Chapter 12

Find the midpoint of the line segment connecting the given points. Then show that the midpoint is the same distance from each point. \((-9,17),(5,-7)\)

The length of each side of a baseball diamond is 90 feet. What is the diagonal distance \(c\) from home plate to second base?

Solve by completing the square. $$ x^{2}+6 x-16=0 $$

Evaluate the expression. $$ 4^{3 / 2} \cdot 4^{1 / 2} $$

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

Find the domain of the function. Then use severalvalues in the domain to make a table of values for the function. $$y=\sqrt{3 x-10}$$

Solve the equation. $$ \sqrt{2 x+4}+1=11 $$

Determine whether the equation has two solutions, one solution, or no real solution. (Lesson 9.7) $$ 8 x^{2}-8 x+2=0 $$

Find the midpoint of the line segment connecting the given points. Then show that the midpoint is the same distance from each point. \((-4,-2),(10,-6)\)

DIAGONAL OF A FIELD A field hockey field is a rectangle 60 yards by 100 yards. What is the length of the diagonal from one corner of the field to the opposite corner?

Solve by completing the square. $$ x^{2}+4 x=12 $$

Evaluate the expression. $$ \left(8^{2 / 3}\right)^{1 / 2} $$

Simplify the expression. $$ \sqrt{2}(\sqrt{8}-4) $$

Find the domain of the function. Then use severalvalues in the domain to make a table of values for the function. $$y=\sqrt{x+1}$$

Solve the equation. $$ 8 \sqrt{x+3}=64 $$

Determine whether the equation has two solutions, one solution, or no real solution. (Lesson 9.7) $$ x^{2}-14 x+49=0 $$

Solve by completing the square. $$ x^{2}+10 x=12 $$

Evaluate the expression. $$ \left(6^{1 / 3}\right)^{6} $$

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

Find the domain of the function. Then use severalvalues in the domain to make a table of values for the function. $$y=4+\sqrt{x}$$

Determine whether the equation has two solutions, one solution, or no real solution. (Lesson 9.7) $$ 3 x^{2}-5 x+1=0 $$

Solve by completing the square. $$ x^{2}+8 x=15 $$

Evaluate the expression. $$ (8 \cdot 27)^{1 / 3} $$

Simplify the expression using the sum and difference pattern. $$ (\sqrt{2}+6)(\sqrt{2}-6) $$

Find the domain of the function. Then use severalvalues in the domain to make a table of values for the function. $$y=\sqrt{x}-3$$

Determine whether the equation has two solutions, one solution, or no real solution. (Lesson 9.7) $$ 6 x^{2}-x+5=0 $$

PLANTING A NEW TREE. You have just planted a new tree. To support the tree, you attach four guy wires from the trunk of the tree to stakes in the ground. Each guy wire has a length of 7 feet. Suppose you put the stakes in the ground 5 feet from the base of the trunk. Approximately how far up the trunk should you attach the guy wires?

Solve by completing the square. $$ x^{2}+10 x=39 $$

Evaluate the expression. $$ (16 \cdot 25)^{1 / 2} $$

Simplify the expression using the sum and difference pattern. $$ (1+\sqrt{13})(1-\sqrt{13}) $$

Find the domain of the function. Then use severalvalues in the domain to make a table of values for the function. $$y=\sqrt{x+9}$$

Determine whether the ordered pair is a solution of the inequality. (Lesson 9.8) $$ y>x^{2}-2 x-5,(1,1) $$

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

Solve by completing the square. $$ x^{2}+16 x=17 $$

Evaluate the expression. $$ \left(2^{3} \cdot 3^{3}\right)^{1 / 3} $$

Simplify the expression using the sum and difference pattern. $$ (\sqrt{2}+\sqrt{3})(\sqrt{2}-\sqrt{3}) $$

Find the domain of the function. Then use severalvalues in the domain to make a table of values for the function. $$y=2 \sqrt{4 x}$$

Determine whether the ordered pair is a solution of the inequality. (Lesson 9.8) $$ y \geq 2 x^{2}-8 x+8,(3,-2) $$

You and a friend go hiking. You hike 3 miles north and 2 miles west. Starting from the same point, your friend hikes 4 miles east and 1 mile south. If you and your friend want to meet for lunch, where could you meet so that both of you hike the same distance? How far do you have to hike?

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

Solve by completing the square. $$ x^{2}-24 x=-44 $$

Evaluate the expression. $$ \left(2^{2 / 3} \cdot 2^{1 / 3}\right)^{6} $$

Simplify the expression using the sum and difference pattern. $$ (\sqrt{7}+\sqrt{2})(\sqrt{7}-\sqrt{2}) $$

Find the domain of the function. Then use severalvalues in the domain to make a table of values for the function. $$y=x \sqrt{x}$$

Determine whether the ordered pair is a solution of the inequality. (Lesson 9.8) $$ y \leq 2 x^{2}-3 x+10,(-2,20) $$

What is the midpoint between \((-2,-3)\) and \((1,7) ?\) A) \(\left(\frac{1}{2},-2\right)\) B) \(\left(-\frac{1}{2}, 2\right)\) C) \(\left(\frac{1}{2}, 2\right)\) D) \(\left(-\frac{1}{2}, 5\right)\)

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$ 12,16,20 $$

Solve by completing the square. $$ x^{2}-6 x-11=0 $$

Evaluate the expression. $$ \left(4^{2} \cdot 5^{2}\right)^{1 / 2} $$

In Exercises 38 and \(39,\) use the following information. When a car skids to a stop, its speed \(S\) (in miles per hour) before the skid can be modeled by the equation \(S=\sqrt{30 d f} .\) where \(d\) is the length of th tires' skid marks (in feet) and \(f\) is the coefficient of friction for the road. In an accident, a car makes skid marks that are 120 feet long. The coefficient of friction is 1.0. What can you say about the speed the car was traveling before the accident?