Provide an appropriate response.Use the Intermediate Value Theorem to prove that 4x3 - 5x2 - 4x + 9 = 0 has a solution between -2 and -1.
What will be an ideal response?
Let f(x) = 4x3 - 5x2 - 4x + 9 and let y0 = 0. f(-2) = -35 and f(-1) = 4. Since f is continuous on 
and since y0 = 0 is between f(-2) and f(-1), by the Intermediate Value Theorem, there exists a c in the interval (-2 , -1) with the property that f(c) = 0. Such a c is a solution to the equation 
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Use the Laws of Exponents to simplify. Write the answer with positive exponents. All variables are nonzero.
A. 
B. 
C. 
D. 
Solve the problem.Assume that the half-life of Carbon-14 is 5700 years. Find the age (to the nearest year) of a wooden axe in which the amount of Carbon-14 is 30% of what it originally had.
Fill in the blank(s) with the appropriate word(s).
Find the product.(10m - 11w)(10m + 11w)
A. 10m2 - 11w2 B. 100m2 - 121w2 C. 100m2 - 220mw - 121w2 D. 100m2 + 220mw - 121w2
Solve the problem.The following graph is the graph of a quadratic function that gives the manufacturing cost in millions of dollars for a company as a function of the number of automobiles (in thousands) that it produces. Find the number of automobiles that must be produced to minimize the cost.
A. 3 thousand automobiles B. 6 thousand automobiles C. 9 thousand automobiles D. 54 thousand automobiles