Which is not the equation of a parabola?

(A) $y=2 x^2+4 x-9$

(B) $3 x+2 y^2+y+1=0$

(C) $x^2+2 y^2+8 y=8$

(D) $x=\frac{1}{2}(y-1)^2+5$

Dos pequeñas esferas de plástico tienen cargas eléctricas positivas. Cuando están separadas $15.0\text{ cm}$, la fuerza de repulsión entre ellas tiene una magnitud de $0.220\text{ N}$. ¿Cuál es la carga de cada esfera

$(a)$ si las dos cargas son iguales.

$(b)$ si una esfera tiene cuatro veces la carga de la otra?

Given $P(x)=\frac{x^2-2}{3 x^2-2 x+5}$, find $P(-2)$.

The successive $I E$ of the first four electrons of a representative element are $738.1 \mathrm{~kJ} / \mathrm{mol}, 1450 \mathrm{~kJ} / \mathrm{mol}$, $7730 \mathrm{~kJ} / \mathrm{mol}$, and $10,500 \mathrm{~kJ} / \mathrm{mol}$. Characterize the element according to the periodic group.

. Deternine the number of moles of $\mathrm{H}$ in each sample. (a) $4.67 \mathrm{~mol} \mathrm{H} \mathrm{O}$ (b) $8.39 \mathrm{~mol} \mathrm{NH}$ (c) $0.117 \mathrm{~mol} \mathrm{~N}_2 \mathrm{H}_4$ (d) $35.8 \mathrm{~mol} \mathrm{C}_{10} \mathrm{H}_{22}$

Show that the equation $x^4 + 4x + c = 0$ has at most two real roots.

Prove that the equation $x^{4}-y^{4}=2 z^{2}$ has no solutions in positive integers $x, y, z$ . [Hint: Because $x, y$ must be both odd or both even, $x^{2}+y^{2}=2 a^{2}, x+y=2 b^{2}$ , $x-y=2 c^{2}$ for some $a, b, c ;$ hence, $a^{2}=b^{4}+c^{4} . ]$

Until his transforming Christmas Eve dream, Ebenezer Scrooge was a(n) ____________________ miser, feared and disliked by everyone for his irritable personality.

Finding the neutral axis of a cross-section.

Using data from Appendix 2, calculate $\Delta H_{rxn}°$ for $\mathrm{H_2}(g)+\mathrm{F_2}(g)\rightarrow2\;\mathrm{HF}(g)$. (a) -271.6 kJ/mol (b) -543.2 kJ/mol (c) +271.6 kJ/mol (d) 0 kJ/mol (e) -135.8 kJ/mol

Find all real roots by using the quadratic formula. $2-2 x+x^{2}=0$

Write the simplest polynomial function with the given roots.

$$1 + \sqrt { 3 } , 2 i$$

Prove that the statement is true for every positive integer n.

$$2^2+4^2+6^2+\cdots+(2 n)^2=\dfrac{2 n(2 n+1)(n+1)}{3}$$

Express as a polynomial.

$$(x+2)^2(x-2)^2$$