Exam 1: Review of Basic Concepts

Solve the problem. Round to two decimal places unless otherwise indicated. -If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 300 } { x + 10 }$ , what is the unit cost for 50 units?

Factor by any method. - $245 x ^ { 10 } - 45$

Find the sum or difference. - $\frac { x ^ { 2 } - 11 x + 18 } { x - 9 }$

Find the sum or difference. - $3 x ^ { 5 } ( - 8 x - 10 )$

Evaluate the expression. - $26 + 28 \cdot 2 + 7$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. -The length of the diagonal of a rectangle is given by $D = \sqrt { L ^ { 2 } + W ^ { 2 } }$ where L and W are the length and width of the rectangle. What is the length of the diagonal, D, of a rectangle that is 84 inches long and 60 inches wide? Round your answer to the nearest tenth of an inch, if necessary.

Write the expression in lowest terms. - $\frac { - 4 ( z - 5 ) } { ( z - 5 ) ( z + 2 ) }$

Find the sum or difference. - $\frac { 20 x ^ { 3 } + 28 x ^ { 2 } - 7 x - 6 } { 5 x + 2 }$

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 5,6,7,8,9,10,11,12,13,14,15 \} , \mathrm { M } = \{ 5,7,9,11 \} , \mathrm { N } = \{ 6,8,10,12,14 \} , \mathrm { Q } = \{ 5,7,9,11,13,15 \}$ , and $\mathrm { R } = \{ 5,6,7,8 \}$ . $M \cap R$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 15 a ^ { - 3 } b ^ { 2 } } { 5 a ^ { - 9 } b ^ { 6 } }$

Factor out the greatest common factor. Simplify the factors, if possible. - $9 \mathrm {~m} ( 9 - \mathrm { m } ) + 5 \mathrm { n } ( 9 - \mathrm { m } )$

Identify the expression as a polynomial or not a polynomial. - $\frac { 7 } { x ^ { 5 } } + \frac { 4 } { x ^ { 3 } } - 9$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $-(-6)^{0}$

Evaluate the expression. - $- | - 2 |$

Evaluate the expression. - $81 - 8 \cdot 3 + 4$

Rationalize the denominator. Assume that all variables represent nonnegative numbers and that the denominator is not zero. -The formula T = 0.07D1.5 can be used to approximate the duration of a storm, where is the time in hours and D is the diameter of the storm in miles. A storm that is 25.5 miles in diameter is heading toward a city. How long Can the residents of the city expect the storm to last? Round you answer to the nearest hundredth of an hour.

Find the sum or difference. - $- 3 x ^ { 5 } \left( 11 x ^ { 4 } + 8 x ^ { 3 } \right)$

List all the elements of set B that belong to the indicated set. - $B = \left\{ 14 , \sqrt { 8 } , - 14,0 , \frac { 0 } { 4 } , \sqrt { 4 } \right\}$ Natural numbers

Determine which property of absolute value justifies the statement. - $| x + y | \leq | x | + | y |$

Calculate the value mentally. - $0.1 ^ { 1 / 2 } \cdot 160 ^ { 1 / 2 }$