Chapter 12

Explain what an extraneous solution is.

Define trigonometric ratio.

Explain the difference between an axiom and a theorem.

What is meant by the midpoint between two points?

The two sides of a right triangle that are not the hypotenuse are the \(\underline{?}\).

The leading coefficient of the polynomial \(3 x^{2}-8 x+4\) is \(\underline{?}\)

Complete the following sentence: Two radical expressions are \(\underline{?}\) if they have the same radicand.

Describe the square root function.

One reason for checking a solution in the original equation is to look for an error in one of the steps of the solution. Give another reason.

Is it true or false that for any right triangle with a \(30^{\circ}\) angle, \(\sin 30^{\circ}=0.5 ?\) Explain.

What is the first step of an indirect proof?

Explain how you can use the Pythagorean theorem to find the distance between any two points in a coordinate plane.

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

Explain why completing the square of the expression \(x^{2}+b x\) is easier to do when \(b\) is an even number.

Write a radical expression and its conjugate.

Does the domain of \(y=\sqrt{x+3}\) include negative values of \(x ?\) Explain.

Is 36 a solution of \(\sqrt{x}=-6 ?\) Why or why not?

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

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 the result to the nearest hundredth. \((1,5),(-3,1)\) (GRAPH CAN'T COPY)

Explain how you can use the converse of the Pythagorean theorem to tell whether three given lengths can be sides of a right triangle.

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

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

Explain how to simplify \(\frac{\sqrt{3}}{\sqrt{3}-1}\)

Solve the equation. Check for extraneous solutions. $$\sqrt{x}-20=0$$

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

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 the result to the nearest hundredth. \((-3,-2),(4,1)\) \((0,0),(20,0),(20,21)\)

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. $$a=7, b=24$$

Find the term that should be added to the expression to create a perfect square trinomial. $$x^{2}+50 x$$

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

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

Solve the equation. Check for extraneous solutions. $$\sqrt{5 x+1}+8=12$$

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

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 the result to the nearest hundredth. \((5,-2),(-1,1)\) \((0,0),(20,0),(20,21)\)

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. $$a=5, c=13$$

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

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

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

Solve the equation. Check for extraneous solutions. $$\sqrt{4 x}-1=3$$

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

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

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. $$b=15, c=17$$

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

Evaluate the function for \(x=0,1,2,3,\) and \(4 .\) Round your answer to the nearest tenth. $$ y=6 \sqrt{x}-3 $$

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

Solve the equation. Check for extraneous solutions. $$\sqrt{x}+6=0$$

State the basic axiom of algebra that is represented. $$y+0=y$$

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

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. $$a=9, c=41$$

Find the term that should be added to the expression to create a perfect square trinomial. $$x^{2}-22 x$$

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