Exam 12: Review of Basic Concepts

Solve the problem. -Use the formula Passing Rating $= 85.68 \left( \frac { \mathrm { C } } { \mathrm { A } } \right) + 4.31 \left( \frac { \mathrm { Y } } { \mathrm { A } } \right) + 326.42 \left( \frac { \mathrm { T } } { \mathrm { A } } \right) - 419.0 \% \left( \frac { \mathrm { I } } { \mathrm { A } } \right)$ , where $\mathrm { A } =$ number of passes attempted, $\mathrm { C } =$ number of passes completed, $\mathrm { Y } =$ total number of yards gained passing, $\mathrm { T } =$ number of touchdown passes, and $\mathrm { I }$ = number of interceptions, to approximate the passing rating for $\mathrm { C }$ . Felix. Round to the nearest tenth.

Evaluate the expression. -Let $x = - 6 , y = 4$ . Evaluate $| x | + | y |$ .

Insert ⊆ or ⊈ in the blank to make the statement true. -{9, 10, 11, 14} ___ {9, 13, 11, 12, 10, 14}

Perform the indicated operations. - $\frac { x } { x ^ { 2 } - 16 } - \frac { 7 } { x ^ { 2 } + 5 x + 4 }$

Insert ⊆ or ⊈ in the blank to make the statement true. -{4, 6, 9, 11} ___ {4, 4, 6, 7, 8, 9}

Find the product. - $\left( - 3 x ^ { 2 } - 9 y \right) \left( 5 x ^ { 2 } - 6 y + z \right)$

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers. - $\frac { x ^ { 1 / 2 } } { x ^ { 3 / 4 } \cdot x ^ { - 3 } }$

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt { \frac { 35 } { x ^ { 4 } } }$

Write the expression with only positive exponents and evaluate if possible. Assume all variables represent nonzero real numbers. - $- 8 x ^ { 0 }$

Provide an appropriate response. -Consider the following figure, which is a square divided into two squares and two rectangles. The length of each side of the large square is $x + 8$ . Use the formula for the area of a square to write the area of the largest square as a power.

Simplify the expression. Assume all variables represent nonzero real numbers. - $\left( - 10 x ^ { 3 } y \right) \left( - 3 x ^ { 2 } y ^ { 4 } \right)$

Perform the indicated operations. - $\frac { 2 a b } { a ^ { 2 } - b ^ { 2 } } - \frac { b } { a - b } + 5$

Identify the set as finite or infinite. - $\{ x \mid x$ is a natural number larger than $3 \}$

Evaluate the expression. - $- 4 \cdot 3 ^ { 2 }$

Perform the indicated operations. Write the result using only positive exponents. Assume all variables represent nonzero real numbers. - $\frac { 5 ^ { 7 } } { 5 ^ { 4 } }$

Tell whether the statement is true or false. - $\{ 8,13,11,14 \} = \{ 11,8,13 \}$

Evaluate the expression. - $\left( - \frac { 1 } { 3125 } \right) ^ { - 2 / 5 }$

Find the product or quotient. - $\frac { z ^ { 2 } + 5 z + 6 } { z ^ { 2 } + 11 z + 24 } \div \frac { z ^ { 2 } + 2 z } { z ^ { 2 } + 6 z - 16 }$

Use these sets to find the following. Identify any disjoint sets. -Let $\mathrm { U } = \{ 3,4,5,6,7,8,9,10,11,12,13 \} , \mathrm { M } = \{ 3,5,7,9 \} , \mathrm { N } = \{ 4,6,8,10,12 \} , \mathrm { Q } = \{ 3,5,7,9,11,13 \}$ , and $R = \{ 3,4,5,6 \}$ . $( \mathrm { R } \cup \mathrm { N } ) \cap \mathrm { M } ^ { \prime }$

Factor the trinomial, if possible. - $6 x ^ { 2 } - 18 x y - 24 y ^ { 2 }$