7. Systems of Equations & Matrices

Solve each system in Exercises 5–18. x+0y+2z=11, x+0y+3z=14, x+2y−0z=5

In Exercises 1–4, determine if the given ordered triple is a solution of the system. (4, 1, 2) x−2y=2, 2x+3y=11, y−4z=−7

In Exercises 1–4, determine if the given ordered triple is a solution of the system. (2,−1, 3) x+ y+0z=4, x−2y−0z=1, 2x−y−2z=−1

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)

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