Lesson 6 All Systems Go Practice Understanding

Ready

Write each exponential expression in radical form.

1.

$10^{\frac{3}{2}}$

2.

$x^{\frac{1}{5}}$

3.

$3 n^{\frac{1}{3}}$

4.

$6^{\frac{2}{7}}$

5.

$7^{\frac{5}{3}}$

6.

$t^{\frac{4}{5}}$

Write each radical expression in exponential form.

7.

$\sqrt[5]{3}$

8.

${(\sqrt[6]{7 a})}^{5}$

9.

$\sqrt{x^{3}}$

10.

$\sqrt[3]{n^{5}}$

11.

${(\sqrt[y]{n})}^{x}$

12.

$\sqrt[p]{n^{q}}$

Explain each strategy for solving quadratic equations and explain the circumstances in which the strategy is most efficient.

13.

Graphing

14.

Factoring

15.

Completing the Square

16.

What other strategies do you know for solving quadratic equations? When would you use them?

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.

17.

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

18.

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

19.

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

20.

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

Go

Solve each of the equations below using an efficient method.

21.

$x^{2} - 5 x = - 6$

22.

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

23.

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

24.

$x^{2} + 1 x - 30 = 0$

25.

$x^{2} + 2 x = 48$

26.

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