91Ó°ÊÓ

(a) determine the polynomial function whose graph passes through the points, and (b) sketch the graph of the polynomial function, showing the points. $$(2,5),(3,2),(4,5)$$

(a) determine the polynomial function whose graph passes through the points, and (b) sketch the graph of the polynomial function, showing the points. $$(-2,28),(-1,0),(0,-6),(1,-8),(2,0)$$

Find a parametric representation of the solution set of the linear equation. $$12 x_{1}+24 x_{2}-36 x_{3}=12$$

Graph the system of linear equations. Solve the system and interpret your answer. $$\begin{array}{r}2 x+y=4 \\\x-y=2\end{array}$$

Find the solution set of the system of linear equations represented by the augmented matrix. $$ \left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & 1 & 2 \end{array}\right] $$

Find an equation of the circle that passes through the points. $$(1,3),(-2,6),(4,2)$$

The U.S. census lists the population of the United States as 249 million in \(1990,282\) million in \(2000,\) and 309 million in 2010 . Fit a second-degree polynomial passing through these three points and use it to predict the populations in 2020 and 2030 . (Source: U.S. Census Bureau)

Solve the system using either Gaussian elimination with back-substitution or Gauss-Jordan elimination. $$ \begin{array}{rr} 2 x+6 y= & 16 \\ -2 x-6 y= & -16 \end{array} $$

28.a) Explain how to use systems of linear equations for polynomial curve fitting. (b) Explain how to use systems of linear equations to perform network analysis.

Tips \(\quad\) A food server examines the amount of money earned in tips after working an 8 -hour shift. The server has a total of \(\$ 95\) in denominations of \(\$ 1, \$ 5,510\), and \(\$ 20\) bills. The total number of paper bills is 26 The number of \(\$ 5\) bills is 4 times the number of \(\$ 10\) bills, and the number of \(\$ 1\) bills is 1 less than twice the number of \(\$ 5\) bills. Write a system of linear equations to represent the situation. Then use matrices to find the number of each denomination.