7. Systems of Equations & Matrices

Find the quadratic function y = ax^2 + bx + c whose graph passes through the points (1, 4), (3, 20), and (-2, 25).

Solve each system in Exercises 12–13. The is a piecewise function

Solve each problem. See Examples 5 and 9. The sum of the measures of the angles of any triangle is 180°. In a certain triangle, the largest angle measures 55° less than twice the medium angle, and the smallest angle measures 25° less than the medium angle. Find the measures of all three angles.

Solve each problem. See Examples 5 and 9. Solve the system of equations (4), (5), and (6) from Example 9.

$25x+40y+20z=2200$ (4)

$4x+2y+3z=280$ (5)

$3x+2y+z=180$ (6)

Find the partial fraction decomposition of 4x²+5x-9/(x³- 6x-9)

Find the partial fraction decomposition for 1/x(x+1) and use the result to find the following sum:

Perform each long division and write the partial fraction decomposition of the remainder term. (x⁴-x²+2)/(x³-x²)

Perform each long division and write the partial fraction decomposition of the remainder term. (x⁵+2)/(x²-1)

Write the partial fraction decomposition of each rational expression. (4x²+3x+14)/(x³ - 8)

Write the partial fraction decomposition of each rational expression. (x³-4x²+9x-5)/(x² -2x+3)²

Write the partial fraction decomposition of each rational expression. $\frac{x^3 + x^2 + 2}{(x^2 + 2)^2}$

Write the partial fraction decomposition of each rational expression. 6x²-x+1/(x³ + x² + x +1)

Write the partial fraction decomposition of each rational expression. x+4/x² (x²+4)

Write the partial fraction decomposition of each rational expression. 5x²+6x+3/(x + 1)(x² + 2x + 2)