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Chapter 2: Problem 28
Find the midpoint of each line segment with the given endpoints. $$(7 \sqrt{3},-6) \text { and }(3 \sqrt{3},-2)$$
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Complete the square and write the equation in standard form. Then give the center and radius of each circle and graph the equation. $$x^{2}+y^{2}+12 x-6 y-4=0$$
Give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation鈥檚 domain and range. $$(x+2)^{2}+y^{2}=16$$
Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$ \begin{aligned} &\text { If } f(x)=x^{2}-4 \text { and } g(x)=\sqrt{x^{2}-4}, \text { then }(f \circ g)(x)=-x^{2}\\\ &\text { and }(f \circ g)(5)=-25 \end{aligned} $$
Exercises \(103-105\) will help you prepare for the material covered in the next section. Let \(\left(x_{1}, y_{1}\right)=(7,2) \quad\) and \(\quad\left(x_{2}, y_{2}\right)=(1,-1) . \quad\) Find \(\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}} .\) Express the answer in simplified radical form.
A department store has two locations in a city. From 2012 through \(2016,\) the profits for each of the store's two branches are modeled by the functions \(f(x)=-0.44 x+13.62\) and \(g(x)=0.51 x+11.14 .\) In each model, \(x\) represents the number of years after \(2012,\) and \(f\) and \(g\) represent the profit, in millions of dollars. a. What is the slope of \(f ?\) Describe what this means. b. What is the slope of \(g ?\) Describe what this means. c. Find \(f+g .\) What is the slope of this function? What does this mean?
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