Solve the system by the method of elimination. Then state whether the system is consistent or inconsistent.

$$\left\{\begin{array}{r} {2 x-3 y=4} \\ {-2 x-y=4} \end{array}\right.$$

Without using a calculator, compute the value of each expression below. a. $-14+(-31)$ b. $-(-8)-(-2)$ c. $\frac{-16}{-8}$ d. $-11 \cdot 24$ e. $\frac{1}{2}-\frac{3}{4}$ f. $46 \div(-23)$

Consider the equation $(x-7)^{2}=9$. a. Solve this equation using all three approaches studied in this lesson. Make sure each team member solves the equation using all three approaches. b. Did you get the same solution using all three approaches? If not, why not? c. Of the three methods, which do you think was the most efficient method for this problem? Why?

The word demagogue derives from the Greek root word agogos, meaning "leader." English words formed from this root word often end with -agogue or -agogy. Look up the words synagogue and pedagogy in a college-level dictionary. Explain how the root word agogos contributes to their meanings.

The end rollers of the uniform 20-lb bar AB move freely in the horizontal and vertical guides as shown. Determine the lowest value of the equilibrium position $\theta$ under the action of the 480-lb-in. couple M and the spring of stiffness k = 1.25 lb/in. The spring is uncompressed when $\theta$ = 0.

Evaluate $\int_{0}^{1} \frac{t^{x}-t^{y}}{\ln t} d t$ for $x>-1, y>-1$.

Air flows through a pipe at a rate of 120 L/s. The pipe consists of two sections of diameters 22 cm and 10 cm with a smooth reducing section that connects them. The pressure difference between the two pipe sections is measured by a water manometer. Neglecting frictional effects, determine the differential height of water between the two pipe sections. Take the air density to be $1.20 \mathrm{kg} / \mathrm{m}^{3}.$

Estimate the limits by substituting smaller and smaller values of h. For trigonometric functions, use radians. Give answers to one decimal place. $\lim _{h \rightarrow 0} \frac{(3+h)^{3}-27}{h}$

Consider a Carnot cycle executed in a closed system with 0.6 kg of air. The temperature limits of the cycle are 300 and 1100 K, and the minimum and maximum pressures that occur during the cycle are 20 and 3000 kPa. Assuming constant specific heats, determine the net work output per cycle.

The variable for the range is called the ________ because it depends on the domain.

A 100-W heater is used to melt 2 kg of solid ice at $-10^{\circ} \mathrm{C}$ to liquid at $+5^{\circ} \mathrm{C}$ at a constant pressure of 150 kPa. a. Find the change in the total volume of the water. b. Find the energy the heater must provide to the water. c. Find the time the process will take assuming uniform T in the water.

Suppose that $T(x, y, z)=x^{3} y+y^{3} z+z^{3} x$ gives the temperature at the point (x , y, z) in 3-space.

Calculate the directional derivative of T at (2, - 1, 0) in the direction toward the point (1, 1, 2).

________ can take on any value, so there is no space between data values for a given domain.

Katie has read 34% of a book. If she has read 85 pages, does she have more than or fewer than 125 pages left to read?