Chapter 12

Evaluate the function for the given value of \(x .\) Round your answer to the nearest tenth. $$y=6 \sqrt{15-x} ;-1$$

Simplify the expression. $$\sqrt{80}-\sqrt{45}$$

Solve the equation. Check for extraneous solutions. $$\sqrt{6 x-2}-3=7$$

Use an indirect proof to prove that the conclusion is true. If \(p\) is an integer and \(p^{2}\) is divisible by \(2,\) then \(p\) is divisible by \(2 .\) (Hint: An odd number can be written as \(2 n+1,\) where \(n\) is an integer. An even number can be written as \(2 n .\) )

Find the distance between the two points. Round the result to the nearest hundredth if necessary. $$\left(\frac{1}{3}, \frac{1}{6}\right),\left(-\frac{2}{3}, \frac{8}{3}\right)$$

Evaluate the function for the given value of \(x .\) Round your answer to the nearest tenth. $$y=\sqrt{21-2 x} ;-2$$

Find the term that should be added to the expression to create a perfect square trinomial. $$x^{2}-40 x$$

Simplify the expression. $$\sqrt{72}-\sqrt{18}$$

Solve the equation. Check for extraneous solutions. $$4=7-\sqrt{33 x-2}$$

Use an indirect proof to prove that the conclusion is true. If \(a

Graph the points. Decide whether they are vertices of a right triangle. $$(4,0),(2,1),(-1,-5)$$

Evaluate the function for the given value of \(x .\) Round your answer to the nearest tenth. $$y=\sqrt{\frac{x}{2}-2} ; 22$$

Simplify the expression. $$\sqrt{147}-7 \sqrt{3}$$

Solve the equation. Check for extraneous solutions. $$10=4+\sqrt{5 x+11}$$

Use an indirect proof to prove that the conclusion is true. If \(a c>b c\) and \(c>0,\) then \(a>b\)

\(.\) Logical REASONING A line with a positive slope passes through the origin, making a \(60^{\circ}\) angle with the positive \(x\) -axis. Write an equation of the line.

Graph the points. Decide whether they are vertices of a right triangle. $$(5,4),(2,1),(-3,2)$$

Evaluate the function for the given value of \(x .\) Round your answer to the nearest tenth. $$y=\sqrt{8 x^{2}+\frac{3}{2}} ; \frac{1}{4}$$

Simplify the expression. $$4 \sqrt{5}+\sqrt{125}+\sqrt{45}$$

Solve the equation. Check for extraneous solutions. $$-5-\sqrt{10 x-2}=5$$

COUNTEREXAMPLES Decide whether the statement is true or false. If it is false, give a counterexample. (Review 2.1 for 12.8) The absolute value of a number is always positive.

Graph the points. Decide whether they are vertices of a right triangle. $$(1,-5),(2,3),(-3,4)$$

Evaluate the function for the given value of \(x .\) Round your answer to the nearest tenth. $$y=\sqrt{\frac{2 x}{3}+5} ; 6$$

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$2,10,11$$

Find the term that should be added to the expression to create a perfect square trinomial. $$x^{2}+\frac{4}{5} x$$

Simplify the expression. $$3 \sqrt{11}+\sqrt{176}+\sqrt{11}$$

Solve the equation. Check for extraneous solutions. $$\sqrt{-x}-\frac{3}{2}=\frac{3}{2}$$

COUNTEREXAMPLES Decide whether the statement is true or false. If it is false, give a counterexample. The opposite of a number is always positive.

Graph the points. Decide whether they are vertices of a right triangle. $$(-1,1),(-3,3),(-7,-1)$$

Evaluate the function for the given value of \(x .\) Round your answer to the nearest tenth. $$y=\sqrt{36 x-2} ; \frac{1}{2}$$

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$15,20,25$$

Find the term that should be added to the expression to create a perfect square trinomial. $$x^{2}-5.2 x$$

Simplify the expression. $$\sqrt{24}-\sqrt{96}+\sqrt{6}$$

Solve the equation. Check for extraneous solutions. $$\sqrt{x}+\frac{1}{3}=\frac{13}{3}$$

USING THE DISTRIBUTIVE PROPERTY Use the distributive property to simplify the expression. $$6(w-3)$$

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

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

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$5,12,13$$

Simplify the expression. $$\sqrt{243}-\sqrt{75}+\sqrt{300}$$

Solve the equation. Check for extraneous solutions. $$\sqrt{\frac{1}{5} x-2}-\frac{1}{10}=\frac{7}{10}$$

Decide how many solutions the equation has. $$x^{2}-2 x+4=0$$

USING THE DISTRIBUTIVE PROPERTY Use the distributive property to simplify the expression. $$-p(p+1)$$

Graph the points. Decide whether they are vertices of a right triangle. $$(3,-1),(2,4),(-3,0)$$

Find the domain of the function. $$y=\sqrt{x-17}$$

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$11,60,61$$

Simplify the expression. $$\sqrt{3} \cdot \sqrt{12}$$

Solve the equation. Check for extraneous solutions. $$x=\sqrt{\frac{3}{2} x+\frac{5}{2}}$$

Decide how many solutions the equation has. $$-2 x^{2}+4 x-2=0$$

USING THE DISTRIBUTIVE PROPERTY Use the distributive property to simplify the expression. $$-(x-8)$$

Graph the points. Decide whether they are vertices of a right triangle. $$(-2,2),(3,4),(4,2)$$