7. Systems of Equations & Matrices

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)

Solve each problem. See Examples 5 and 9. A sparkling-water distributor wants to make up 300 gal of sparkling water to sell for $6.00 per gallon. She wishes to mix three grades of water selling for $9.00, $3.00, and $4.50 per gallon, respectively. She must use twice as much of the $4.50 water as of the $3.00 water. How many gallons of each should she use?

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:

In Exercises 43–46, perform each long division and write the partial fraction decomposition of the remainder term. (x^4-x^2+2)/(x^3-x^2)

In Exercises 43–46, perform each long division and write the partial fraction decomposition of the remainder term. (x^5+2)/(x^2-1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (4x^2+3x+14)/(x^3 - 8)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. (x^3-4x^2+9x-5)/(x^2 -2x+3)^2

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x^3+x^2+2/(x² + 2)²

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 6x^2-x+1/(x^3 + x²+x+1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x+4/x² (x²+4)

In Exercises 9–42, write the partial fraction decomposition of each rational expression.5x^2+6x+3/(x + 1)(x² + 2x + 2)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. 5x^2 -6x+7/(x − 1) (x² + 1)

In Exercises 9–42, write the partial fraction decomposition of each rational expression. x^2/(x − 1)² (x + 1)