Define a variable and write an equation for each situation. Then solve. Two college friends rent an apartment. They have to pay the landlord two months' rent and a $500 security deposit when they sign the lease. The total amount they pay the landlord is$2800. What is the rent for one month?

Ms. Chung has a set of 10 markers in different colors. She asks her class to use two to complete an assignment. How many different color combinations could the class use?

Describe the major difference between a synovial joint and a cartilaginous joint:

Completa el texto con la forma apropiada de los verbos del recuadro: contratar, fundar, hacer, tener, ir, ver, salir, vestirse, seguir, entrar. Visita a una mina de Potosí. El año pasado, mi familia y yo_____ a una mina de plata situada a 4.700 metros de altura en Potosí (Bolivia). La ciudad la_____ los españoles en el siglo XVI. Ellos_____ que llevar todo allí desde Cuzco, Arica y Córdoba. Hoy Potosí es una ciudad importante, de unos 133.000 habitantes. del hotel a las 9 de la mañana y ______ un guía. Los guías son antiguos minero. Primero nos como mineros, con casco (hardhat) y lámpara eléctrica, Luego_____ al guía y_________ en la mina. Nos pareció un laberinto terrible, pero muy interesante. __________ el museo y a la salida__________fotos del paisaje. Para nosotros fue una experiencia inolvidable (unforgettable).

Verify that each equation is an identity.

$$\cot \theta + \tan \theta = \frac { \sec ^ { 2 } \theta } { \tan \theta }$$

Use the formula for the sum of the first n terms of a geometric sequence to solve. You save $1 the first day of a month,$2 the second day, $4 the third day, continuing to double your savings each day. What will your total savings be for the first 15 days?

A quadratic equation of the form x² + bx + c = 0 has a solution of -2. Its related function has a vertex at (2.5, -20.25). What is the other solution to the equation? A. -11 B. -4.5 C. 0.5 D. 7 E. 9

Use an appropriate substitution and then a trigonometric substitution to evaluate the integrals.

$$\int _ { \ln ( 3 / 4 ) } ^ { \ln ( 4 / 3 ) } \frac { e ^ { t } d t } { \left( 1 + e ^ { 2 t } \right) ^ { 3 / 2 } }$$

Sketch the polyhedron. Hexagonal prism.

Determine whether the following statements are true and give an explanation or counterexample.

To evaluate $\int _ { 0 } ^ { 2 } \frac { d x } { 1 - x }$, one could expand the integrand in a Taylor series and integrate term by term.

The half-life of an antibiotic in the bloodstream is 10 hours. If an initial dose of 20 milligrams is administered, the quantity left after t hours is modeled by Q(t)=

$$20 e ^ { - 0.0693 t }$$

, for

$$t \geq 0$$

. Find the instantaneous rate of change of the amount of antibiotic in the bloodstream, for

$$t \geq 0$$

.

How does the theory of plate tectonics explain the location of most earthquakes and volcanoes?

Add or subtract. Write the result in the form a + bi. (3 - i) - (-3 + i).

Use synthetic substitution to evaluate the polynomial function for the given value of x.

$$f(x) = 2x^4 + x^3 - 2x^2 + x; x = 2$$