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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:
$(x-3)^{2}-5$
In the expression $3(2x^{2}+px+8)-16x(p+4)$, $p$ is a constant. This expression is equivalent to the expression $6x^{2}-155x+24$. What is the value of $p$?
Difficulty: Hard
A:
$-3$
B:
7
C:
13
D:
155
$(x+2)(x+3)=(x-2)(x-3)+10$
Which of the following is a solution to the given equation?
Difficulty: Medium
A:
$1$
B:
$0$
C:
$-2$
D:
$-5$
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