BigBurger

$\boxed{\textbf{True}},$ because rectangles have varying side lengths $a$ and $b$, and when $a=b$ the rectangle is a square. Therefore, rectangles are somtimes squares, but not always.

Given this recursion equation, we can use the given $a_0=1$ and $a_1 = 5$ conditions to solve for $a_2,$ and then $a_3$. If we first let $n=1,$ we get $$(a_1)^2 - a_0 a_2 = (-1)^1,$$

$$25 - 1(a_2) = -1,$$

$$a_2 = 26.$$

Using this same logic, try to figure out $a_3$ by substituting into the relation $n=2.$

The ratio of $\triangle ABC$ to $\triangle ACD$ to $\triangle ADE, $ which is just the ratio of the bases $BC$ to $CD$ to $DE$ (because the height for each of the triangles is the same). Therefore, we can write equations corresponding to these ratios. $$\frac{BC}{[ABC]} = \frac{DE}{[ADE]}, $$  $$\frac{5-CD}{24} = \frac{4-CD}{18}.$$

Solving this set of equations, we find $$90-18CD = 96-24CD,$$ $$6CD=6,$$ $$CD = 1.$$

Therefore, we can use this value of $CD$ to substitute back into the original equation. $$\frac{CD}{[ACD]} = \frac{DE}{[ADE]}, $$ $$\frac{1}{[ACD]} = \frac{3}{18}, $$ $$[ACD] = 6.$$

Thus, our answer is $\boxed{[ACD] = 6}.$

(Note: The diagram is not drawn to scale).

Since each person forwards to email to 3 other people, the expression for the number of additional people who received it after $n$ rounds (including Elijah) is $3^0 + 3^1 + 3^2 + 3^3 + \dots + 3^n. $ We can rewrite this as $\boxed{\sum_{k=0}^n 3^n}.$

The sum of the angles in a triangle is $180°, $ and we find that $$(180-106) + 45+ 31+ x = 180°.$$ We know this because vertical angles are equal, so the vertical angle to the angle of $x°$ is also equal to $x°.$ 

Now you can try to solve this equation yourself.

The area of the triangular pyramid is $\frac{1}{3} bh. $ We can make the base the top face, and the base has an area of $\frac{3 \cdot 4}{2} = 6.$ The height that is given is $\frac{1}{2} \cdot 4 = 2.$ Now, we can plug these values in, and we get $$V = \frac{1}{3} bh. $$ $$V = \frac{1}{3} (6)(2)$$ $$\boxed{V = 4 \text{ in}^3}.$$