Given \(i = \sqrt{-1}\) , what is \( \dfrac{i^2 + 1}{i} ÷ \dfrac{i − 1}{i^2 − 1} = \; ?\)

The coordinates \((x, y)\) represent the midpoint of \((-2, 9)\) and \((10, -4)\). What is the value of \(x + y\) ?

Let events \(A\) and \(B\) be independent events in a sample space. If \(P(A) = 0.4\) and the probability of \(A\) or \(B\) occurring, denoted as \(P(A ∪ B)\), is \(0.7\), what is the probability of event \(B, P(B)\)?

For the figure shown, \(A, C, D,\) and \(E\) are collinear; \(B, C,\) and \(F\) are collinear; and \(∠ABC, ∠FDE,\) and \(∠CFE\) are right angles. Which of the following is NOT supported by the figure?

For all \(x > 0\), which of the following expressions is equivalent to the expression below?

\(\dfrac{x^2 \times \sqrt[3]{x^4}}{x^{−\frac{1}{2}}}\)

The graph of the trigonometric function \(y = f(x)\) is shown in the standard \((x,y)\) coordinate plane above. Which of the following equations defines the function?

What is the simplified form of the rational expression below?

\(\dfrac{3}{(x^2 − 9)} − \dfrac{1}{(x − 3)}\)

The curve \(y = 0.01x² − 2x + 100\) for \(0 ≤ x ≤ 100\) and the line segment from \(F(0, 100)\) to \(G(100, 0)\) are shown in the standard \((x, y)\) coordinate plane.

For a point on the curve, a vertical segment is drawn to the point on \(\overline{FG}\) having the same \(x\)-coordinate. At which of the following points on the curve would this vertical segment have the greatest length?

For a certain angle \(\theta\) between 0 and \(2 \pi \ \text{radians}, \text{sin}(\theta) = \frac{−5}{13}\) and \(\text{tan}(\theta) \gt 0\). What is the value of \(\text{cos}(\theta)\)?

A manufacturer is redesigning a cylindrical soup can. The original can has a radius of \(r\) and a height of \(h\), yielding a volume of \(V\). If the manufacturer doubles the radius and halves the height for the new design, what will be the volume of the new can in terms of \(V\)?