Exam 1: Review of Basic Concepts

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $( 9 + x ) ( 3 x + 7 )$

Evaluate the expression. -Let $x = 10 , y = - 2$ . Evaluate $| 14 x |$ .

Solve the problem. -A formula for calculating the distance, d, one can see from an airplane to the horizon on a clear day is $\mathrm { d } = 1.22 \mathrm { x } ^ { 1 / 2 }$ , where $\mathrm { x }$ is the altitude of the plane in feet and $\mathrm { d }$ is given in miles. How far can one see in a plane flying at 24,000 feet? Round your answer to the nearest tenth mile, if necessary.

Factor by any method. - $81 k ^ { 2 } - 169 m ^ { 2 }$

Identify the property illustrated by the statement. Assume all variables represent real numbers. -3(x + 6) = 3x + 18

Simplify the expression. Assume all variables represent positive real numbers. - $8 \sqrt [ 3 ] { 3 } + 14 \sqrt [ 3 ] { 3 }$

Find the values of a, b, and c for which the quadratic equation ax2 + bx + c = 0 has the given numbers as solutions. Then use those values to write a quadratic equation. - $( x - 7 y ) ( x + 12 y )$

Evaluate the expression. - $4 ^ { 3 }$

Tell whether the statement is true or false. -Let $\mathrm { A } = \{ 4,5,6,7,8,9 \} , \mathrm { B } = \{ 6,8,10 \} , \mathrm { C } = \{ 4,5,7,9 \} , \mathrm { D } = \{ 5,9 \}$ , and $\mathrm { U } = \{ 4,5,6,7,8,9,10 \}$ . $\mathrm { U } \subseteq \mathrm { C }$

Evaluate the expression for x = -2, y = 3, and a = -4. - $x ^ { 3 } - 6 y + 7 a$

Factor the polynomial by substitution. - $10 y ^ { 4 } - 19 y ^ { 2 } - 15$

Perform the indicated operations. - $\frac { 2 a b } { a ^ { 2 } - b ^ { 2 } } - \frac { b } { a - b } + \frac { 6 } { 2 }$

Find the product or quotient. - $\frac { ( x - y ) ^ { 2 } - 49 } { ( x + y ) ^ { 2 } - 49 } \div \frac { x - y - 7 } { x + y + 7 }$

Write in radical form. Assume all variables represent positive real numbers. - $\mathrm { m } ^ { 8 / 3 }$ $\quad$

Evaluate the expression. -Let $x = 24 , y = - 5$ . Evaluate $| - 5 y - 7 x | - | 10 y |$ .

Simplify the expression. Assume all variables represent positive real numbers. - $\sqrt [ 3 ] { \frac { 5 } { 9 x ^ { 2 } } }$

Tell whether the statement is true or false. -Let $A = \{ 5,6,7,8,9,10 \} , B = \{ 7,9,11 \} , C = \{ 5,6,8,10 \} , D = \{ 5,10 \}$ , and $U = \{ 5,6,7,8,9,10,11 \}$ . $\mathrm { C } \subset \mathrm { A }$

Find the sum or difference. - $2 \left( - 2 r ^ { 4 } + 9 r ^ { 3 } - 3 r \right) - 3 \left( 8 r ^ { 4 } - 9 r ^ { 3 } + 6 r ^ { 2 } - 2 r \right)$

Factor the polynomial by substitution. - $48 z ^ { 6 } + 52 z ^ { 4 } + 12 z ^ { 2 }$

Solve the problem. - $\frac { - 32 x ^ { 8 } - 32 x ^ { 6 } - 56 x ^ { 4 } } { - 8 x ^ { 6 } }$