Rationalize the denominator and simplify. Assume that the variable represents a positive real number. \[ \sqrt{\frac{2}{w}} \]

Use the properties of logarithms to expand the following expression. \[ \log \left(\frac{y^{7}}{\sqrt{x z^{3}}}\right) \] Each logarithm should involve only one variable and should not have any radicals or exponents. You may assume that all variables are positive. \( \log \left(\frac{y^{7}}{x z^{3}}\right)=\square \)

Suppose that the function \( h \) is defined, for all real numbers, as follows. \[ h(x)=\left\{\begin{array}{ll}\frac{1}{4} x+2 & \text { if } x<-2 \\ (x+1)^{2}-2 & \text { if }-2 \leq x \leq 2 \\ 3 & \text { if } x>2\end{array}\right. \] Find \( h(-2), h(1) \), and \( h(5) \) \( h(-2)=\square \)

Finding a specified term of an arithmetic sequence givent Find the \( 50^{\text {th }} \) term of the following arithmetic sequence. \[ 17,26,35,44, \ldots \]

Finding a specified term of an arithmetic sequence given the common... Find the \( 19^{\text {th }} \) term of the arithmetic sequence whose common difference is \( d=5 \) and whose first term is \( a_{1}=2 \).

\[ \text { Relation } 4 \] \[ \{(8, w),(0, a),(8, d),(8, z)\} \] Function Not a function