Chapter 12

Explain the difference between an axiom and a theorem.

Complete: Sides of a right triangle that are not the hypotenuse are the ____.

The distance formula is related to which theorem?

Explain how to complete the square of the expression \(x^{2}+b x\)

What is meant by the midpoint of a line segment?

Write "the cube root of \(27 "\) in both radical notation and rational exponent notation.

Explain what a radical equation is.

Complete: In the expression " \(3 \sqrt{2} ", 2\) is called the ___

1\. Describe the square root function.

What is the first step in an indirect proof?

State the hypothesis and the conclusion of the statement "If \(x\) is an even number, then \(x^{2}\) is an even number."

Use the coordinate plane to estimate the distance between the two points. Then use the distance formula to find the distance between the points. Round your solution to the nearest hundredth. $$ (1,5),(-3,1) $$

Give two methods for checking the midpoint of a line segment.

Evaluate the expression without using a calculator. $$\sqrt[3]{125}$$

Explain what an extraneous solution is.

Which of the following is the simplest form of the radical expression \(\frac{4}{\sqrt{3}} ?\) $$A.\quad \frac{4 \sqrt{3}}{9}\quad B.\quad \frac{4 \sqrt{3}}{3} \quad c.\quad \frac{4}{\sqrt{3}}\quad D.\quad \frac{\sqrt{12}}{3}$$

State the basic axiom of algebra that is represented. $$ y(1)=y $$

Find the missing length of the right triangle if \(a\) and \(b\) are the lengths of the legs and \(c\) is the length of the hypotenuse. $$ a=7, b=24 $$

Use the coordinate plane to estimate the distance between the two points. Then use the distance formula to find the distance between the points. Round your solution to the nearest hundredth. $$ (-3,-2),(4,1) $$

Find the term that should be added to the expression to create a perfect square trinomial. $$ x^{2}+20 x $$

Find the midpoint of the line segment with the given endpoints. \((4,4),(-1,2)\)

Evaluate the expression without using a calculator. $$49^{1 / 2}$$

Solve the equation. Check for extraneous solutions. $$ 8=\sqrt{x} $$

Simplify the expression. $$ 4+\sqrt{5}+5 \sqrt{5} $$

Evaluate the function for x 0, 1, 2, 3, and 4. Round your answers to the nearest tenth. $$y=4 \sqrt{x}$$

State the basic axiom of algebra that is represented. $$ 2 x+3=3+2 x $$

Find the missing length of the right triangle if \(a\) and \(b\) are the lengths of the legs and \(c\) is the length of the hypotenuse. $$ a=5, c=13 $$

Use the coordinate plane to estimate the distance between the two points. Then use the distance formula to find the distance between the points. Round your solution to the nearest hundredth. $$ (5,-2),(-1,1) $$

Find the term that should be added to the expression to create a perfect square trinomial. $$ x^{2}+30 x $$

Find the midpoint of the line segment with the given endpoints. \((6,2),(2,-3)\)

Evaluate the expression without using a calculator. $$ (\sqrt[3]{8})^{5} $$

Solve the equation. Check for extraneous solutions. $$ \sqrt{x}=11 $$

Simplify the expression. $$ 3 \sqrt{7}-2 \sqrt{7} $$

Evaluate the function for x 0, 1, 2, 3, and 4. Round your answers to the nearest tenth. $$y=-\sqrt{x}$$

State the basic axiom of algebra that is represented. $$ 5(x+y)=5 x+5 y $$

Find the missing length of the right triangle if \(a\) and \(b\) are the lengths of the legs and \(c\) is the length of the hypotenuse. $$ b=15, c=17 $$

Determine whether the points are vertices of a right triangle. $$ (0,0),(20,0),(20,21) $$

Find the term that should be added to the expression to create a perfect square trinomial. $$ x^{2}-10 x $$

Find the midpoint of the line segment with the given endpoints. \((-5,3),(-3,-3)\)

Evaluate the expression without using a calculator. $$ 25^{3 / 2} $$

Solve the equation. Check for extraneous solutions. $$ 14=\sqrt{x} $$

Simplify the expression. $$ 3 \sqrt{6}+\sqrt{24} $$

Evaluate the function for x 0, 1, 2, 3, and 4. Round your answers to the nearest tenth. $$y=3 \sqrt{x}+4$$

State the basic axiom of algebra that is represented. $$ (4 x) y=4(x y) $$

Find the missing length of the right triangle if \(a\) and \(b\) are the lengths of the legs and \(c\) is the length of the hypotenuse. $$ a=9, c=41 $$

Determine whether the points are vertices of a right triangle. $$ (4,0),(4,-4),(10,-4) $$

Find the term that should be added to the expression to create a perfect square trinomial. $$ x^{2}-14 x $$

Find the midpoint of the line segment with the given endpoints. \((-4,4),(2,0)\)

Evaluate the expression without using a calculator. $$ 121^{1 / 2} $$

Solve the equation. Check for extraneous solutions. $$ \sqrt{x}=-7 $$