Chapter 12

Simplify the expression. $$ \sqrt{3} \cdot \sqrt{8} $$

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

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

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. $$ b=11, c=61 $$

Determine whether the points are vertices of a right triangle. $$ (-2,0),(-1,0),(1,7) $$

Find the midpoint of the line segment with the given endpoints. \((0,0),(0,10)\)

Evaluate the expression without using a calculator. $$ 9^{3 / 2} $$

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

Simplify the expression. $$ (3+\sqrt{7})^{2} $$

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

State the basic axiom of algebra that is represented. $$ x+(-x)=0 $$

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. $$ a=12, b=35 $$

Determine whether the points are vertices of a right triangle. $$ (2,0),(-2,2),(-3,-5) $$

Find the term that should be added to the expression to create a perfect square trinomial. $$ x^{2}+24 x $$

Find the midpoint of the line segment with the given endpoints. \((2,1),(14,6)\)

Evaluate the expression without using a calculator. $$ \sqrt[3]{343} $$

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

Simplify the expression. $$ \sqrt{3}(5 \sqrt{3}-2 \sqrt{6}) $$

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

Copy and complete the proof of the statement: For all real numbers a and b, \((a+b)-b=a\) $$ \begin{aligned} (a+b)-b &=(a+b)+(-b) \\ &=a+[b+(-b)] \\ &=a+0 \\ &=a \end{aligned} $$ Definition of subtraction. Associative property of addition ? _____ ? _____

Solve \(x^{2}-3 x=8\) by completing the square. Solve the equation by using the quadratic formula. Which method did you find easier?

Find the midpoint of the line segment with the given endpoints. Then show that the midpoint is the same distance from each given point. \((-2,0),(6,2)\)

Evaluate the expression without using a calculator. $$ (\sqrt{81})^{3} $$

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

Simplify the expression. $$ \frac{4}{\sqrt{13}} $$

Find the domain and the range of the function. $$y=5 \sqrt{x}$$

Prove the theorem. Use the basic axioms of algebra and the definition of subtraction given in Example 1. If \(a\) and \(b\) are real numbers, then \(a-b=-b+a\)

Find the distance between the two points. Round your solution to the nearest hundredth if necessary. $$ (2,0),(8,-3) $$

Solve the quadratic equation by completing the square. $$ x^{2}-2 x-18=0 $$

Find the midpoint of the line segment with the given endpoints. Then show that the midpoint is the same distance from each given point. \((-2,2)(2,-10)\)

Rewrite the expression using rational exponent notation. $$ \sqrt{14} $$

Simplify the expression. $$ \frac{3}{8-\sqrt{10}} $$

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

Find the domain and the range of the function. $$y=\sqrt{x}$$

Prove the theorem. Use the basic axioms of algebra and the definition of subtraction given in Example 1. If \(a, b,\) and \(c\) are real numbers, then \((a-b) c=a c-b c\)

Find the distance between the two points. Round your solution to the nearest hundredth if necessary. $$ (2,-8),(-3,3) $$

Solve the quadratic equation by completing the square. $$ x^{2}+10 x-10=0 $$

Find the midpoint of the line segment with the given endpoints. Then show that the midpoint is the same distance from each given point. \((2,6),(4,2)\)

Rewrite the expression using rational exponent notation. $$ \sqrt[3]{11} $$

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

Simplify the expression. $$ \frac{6}{\sqrt{10}} $$

Find the domain and the range of the function. $$y=\sqrt{x}-10$$

MAKING A CONJECTURE A student proposes the following conjecture: The sum of the first n odd integers is \(\mathrm{n}^{2}\). She gives four examples: \(1=1^{2}, 1+3=4=2^{2}, 1+3+5=9=3^{2},\) and \(1+3+5+7=16=4^{2} .\) Do the examples prove her conjecture? Explain. Do you think the conjecture is true?

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 distance between the two points. Round your solution to the nearest hundredth if necessary. $$ (3,-2),(0,3) $$

Solve the quadratic equation by completing the square. $$ x^{2}+8 x=-3 $$

Find the midpoint of the line segment with the given endpoints. Then show that the midpoint is the same distance from each given point. \((-6,0),(-10,-2)\)

Rewrite the expression using rational exponent notation. $$ (\sqrt[3]{5})^{2} $$

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

Find the domain and the range of the function. $$y=\sqrt{x}+6$$