Exam 8: Systems of Equations and Inequalities

Three solutions contain a certain acid. The first contains 10% acid, the second 30%, and the third 50%. A chemist wishes to use all three solutions to obtain a 100-liter mixture containing 28% acid. If the chemist wants to use twice as much of the 50% solution as of the 30% solution, how many liters of each solution should be used?

Find the values of b such that the system $\left\{ \begin{aligned}x ^ { 2 } + y ^ { 2 } & = 9 \\y & = x + b\end{aligned} \right.$ has no solution.

Find the determinant of the matrix. $\left[ \begin{array} { r r r } 38 & - 17 & 96 \\- 31 & 88 & - 33 \\48 & 10 & 14\end{array} \right]$

Solve the system $\left\{ \begin{array} { l } 7 x + 4 y = - 24 \\8 x + 7 y = - 25\end{array} \right.$ using the inverse method.

Find the partial fraction decomposition. $\frac { 3 x ^ { 3 } + 13 x ^ { 2 } + 26 x + 7 } { x ( x + 1 ) ^ { 3 } }$