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$$f(x)=|59-2x|$$
The function $f$ is defined by the given equation. For which of the following values of $k$ does $f(k)=3k$?
Difficulty: Hard
A:
$\frac{59}{5}$
B:
$\frac{59}{2}$
C:
$\frac{177}{5}$
D:
$59$
$$\frac{14x}{7y}=2\sqrt{w+19}$$
The given equation relates the distinct positive real numbers $w$, $x$, and $y$. Which equation correctly expresses $w$ in terms of $x$ and $y$?
Difficulty: Hard
A:
$w=\sqrt{\frac{x}{y}}-19$
B:
$w=\sqrt{\frac{28x}{14y}}-19$
C:
$w=\left(\frac{x}{y}\right)^{2}-19$
D:
$w=\left(\frac{28x}{14y}\right)^{2}-19$
$x^{2}+6x + 4$
Which of the following is equivalent to the expression above?
Difficulty: Medium
A:
$(x+3)^{2}+5$
B:
$(x+3)^{2}-5$
C:
$(x-3)^{2}+5$
D:
$(x-3)^{2}-5$
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