Chapter 12

Find the domain of the function. $$y=\sqrt{3 x-10}$$

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$7,24,26$$

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

Simplify the expression. $$\sqrt{5} \cdot \sqrt{8}$$

Solve the equation. Check for extraneous solutions. $$\sqrt{\frac{1}{4} x-4}-3=5$$

Decide how many solutions the equation has. $$8 x^{2}-8 x+2=0$$

USING THE DISTRIBUTIVE PROPERTY Use the distributive property to simplify the expression. $$(x+3) x$$

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

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

Determine whether the given lengths are sides of a right triangle. Explain your reasoning. $$9.9,2,10.1$$

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

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

Solve the equation. Check for extraneous solutions. $$6-\sqrt{7 x-9}=3$$

Find the midpoint between the two points \((3,0),(-5,4)\)

Decide how many solutions the equation has. $$x^{2}-14 x+49=0$$

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

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

State the hypothesis and the conclusion of the statement. If today is Tuesday, then yesterday was Monday.

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

Find the midpoint between the two points \((0,0),(0,8)\)

Solve the equation. Check for extraneous solutions. $$\sqrt{\frac{1}{9} x+1}-\frac{2}{3}=\frac{5}{3}$$

Decide how many solutions the equation has. $$-3 x^{2}-5 x+1=0$$

USING THE DISTRIBUTIVE PROPERTY Use the distributive property to simplify the expression. $$(4+x)(-6 x)$$

Find the domain of the function. $$y=\sqrt{x}-3$$

State the hypothesis and the conclusion of the statement. If a polygon is a square, then it is a parallelogram.

Solve the equation by completing the square. $$x^{2}-8 x+12=0$$

Simplify the expression. $$\sqrt{6}(7 \sqrt{3}+6)$$

Find the midpoint between the two points \((1,2),(5,4)\)

Solve the equation. Check for extraneous solutions. $$x=\sqrt{35+2 x}$$

Decide how many solutions the equation has. $$6 x^{2}-x+5=0$$

SUBTRACTING VERTICALLY Use a vertical format to subtract the second polynomial from the first polynomial. $$6 x^{2}-3 x+2,2 x^{2}+x+7$$

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

State the hypothesis and the conclusion of the statement. $$\text { If } \frac{x}{3}=-15, \text { then } x=-45$$

Solve the equation by completing the square. $$x^{2}+5 x-\frac{11}{4}=0$$

Simplify the expression. $$(\sqrt{6}+5)^{2}$$

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

Find the midpoint between the two points \((-1,2),(7,4)\)

Decide how many solutions the equation has. $$x^{2}-2 x-15=0$$

SUBTRACTING VERTICALLY Use a vertical format to subtract the second polynomial from the first polynomial. $$4 x^{3}+3 x^{2}+8 x+6,2 x^{3}-3 x^{2}-7 x$$

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

State the hypothesis and the conclusion of the statement. If the area of a square is 25 square feet, then the length of a side is 5 feet.

Solve the equation by completing the square. $$x^{2}+11 x+\frac{21}{4}=0$$

Simplify the expression. $$(\sqrt{a}-b)^{2}$$

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

Solve the equation. Check for extraneous solutions. $$x=\sqrt{6 x-9}$$

Decide how many solutions the equation has. $$x^{2}+16 x+64=0$$

SUBTRACTING VERTICALLY Use a vertical format to subtract the second polynomial from the first polynomial. $$10 x^{3}+15,17 x^{3}-4 x+5$$

Find the domain of the function. $$y=2 \sqrt{4 x}$$

State the hypothesis and the conclusion of the statement. If a triangle has sides that are 8 inches and 9 inches long, then the length of the third side is greater than 1 inch and less than 17 inches.

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