52. \( |x+1|+6=2 \) 54. \( |3 x-2|+4=4 \)

dation \( \log _{3}(2 x-1)=3 \)

1) \( \left(4 x^{2}+5\right)\left(x^{2}-2\right)\left(x^{2}+2\right)=0 \) A) \( \left\{\frac{i \sqrt{5}}{2},-\frac{i \sqrt{5}}{2}, \sqrt{2},-\sqrt{2}, i \sqrt{2},-i \sqrt{2}\right\} \) B) \( \left\{\frac{i \sqrt{10}}{2},-\frac{i \sqrt{10}}{2}, \sqrt{2},-\sqrt{2}, i \sqrt{2},-i \sqrt{2}\right\} \) C) \( \left\{\frac{i \sqrt{15}}{3},-\frac{i \sqrt{15}}{3}, i \sqrt{3},-i \sqrt{3}, i \sqrt{2},-i \sqrt{2}\right\} \) D) \( \left\{\right. \) mult. \( \left.2, \frac{i \sqrt{5}}{2},-\frac{i \sqrt{5}}{2}, \sqrt{2},-\sqrt{2}\right\} \)

\( 1 \leftarrow \quad \) Given vectors \( \mathbf{u} \) and \( \mathbf{v} \), find (a) \( 7 \mathbf{u} \) \( \mathbf{u}=6 \mathbf{i}, \mathbf{v}=3 \mathbf{i}+6 \mathbf{j} \) (b) \( 7 \mathbf{u}+2 \mathbf{v} \) (c) \( \mathbf{v}-2 \mathbf{u} \). (a) \( 7 \mathbf{u}=42 \mathbf{i} \) (Type your answer in terms of iand \( \mathbf{j} \).) (b) \( 7 \mathbf{u}+2 \mathbf{v}=\square \) (Type your answer in terms of \( \mathbf{i} \) and \( \mathbf{j} \).)

Write the expression as a single logarithm. \( 6 \log _{c} x+7 \log _{c} y-\frac{1}{3} \log _{c} z \) A. \( 6 \log _{c} x+7 \log _{c} y-\frac{1}{3} \log _{c} z=\log _{c} \frac{y^{7} z^{1 / 3}}{x^{6}} \) B. \( 6 \log _{c} x+7 \log _{c} y-\frac{1}{3} \log _{c} z=\log _{c} \frac{x^{6} y^{7}}{z^{3}} \) O. \( 6 \log _{c} x+7 \log _{c} y-\frac{1}{3} \log _{c} z=\log _{c} \frac{x^{6} y^{7}}{z^{1 / 3}} \) O. \( 6 \log _{c} x+7 \log _{c} y-\frac{1}{3} \log _{c} z=\log _{c} \frac{x^{6} z^{1 / 3}}{y^{7}} \)

The following function is given. \( f(x)=3 x^{3}-7 x^{2}-75 x+175 \) a. List all rational zeros that are possible according to the Rational Zero Theorem. Choose the correct answer below.