7 A company produces and sells books. The weekly cost, in euros, for producing x books is € (0.1x² + 400). The weekly income from selling x books is € (-0.12x² + 30x). a Show that the weekly profit, P(x), can be written as P(x) = -0.22x² + 30x-400. b Plot a graph of this equation and hence sketch it on paper, showing the coordinates of the vertex and axes intercepts. c State what the x-intercepts represent in the context of the problem.

what is the slope and the y-intercept of the function?  f(x)= 3x-4

The data in the table shows the number of mother-to-child HIV infections diagnosed in the United States in various years from 1985 to 2005. How can we learn from the data? Practice the following questions: 1. Make a scatter plot to display the data. You can use any graphing technology. Why would a quadratic model make sense? 2. Determine an equation for this relation. Which form (standard, vertex or factored) do you think is the best for these data and why? 3. Based on your model, will the number of HIV cases ever be reduced to zero? If so, when? Explain reasoning.

A company selling widgets has found that the number of items sold, x, depends upon the price, p at which 70000 they're sold, according the equation a (0.5p + 1)² Due to inflation and increasing health benefit costs, the company has been increasing the price by $0.06 per month. Find the rate at which revenue is changing when the company is selling widgets at $4 each. Revenue is changing at a rate of dollars per month.