Provide an appropriate response.Use the Intermediate Value Theorem to prove that x(x - 2)2 = 2 has a solution between 1 and 3.

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Let f(x) = x(x - 2)2 and let y0 = 2.   and  Since f is continuous on  and since  is between  and  by the Intermediate Value Theorem, there exists a c in the interval  with the property that  Such a c is a solution to the equation 

Mathematics

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Provide an appropriate response. ;   g(x) = 1 - 4x. Find:(a)f(0)(b)f(-1)(c)f(4) - f(-2)(d)f(g(0))(e)g(f(0))

What will be an ideal response?

Mathematics

Determine whether the specified paradox occurs.A country with two states has 16 seats in the legislature. The population of each state (in thousands) is given by: A third state is added with 3 additional seats as shown below. Does the new-states paradox occur using Hamilton's method of apportionment?

A. Yes B. No

Mathematics

Solve the compound inequality. Express the solution using interval notation. Graph the solution set.x ? 2 or x ? 8

A. (-2, 8)

B. [-8, -2]

C. (-?, 2] ? [8, ?)

D. (2, 8)

Mathematics

Decide whether or not the equation defines y as a function of x.y = 

A. No B. Yes

Mathematics