True or false? Justify your reasoning.

d. All equilateral triangles are similar.

Does the inverse function $f^{-1}(x)=\sqrt{x}$ have an asymptote? Explain your reasoning.

True or false: x/4 is equivalent to (1/4)x. Explain your reasoning.

$\sqrt { 5 }$ is between which two integers? Explain your reasoning.

What score should the student's answer receive? Explain your reasoning.

Which point on a parabola is closest to the focus? Explain your reasoning.

Estimate $\lim _{x \rightarrow \infty} \frac{1}{x}$. Explain your reasoning.

About how fast are molecules of nitrogen in air at room temperature moving? As fast as a (a) tortoise. (b) sprinter. $(c)$ car at the highway speed limit. (d) passenger jet plane. (e) satellite in orbit around the Earth.

Critique Reasoning Stephanie says that the graphs of y=3 x+2 and y=3 x-2 are parallel. Isabella says that the graphs are perpendicular.

Who is correct? Explain your reasoning.

Is $0.040040004 \ldots$ a rational number? Explain your reasoning.

Write a problem for which the following mathematical statement can be a solution: $1 \mathrm{A}=\frac{\varepsilon-(1 \mathrm{A})(3 \Omega)}{R}$

Classify the following statement as true, false, or not a valid mathematical statement. Explain your answer.

$4 \neq 2+2$ and $7<\sqrt{50}$.

Which mathematical operation could you use to find the number of sushi rolls that Antoine can make? Explain.

In this exercise, use mathematical induction to prove that the statement is true for every positive integer $n$.

$2$ is a factor of $n^2+3 n$.