Solve the following equation by making the appropriate substitution. Write the exact, fully simplified answer. No decimals or rounding.  

Use the given function,

Given the following equation of a circle, in general form, answer the following.

Given the graph of parent and child function, identify the transformations used to change the parent into the child function. Graph of parent and child functions Parent Function Child Function   If the transformation does not apply, enter none; otherwise, enter the magnitude of the transformation. For instance, if the graph is shifted up eleven units, then for vertical shift up, type 11, and vertical shift down would be none. Horizontal shift left: [hsl] Horizontal shift right: [hsr] Vertical stretch: [vs] Vertical shrink: [vss] Reflection over x-axis:[rx] Reflection over y-axis: [ry] Vertical shift up: [vsu] Vertical shift down: [vsd]

Given the rational function, answer the following questions.

Solve the following logarithmic equation. Be sure to reject any values that are not in the domain. $$\log_{3}(x+3) + \log_{3}(x+5) = 1$$

Use the properties of logarithms to condense the following logarithmic expression as much as possible. $$ \ln(7) +2 \ln(x) – 5\ln(w) – \ln(z) $$

Suppose that y varies jointly as x and z. Then y = 154.7 when x = 17 and z = 5.2.   What is the coefficient of variation (Round to the tenth place)? k = [cov] What is y when x = 3.2 and z = 15 (Round to the tenth place)? y = [y2]

Find the difference quotient,

Evaluate the following piecewise function at the indicated values.