Exam 8: Special Topics in Algebra

Graph the solution set of the system of inequalities. - $\left\{ \begin{array} { l } y \leq - x ^ { 2 } - 6 x - 4 \\y \geq x ^ { 2 } + 6 x + 4\end{array} \right.$

Write the equation in the form $y = f ( x )$ f(x) by solving for y. - $24 x ^ { 2 } - 3 y = 15$

Graph the inequality. - $x-y>-2$

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the objective function. - $\mathrm { f } = 7 \mathrm { x } + 6 \mathrm { y }$ subject to the constraints $\left\{ \begin{array} { l } 3 x + 4 y \leq 165 \\x + 2 y \leq 77 \\x \geq 0 , y \geq 0\end{array} \right.$

Find the sum of the series, if possible. - $8 + 2 + \frac { 1 } { 2 } + \frac { 1 } { 8 } + \ldots$

Use the given feasible region determined by the constraint inequalities to find the minimum possible value of the objective function. -Find the minimum possible value of $\mathrm { f } = 2 \mathrm { x } + 4 \mathrm { y }$ subject to the following constraints: $\left\{ \begin{array} { l } x + 2 y \geq 10 \\3 x + y \geq 10 \\x \geq 0 , y \geq 0\end{array} \right.$

Write the indicated term of the binomial expansion. - $( 3 x - 2 y ) ^ { 12 } ; 9$ th term

Graph. - $x y = - 3$

Graph. - $6 x ^ { 2 } - y ^ { 2 } - 72 x + 14 y - 49 = 0$

An airline with two types of airplans, P1 and P2, has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers . for a certain trip, airplane P1 costs $10,00 to operate and can accommodate 20 first class, 50 tourist class, 110 economy class passengers. Airplane P2 costs $8500 to operate and can accommodate 18 first class, 30 rourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

Write four additional terms of the geometric sequence. -Find the first six terms of the sequence with first term $- 1$ and nth term $a _ { n } = 3 - a _ { n - 1 }$ .

Rewrite the expression as a sum, difference, or multiple of logarithms. -Find where $f ^ { \prime } ( x ) = 0$ if $f ^ { \prime } ( x ) = 3 x ^ { 3 } + 17 x ^ { 2 } - 6 x$ .

Graph the solution region for the system of inequalities and identify the corners of the region. - $\left\{\begin{array}{l}3 y+x>0 \\y+2 x \leq 10 \\y \geq 0\end{array}\right.$

Round your answer to the nearest cent. -Find the 12-year future value of an ordinary annuity with a contribution of $1000 per year into an account that pays 6% per year, compounded annually.

Find the sum of the first 5 terms of the geometric sequence $\frac { 2 } { 3 } , \frac { 4 } { 3 } , \frac { 8 } { 3 } , \ldots$

Write the function without radicals by using fractional exponents. - $y = \sqrt [ 3 ] { x ^ { 2 } + 6 }$

Write four additional terms of the geometric sequence. -8, 12, 18, . . .

A collection of dimes is arranged in a triangular array, with 15 coins in the base row, 14 in the next, 13 in the next, and so forth. Find the value of the collection.

Find the sum of the first 4 terms of the arithmetic sequence with first term -13 and common difference -2 .

The left semicircle centered at (0, 0) with radius 4