Solve each minimum problem using the duality principle. Minimize

$$C = x_1 +2x_2 + 3x_3 +4x_4$$

subject to the constraints 2

$$\left\{ \begin{array}{ccccccc} x_1 & & +x_3 & \geq 1 \\ & x_2 & & +x_4 \geq1 \\ - x_1 &-x_2 &-x_3 &-x_4 \geq -3 \\ x_1 \geq 0, & x_2 \geq 0, & x_3 \geq 0 & x_4 \geq 0 \end{array} \right.$$

Use ratios and proportions to solve. An African elephant weighs 6 tons. What is the weight of the elephant in pounds?

Find the product.

$$\left( 4 x ^ { 2 } + x - 5 \right) ( 2 x + 1 )$$

How might a reform of the electoral college system affect state and local governments?

a. Are the sets equivalent ? Explain. b. Are the sets equal? Explain.

$$\begin{array} { l } { A = \{ 1.3,5,7,9 \} } \\ { B = \{ 2,4,6,8,10 \} } \end{array}$$

Determine whether each statement is sometimes, always, or never true. Explain. if a>c, then a+b>c+b.

A beverage company is changing its juice package size. Currently, there are 8 ounces of juice in each package. The new package will contain 12 ounces. What percent more juice will be in the new package?

True or False? An interpreter is a program that both translates and executes the instructions in a highlevel language program.

Solve the equation for the specified variable.

$$h = \sqrt [ 3 ] { \frac { 12 I } { b } } \text { for } I$$

Factor the sum or difference of cubes. Factor out the GCF first.

$$2 x ^ { 6 } + 54 x ^ { 3 }$$

Your friend says that a relation is not a function when two ordered pairs have the same y-coordinate. Explain your friend’s error.

Unos estudiantes hablan de sus equipos favoritos. Di como compitieron los equipos en el campeonato ayer. (Say how each team competed yersterday.)

How are divergent thinking and creativity related?

Compare. Write< or >.

$$-9 \square 2$$