Do you remember learning about the discriminant? For a quadratic equation of the form: The discriminant is equal to:

It tells us how many solutions a quadratic equation has. The discriminant can give us three results regarding the roots of an equation.

a) What are these three different results? What must the discriminant be in order to get each result? Describe what a graphed quadratic equation would look like with each result.
b) Where does the discriminant come from?
c) Use the ideas from parts A and B to prove that every quadratic polynomial has exactly two roots.

Zahra runs a 500-meter race at a constant speed. which graph shows her distance from the finish line during the race?

Acell phone company offers two plans to its subscribers. at the time new subscribers sign up, they are asked to provide some demographic information. the mean yearly income for a sample of 40 subscribers to plan a is $45,000 with a standard deviation of $9,200. for a sample of 25 subscribers to plan b, the mean income is $64,300 with a standard deviation of $7,100. at the 0.025 significance level, is it reasonable to conclude the mean income of those selecting plan b is larger? assume unequal population standard deviations. hint: for the calculations, assume the plan a as the first sample. what is the decision rule? (negative amount should be indicated by a minus sign. round your answer to 3 decimal places.) compute the value of the test statistic. (negative amount should be indicated by a minus sign. round your answer to 2 decimal places.) what is your decision regarding h0 ? reject h0 fail to reject h0 compute the p-value. less than 0.01 between 0.01 and 0.025 between 0.025 and 0.05 between 0.05 and 0.10 greater than 0.10

Find the combined area of the triangles. click on the answer until the correct answer is showing.possible answers: a = 4 pi - 8a = 9 pi - 9/2 √3a = 16/3 pia = 16a = 27 pi