Exam 1: Review of Basic Concepts

Solve the problem. -At an altitude of $h$ feet above the surface of the earth, the approximate distance in miles that a person can see is given by $\mathrm { d } = 1.2247 \sqrt { \mathrm { h } }$ . How far can a person see if if he or she is 830 feet above the earth's surface? Round your answer to the nearest tenth of a mile.

Find the product. - $\left( - 3 x ^ { 4 } y ^ { 4 } \right) \left( - 4 x ^ { 3 } y ^ { 2 } \right)$

Factor, using the given factor. Assume all variables represent positive real numbers. - $2 m ^ { 5 / 4 } - 3 m ^ { - 1 / 2 } ; \quad m ^ { - 1 / 2 }$

Evaluate the expression for x = -2, y = 3, and a = -4. --4a - 7y - 3x

Decide whether the statement is true or false. If false, correct the statement so it is true. - $| - 6 \cdot 9 | = | - 6 | \cdot | 9 |$

Perform the indicated operations. - $\frac { 2 a b } { a ^ { 2 } - b ^ { 2 } } - \frac { b } { a - b } + 7$

Factor, using the given factor. Assume all variables represent positive real numbers. - $x ^ { - 7 } - 3 x ^ { - 3 } ; \quad x ^ { - 7 }$

Provide an appropriate response. -The formula used to find the volume of the frustum of a square pyramid is $V = \frac { 1 } { 3 } h \left( a ^ { 2 } + a b + b ^ { 2 } \right)$ where $\mathrm { b }$ is the length of the base, $a$ is the length of the top, and $\mathrm { h }$ is the height. Visualize the figure if $a = b = h$ . What would the figure be?

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $6 ^ { - 2 }$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { x ^ { 1 / 2 } } { \left( x ^ { 2 } \right) ^ { - 1 / 2 } } \cdot \frac { x ^ { 2 / 5 } } { x ^ { - 3 / 10 } }$

Evaluate the expression. - $64 ^ { 1 / 3 }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $( - 4 ) ^ { 0 }$

Perform the indicated operation and write your answer with positive integer exponents. - $\frac { \mathrm { m } ^ { - 1 } - \mathrm { n } ^ { - 1 } } { ( \mathrm { mn } ) ^ { - 1 } }$

Factor by grouping. - $15 x ^ { 2 } - 12 x + 10 x - 8$

Solve the equation - $\frac { 25 y ^ { 4 } + 20 y ^ { 3 } + 4 y - 1 } { 5 y ^ { 2 } + 1 }$

Simplify the rational expression. Use factoring, and assume all variable expressions represent positive real numbers. -If the lengths of the sides of a square are tripled, by what factor will the area change?

Decide whether the expression has been simplified correctly. - $\left( \frac { x } { 9 } \right) ^ { 5 } = \frac { x ^ { 5 } } { 9 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 16 r ^ { 3 } \left( r ^ { 4 } \right) ^ { 5 } } { 11 \left( r ^ { - 5 } \right) ^ { - 3 } }$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 2,3,4,5,6,7 \} , \mathrm { B } = \{ 4,6,8 \} , \mathrm { C } = \{ 2,3,5,7 \} , \mathrm { D } = \{ 2,7 \}$ , and $\mathrm { U } = \{ 2,3,4,5,6,7,8 \}$ . $\mathrm { A } \subseteq \mathrm { B }$

Factor the trinomial, if possible. - $12 x ^ { 2 } + 17 x y + 6 y ^ { 2 }$