Chapter 12

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

Find the midpoint between the two points \((2,7),(4,3)\)

Solve the equation. Check for extraneous solutions. $$x=\sqrt{30-x}$$

Decide how many solutions the equation has. $$x^{2}+11 x+30=0$$

SUBTRACTING VERTICALLY Use a vertical format to subtract the second polynomial from the first polynomial. $$-2 x^{3}+5 x^{2}-x+8,-2 x^{3}+3 x-4$$

Find the domain of the function. $$y=0.2 \sqrt{x}$$

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 the equation by completing the square. $$x^{2}+\frac{3}{5} x-1=0$$

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

Solve the equation. Check for extraneous solutions. $$x=\sqrt{11 x-28}$$

Find the midpoint between the two points \((-1,1),(-4,-4)\)

Decide whether the ordered pair is a solution of the inequality. $$y

SIMPLIFYING RATIONAL EXPRESSIONS Simplify the expression. $$\frac{3}{x}+\frac{x+9}{x}$$

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

You have a rope with 30 equally spaced knots in it. How can you use the rope to check that a corner is a right angle?

Solve the equation by completing the square. $$x^{2}+x-1=0$$

Simplify the expression. $$\frac{5}{\sqrt{7}}$$

Find the midpoint between the two points \((-4,0),(-1,-5)\)

Solve the equation. Check for extraneous solutions. $$\sqrt{-10 x-4}=2 x$$

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

SIMPLIFYING RATIONAL EXPRESSIONS Simplify the expression. $$\frac{8}{4 a+1}-\frac{5}{4 a+1}$$

Find the domain of the function. $$y=\sqrt{x+9}$$

Solve the equation by completing the square. $$4 x^{2}+4 x-11=0$$

Simplify the expression. $$\frac{2}{\sqrt{2}}$$

Find the midpoint between the two points \((5,1),(1,-5)\)

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

Solve the equation. Check for extraneous solutions. $$x=\sqrt{200-35 x}$$

SIMPLIFYING RATIONAL EXPRESSIONS Simplify the expression. $$\frac{2}{2 x}+\frac{12}{x}$$

Find the domain of the function. $$y=8 \sqrt{\frac{5}{2} x}$$

Solve the equation by completing the square. $$3 x^{2}-24 x-1=0$$

Simplify the expression. $$\frac{9}{5-\sqrt{7}}$$

Decide whether the ordered pair is a solution of the inequality. $$y>4 x^{2}-48 x+61 ;(1,17)$$

Solve the equation. Check for extraneous solutions. $$\sqrt{110-x}=x$$

Find the midpoint between the two points \((0,-3),(-4,2)\)

SIMPLIFYING RATIONAL EXPRESSIONS Simplify the expression. $$\frac{5}{4 x}-\frac{7}{3 x}$$

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

Simplify the expression. $$\frac{3}{\sqrt{48}}$$

Solve the equation by completing the square. $$4 x^{2}-40 x-7=0$$

Decide whether the ordered pair is a solution of the inequality. $$y \geq x^{2}+4 x ;(-2,-4)$$

Find the midpoint between the two points \((5,-5),(-5,1)\)

Solve the equation. Check for extraneous solutions. $$2 x=\sqrt{-13 x-10}$$

SIMPLIFYING RATIONAL EXPRESSIONS Simplify the expression. $$\frac{2 x}{x+1}+\frac{5}{x+3}$$

Find the domain of the function. $$y=\frac{\sqrt{4-x}}{x}$$

Simplify the expression. $$\frac{6}{10+\sqrt{2}}$$

Solve the equation by completing the square. $$2 x^{2}-8 x-13=7$$

Find the midpoint between the two points \((-4,-3),(-1,-5)\)

Decide whether the ordered pair is a solution of the inequality. $$y<3 x^{2}-2 x ;(5,10)$$

Solve the equation. Check for extraneous solutions. $$x=\sqrt{4 x+45}$$

SIMPLIFYING RATIONAL EXPRESSIONS Simplify the expression. $$\frac{6 x}{x+1}-\frac{2 x+4}{x+1}$$

Find the domain and the range of the function. Then sketch the graph of the function. $$y=7 \sqrt{x}$$