equation defines y as a function of x. $y=\pm \sqrt{x-2}$

An invertible matrix $A$ satisfies $A^{-1}=A$. Show that $\operatorname{det} A=\pm 1$.

What can you say about two lines with the same x-intercept and the same y-intercept? Assume that the x-intercept is not 0.

Solve the exponential equation algebraically. Approximate the result to three decimal places. $3 e^{x}=9$

Verify the formula. $\arccos z=i \ln (z \pm \sqrt{z^{2}-1})$

Use a calculator to evaluate the logarithm. Round your result to three decimal places. 2 In 9

Punctuating Direct Quotations. One or two punctuation marks have been left out of each sentence. Add them correctly to the sentences: He screamed. "Stop the car"

Solve the exponential equation algebraically. Approximate the result to three decimal places. $5 e^{x}=20$

Let A be an integral domain. Prove:

If p is a prime, and there is a nonzero element $a \in A$ such that $\mathrm{p}^{\mathrm{m}} \cdot a=0$ for some integer m, then A has characteristic p.