91Ó°ÊÓ

To solve for a variable involving an nth root, raise both sides of the equation to the nth power: \(\left.(\sqrt[n]{y})^{n}=y .\right)\). $$f(x)=\sqrt{x}+2$$

Make Sense? In Exercises \(59-62,\) determine whether each statement makes sense or does not make sense, and explain your reasoning. The function \(f(x)=30 x+0.08\) is a reasonable model for the monthly cost, \(f,\) in dollars, for a text message plan in terms of the number of monthly text messages, \(x\).

For each \(\$ 1\) increase in the price of a \(\$ 300\) plane ticket. an airline will lose 60 passengers, so if the ticket price is increased to \(\$ x,\) the decrease in passengers is modeled by \(60(300-x)\)

a. Rewrite the given equation in slope-intercept form. b. Give the slope and y-intercept. c. Use the slope and y-intercept to graph the linear function. $$8 x-4 y-12=0$$

Explain why (5,-2) and (-2,5) do not represent the same point.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I used the ordered pairs \((-2,2),(0,0),\) and (2,2) to graph a straight line.

Find the slope of the line passing through each pair of points or state that the slope is undefined. Assume that all variables represent positive real numbers. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. $$(a-b, c) \text { and }(a, a+c)$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. To avoid sign errors when finding \(h\) and \(k,\) I place parentheses around the numbers that follow the subtraction signs in a circle's equation.

Show that the points \(A(1,1+d), B(3,3+d),\) and \(C(6,6+d)\) are collinear (lie along a straight line) by showing that the distance from \(A\) to \(B\) plus the distance from \(B\) to \(C\) equals the distance from \(A\) to \(C\).

Find the area of the donut-shaped region bounded by the graphs of \((x-2)^{2}+(y+3)^{2}=25\) and \((x-2)^{2}+(y+3)^{2}=36\).