The cost y (in dollars) for x pounds of deli meat is represented by the equation y = 3.5x. Graph the equation and interpret the slope.

For the following equation: a. State the operation you select to isolate the variable. b. Describe how to perform the operation and keep the equation balanced. c. Write a line-by-line solution to the equation. d. Show the check of the solution. 4w = 132

Determine all positive numbers replacements (less than the modulus) for the question mark that make the statement true. 5

Apply the eigenvalue method of this section to find a general solution of the given system. If initial values are given, find also the corresponding particular solution. For each problem, use a computer system or graphing calculator to construct a direction field and typical solution curves for the given system.

$$x _ { 1 } ^ { \prime } = 3 x _ { 1 } + 4 x _ { 2 } , \quad x _ { 2 } ^ { \prime } = 3 x _ { 1 } + 2 x _ { 2 } ; x _ { 1 } ( 0 ) = x _ { 2 } ( 0 ) = 1$$

Show that the given value(s) of c are zeros of P(x), and find all other zeros of P(x).

$$P ( x ) = 3 x ^ { 4 } - 8 x ^ { 3 } - 14 x ^ { 2 } + 31 x + 6 ,\quad c = - 2,3$$

Expand each expression using the Binomial Theorem. $(x+1)^{5}$

Solve.

$$\frac { x } { 5 } = \frac { 0.42 } { 0.3 }$$

The cost y (in dollars) to rent a kayak is proportional to the number x of hours that you rent the kayak. It costs $ 27 to rent the kayak for 3 hours. a. Write an equation that represents the situation. b. Interpret the slope. c. How much does it cost to rent the kayak for 5 hours?

For each polyhedron, use Euler's Formula to find the missing number.

$$\begin{array} { l } { \text { faces: } 8 } \\ { \text { edges: }\square } \\ { \text { vertices: } 6 } \end{array}$$

Use the GCF of the terms to write each expression as the product of two factors.

$$8 x ^ { 3 } + 2 x ^ { 2 } + 4 x$$

A gas within a piston-cylinder assembly undergoes an isothermal process at 400 K during which the change in entropy is -0.3 kJ/K. Assuming the ideal gas model for the gas and negligible kinetic and potential energy effects, evaluate the work, in kJ.

Laurie borrows $50 000 for 10 years at 6.6%/a compounded monthly. How much sooner can she pay off the loan if she doubles the monthly payment after 4 years?

In the Sixth Meditation, Descartes writes I first take notice here that there is a great difference between the mind and the body, in that the body, from its nature , is always divisible and the mind is completely indivisible . Descartes 's argument can be expressed as follows : All bodies are divisible.

$$\frac { \text { No minds are divisible.} } { \text { Therefore , no minds are bodies.} }$$

Use an Euler diagram to determine whether the argument is valid or invalid.

Is air matter? How can you tell?