Simplify the following given expression. Assume all variables are positive.

$$\sqrt[6]{2 x^6}$$

Factor. Assume that variables used as exponents represent positive integers.

$$2 x^{2 n}+11 x^n+5$$

Write two different proportions using each set of numbers. Use cross products to justify your answer. A. $1.80,$1.20, 14, 21 B. 1, 3.5, 31.50, 9.0 C. 11.7, 8424, 0.02, 14.4

Carmelita is planning to swim in a charity swim- a- thon. several relatives said they would sponsor her.

Grandmother: I will give you $1 if you swim 1 lap,$3 if you swim 2 laps, $5 if you swim 3 laps,$7 if you swim 4 laps, and so on.

Father: I will give you $1 if you swim 1 lap,$3 if you swim 2 laps, $9 if you swim 3 laps,$27 if you swim 4 laps, and so on.

Aunt Josie: I will give you $2 if you swim 1 lap,$3.50 if you swim 2 laps, $5 if you swim 3 laps,$6.50 if you swim 4 laps, and so on.

Uncle Sebastian: I will give you $1 if you swim 1 lap,$2 if you swim 2 laps, $4 if you swim 3 laps,$8 if you swim 4 laps, and so on.

For each relative, write an equation for the total donation d if Carmelita swims n laps. Which variable is the independent variable? Dependent variable?

Complete each sentence by writing the form of the verb indicated in parentheses.

The lost hikers ________ to the cleared path. (past tense of retreat)

Describe the formation of an oxbow lake.

Let

$$Q \left( x ^ { \prime } , y ^ { \prime } \right)$$

be any point of L' different from

$$P \left( x _ { 1 } , y _ { 1 } \right)$$

Explain why

$$\frac { y ^ { \prime } - y _ { 1 } } { x ^ { \prime } - x _ { 1 } } = m$$

.

Complete each sentence by writing the form of the verb indicated in parentheses.

_________ anyone _________ my little brother? (present perfect of see)

When writing electron confi gurations for elements in period 4, why are electrons placed in the 4s sublevel before the 3d sublevel?

Find an equation of the tangent line to the graph at the given point.

Rotated ellipse: $7x^2-6\sqrt{3}xy+13y^2-16=0$ Point: $\left(\sqrt{3},1\right)$

Find an equation of the tangent line to the given curve $2\left(x^2+y^2\right)^2=25\left(x^2-y^2\right)$ at the point $(3,1)$.

Find an equation of the tangent line to the graph of the function at the given point.

$$\begin{matrix} \text{Function} & \text{Point}\\ \text{y=tan x} & \text{}{\left(-\frac{\pi}{4},-1\right)}\\ \end{matrix}$$

Complete each sentence by writing the form of the verb indicated in parentheses.

Greg and Chip _________ to dunk basketballs. (base form of try)

Describe the formation of an aqueous KI solution.