Lesson 10 All Systems Go Practice Understanding

Ready

Write an explicit equation for the function which fits the values represented in each table.

1.

$x$	$f (x)$
$- 1$	$2$
$0$	$6$
$1$	$18$
$2$	$54$
$3$	$162$

2.

$n$	$g (n)$
$- 2$	$2$
$- 1$	$6$
$0$	$10$
$1$	$14$
$2$	$18$

3.

$x$	$h (x)$
$1$	$200$
$2$	$100$
$3$	$50$
$4$	$25$
$5$	$12.5$

4.

$n$	$r (n)$
$2$	$36$
$3$	$27$
$4$	$18$
$5$	$9$
$6$	$0$

5.

$x$	$q (x)$
$10$	$32$
$15$	$47$
$20$	$62$
$25$	$77$
$30$	$92$

6.

$n$	$f (n)$
$8$	$13$
$14$	$31$
$20$	$49$
$26$	$67$
$32$	$85$

Set

Solve the system of equations using matrices. Create a matrix equation for the system of equations that can be used to find the solution. Then find the solution using an inverse matrix.

7.

${\begin{cases} 2 x - 4 y + z = 0 \\ 5 x - 4 y - 5 z = 12 \\ 4 x + 4 y + z = 24 \end{cases}$

8.

${\begin{cases} x + 2 y + 5 z = - 15 \\ x + y - 4 z = 12 \\ x - 6 y + 4 z = - 12 \end{cases}$

9.

${\begin{cases} 4 p + q - 2 r = 5 \\ - 3 p - 3 q - 4 r = - 16 \\ 4 p - 4 q + 4 r = - 4 \end{cases}$

10.

${\begin{cases} - 6 x - 4 y + z = - 20 \\ - 3 x - y - 3 z = - 8 \\ - 5 x + 3 y + 6 z = - 4 \end{cases}$

Go

Solve each of the equations below using an appropriate and efficient method.

11.

$5 + x^{2} = 30$

12.

$3 x^{2} - 5 = 0$

13.

$5 x^{2} - 10 = 0$

14.

$3 (x - 5) = 2 (2 x + 5)$

15.

$2 x - 37 = 4 (x - 5) + 3$

16.

$2 (- 3 x + 17) = 2 (x - 7)$