Solve the equation by graphing.

$$2x^2 - x = 3$$

Simplify. If no simplification is possible, say so.

$$\sqrt { 18 } + 2 \sqrt { 3 }$$

you studied the differences among stars, planets, and moons. Which are luminous, and which are non-luminous? Explain why this second group is classified as non-luminous.

When the viola section of an orchestra with six members plays together, is the sound 6 times as loud as when a single viola plays? Explain. Is the intensity 6 times what it would be for a single viola? [Hint: The six sound waves are not coherent.]

Write each number in scientific notation. 0.00725

Solve the inequality. Graph your solution. -7r > 49

Consider the diffusion of oxygen through a low-density polyethylene (LDPE) sheet 15 mm thick. The pressures of oxygen at the two faces are 2000 kPa and 150 kPa, which are maintained constant. Assuming conditions of steady state, what is the diffusion flux [in $\left.\left(\mathrm{cm}^{3} \mathrm{STP}\right) / \mathrm{cm}^{2} \cdot \mathrm{s}\right]$ at 298 K?

Given the reaction $\mathrm { A } ( g ) + \mathrm { B } ( g ) \rightleftharpoons \mathrm { C } ( g ) + \mathrm { D } ( g ) ,$ consider the following situations: i. You have 1.3 M A and 0.8 M B initially. ii. You have 1.3 M A, 0.8 M B, and 0.2 M C initially. iii. You have 2.0 M A and 0.8 M B initially. After equilibrium has been reached, order i-iii in terms of increasing equilibrium concentrations of D. Explain your sequence. Then give the order in terms of increasing equilibrium concentration of Band explain.

A bouquet of 40 flowers is made up of roses, carnations, and daisies. The bouquet is 45% roses and 15% carnations. How many of the flowers are roses? carnations?

Describe how the Law of Cosines can be used to solve the ambiguous case of the oblique triangle ABC, where a=12 feet, b=30 feet, and A = 20° Is the result the same as when the Law of Sines is used to solve the triangle? Describe the advantages and the disadvantages of each method.

determine the null and alternative hypotheses. The standard deviation in the pressure required to open a certain valve is known to be $\sigma$=0.7 psi. Due to changes in the manufacturing process, the quality-control manager feels that the pressure variability has been reduced.

A 350-kg sailboat has an acceleration of

$$0.62 \mathrm { m } / \mathrm { s } ^ { 2 }$$

at an angle of

$$64 ^ { \circ }$$

north of east. Find the magnitude and direction of the net force that acts on the sailboat.

An equation of an ellipse is given. Sketch a graph of the ellipse. $x^{2}+4 y^{2}=16$

Write the given number in the form $a+i b$. $i(1-i)(2-i)(2+6 i)$