Chapter 12

Solve the equation. $$ \sqrt{x}-9=0 $$

In Exercises 18 and \(19,\) use the following information. For a particular fire hose, the flow rate \(f\) (in gallons per minute) can be modeled by \(f=120 \mathrm{V} p,\) where \(p\) is the nozzle pressure in pounds per square inch. Find the domain of the flow rate model. Then sketch its graph.

Use an indirect proof to prove that the conclusion is true. Your bus leaves a track meet at 4: 30 P.M. and does not travel faster than 60 miles per hour. The meet is 45 miles from home. Your bus will not get you home in time for dinner at 5: 00 P.M.

USING THE PYTHAGOREAN THEOREM 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. $$ a=2, b=8 $$

Find the distance between the two points. Round your solution to the nearest hundredth if necessary. $$ (7,12),(-7,-4) $$

Find the midpoint of the line segment connecting the given points. \((-3,3),(2,-2)\)

Choose a method and solve the quadratic equation. Explain your choice. $$ 3 x^{2}-2=0 $$

Evaluate the expression without using a calculator. $$ \sqrt{10,000} $$

Simplify the expression. $$ \sqrt{32}+\sqrt{2} $$

Solve the equation. $$ \sqrt{x}-1=0 $$

In Exercises 18 and \(19,\) use the following information. For a particular fire hose, the flow rate \(f\) (in gallons per minute) can be modeled by \(f=120 \mathrm{V} p,\) where \(p\) is the nozzle pressure in pounds per square inch. If the nozzle pressure is 100 pounds per square inch, what is the flow rate?

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

USING THE PYTHAGOREAN THEOREM 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. $$ a=11, b=15 $$

Find the distance between the two points. Round your solution to the nearest hundredth if necessary. $$ (2,1),(8,4) $$

Find the midpoint of the line segment connecting the given points. \((5,-5),(-5,1)\)

Find the term that should be added to the expression to create a perfect square trinomial. $$ x^{2}-12 x $$

Evaluate the expression without using a calculator. $$ 512^{1 / 3} $$

Simplify the expression. $$ \sqrt{75}+\sqrt{3} $$

Solve the equation. $$ \sqrt{x}-5=0 $$

Evaluate the function for the given value of x. $$y=2 \sqrt{x} ; 9$$

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

Find the distance between the two points. Round your solution to the nearest hundredth if necessary. $$ (2,1),(-4,16) $$

USING THE PYTHAGOREAN THEOREM 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. $$ b=3, c=10 $$

Find the midpoint of the line segment connecting the given points. \((-1,1),(-4,-4)\)

Find the term that should be added to the expression to create a perfect square trinomial. $$ x^{2}+8 x $$

Evaluate the expression without using a calculator. $$ 4^{1 / 2} $$

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

Solve the equation. $$ \sqrt{x}-10=0 $$

Evaluate the function for the given value of x. $$y=-2 \sqrt{x}, 25$$

Find the distance between the two points. Round your solution to the nearest hundredth if necessary. $$ (-1,9),(0,7) $$

USING THE PYTHAGOREAN THEOREM 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. $$ b=1, c=3 $$

Find the midpoint of the line segment connecting the given points. \((-4,0),(-1,-5)\)

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

Evaluate the expression without using a calculator. $$ 1^{1 / 3} $$

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

Solve the equation. $$ \sqrt{x}-15=0 $$

Evaluate the function for the given value of x. $$y=\sqrt{32 x} ; 2$$

Find the distance between the two points. Round your solution to the nearest hundredth if necessary. $$ (4,11),(-5,2) $$

USING THE PYTHAGOREAN THEOREM 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. $$ a=4, c=7 $$

Find the midpoint of the line segment connecting the given points. \((-4,-3),(-1,-5)\)

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

Evaluate the expression without using a calculator. $$ 256^{1 / 2} $$

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

Solve the equation. $$ \sqrt{x}-16=0 $$

Evaluate the function for the given value of x. $$y=\sqrt{3 x} ; 12$$

What is the first step to prove the following theorem: If a and b are real numbers and \((\mathrm{x}+\mathrm{a})=\mathrm{b},\) then \(\mathrm{x}=\mathrm{b}-\mathrm{a}\). A. \(x+(a-a)=b-a\) B. \(x=b-a\) C. \((x+a)-a=b-a\) D. \(x+0=b-a\)

Find the distance between the two points. Round your solution to the nearest hundredth if necessary. $$ (-10,-2),(1,7) $$

USING THE PYTHAGOREAN THEOREM 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. $$ a=8, c=10 $$

Find the midpoint of the line segment connecting the given points. Then show that the midpoint is the same distance from each point. \((7,-3),(-1,-9)\)

Evaluate the expression without using a calculator. $$ (\sqrt{16})^{4} $$