Lesson 6 All for One, One for All Solidify Understanding

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Find the value of each square root.

$\sqrt{49}$

$\sqrt{169}$

$\sqrt{9}$

$\sqrt{100}$

$\sqrt{64}$

$\sqrt{81}$

Solve for $x$ .

$3^{x} = 81$

$4^{x} = 64$

$2^{x} = 32$

$x^{2} = 144$

$x^{3} = 125$

$x^{2} = 256$

Constraints $A$ , $B$ , and $C$ are graphed as shown. Constraint $A$ is blue, constraint $B$ is green, and constraint $C$ is purple.

Indicate where on the grid each of the following might exist by labeling it.

Where can coordinate pairs that satisfy only constraint $A$ and constraint $B$ be found?
Where can coordinate pairs that satisfy only constraint $B$ and constraint $C$ be found?
Where can coordinate pairs that satisfy only constraint $A$ and constraint $C$ be found?
Where can coordinate pairs that satisfy all three constraints be found?

Write the inequality that represents the shaded region for each graph in slope-intercept form.

For each inequality and graph, shade the half plane that contains the solutions.

$y \leq \frac{1}{5} x - 4$

$y \geq - 3 x + 5$

$5 x - 2 y \leq 10$

$3 x + 4 y \geq 24$