Exam 12: Review of Basic Concepts

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\mathrm { x } ^ { 1 / 3 } \cdot \mathrm { x } ^ { 2 / 3 }$

Solve the problem. -As the relative humidity increases, the temperature seems higher than it is. The formula $\mathrm { T } = 0.113 \mathrm { x }$ + $82.57$ approximates the apparent temperature for an actual temperature of $90 ^ { \circ } \mathrm { F }$ , where $\mathrm { x }$ is the relative humidity. What is the apparent temperature (to the nearest degree) for a relative humidity of $50 \%$ ?

Find the sum or difference. - $\left( 2 a ^ { 4 } + 6 a ^ { 3 } \right) + \left( 6 a ^ { 4 } + 8 a ^ { 3 } \right)$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\left( 3 x ^ { - 3 } \right) ^ { 3 } \left( x ^ { 2 } \right) ^ { - 5 }$

Factor by any method. - $192 \mathrm { k } ^ { 3 } \mathrm {~m} - 375 \mathrm {~m} ^ { 4 }$

Factor the trinomial, if possible. - $10 y ^ { 2 } + 23 y + 12$

Factor the trinomial, if possible. - $( m - 4 n ) ^ { 2 } - 4 ( m - 4 n ) + 4$

Solve the problem. -If a rock falls from a height of 100 meters above the ground, the height $\mathrm { H }$ (in meters) after $\mathrm { x }$ seconds can be approximated using the formula $\mathrm { H } = 100 - 4.9 \mathrm { x } ^ { 2 }$ . What is the height of the rock after 2 seconds?

Evaluate the expression. - $\left( \frac { 4 } { 9 } \right) ^ { - 1 / 2 }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -8 + (-8) = 0

Evaluate the expression. -Let $x = 24 , y = 17$ . Evaluate $| 8 y - 9 x |$ .

Divide. - $\frac { 30 x ^ { 6 } - 36 x ^ { 3 } } { - 6 x ^ { 6 } }$

Solve the problem. -A manufacturer's cost is given by $\mathrm { C } = 200 \mathrm { n }^{ 1 / 3} + 1400$ , where $\mathrm { C }$ is the cost in dollars and $\mathrm { n }$ is the number of parts produced. Find the cost when 729 parts are produced.

List all the elements of set B that belong to the indicated set. - $B = \left\{ 10 , \sqrt { 6 } , - 21,0 , \frac { 0 } { 5 } , \sqrt { 4 } , \frac { - 8 } { 0 } , 0.27 \right\}$ Rational numbers

Evaluate the expression. - $( - 81 ) ^ { 1 / 2 }$

Insert ⊆ or ⊈ in the blank to make the statement true. -{0, 9, 11, 14} ___ {9, 11, 14, 15, 16, 17}

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( x ^ { 2 } \right) ^ { 5 }$

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( 2 a ^ { 7 } \right) \cdot \left( 5 a ^ { 2 } \right)$

Evaluate the expression for x = -2, y = 3, and a = -4. - $\frac { 2 x + 2 ( 1 + a ) ^ { 2 } } { y + 1 }$

Write in radical form. Assume all variables represent positive real numbers. - $\left( 8 m ^ { 4 } + 3 k ^ { 2 } \right) ^ { 2 / 5 }$