Chapter 14

Solve the system of equations. $$\begin{aligned} x+y+z &=2 \\ 6 x-4 y+5 z &=31 \\ 5 x+2 y+2 z &=13 \end{aligned}$$

Solve the exponential equation algebraically. Then check using a graphing calculator. $$3^{x}=81$$

Solve. $$\frac{1}{4}+\frac{1}{5}=\frac{1}{t}$$

Write an equivalent expression without negative exponents. $$3^{-7}$$

When solving a quadratic inequality, how do you know when to include and when to exclude the endpoints in the solution set?

If a nonlinear system consists of equations with the following graphs, a) sketch the different ways in which the graphs can intersect. b) make a sketch in which the graphs do not intersect. c) how many possible solutions can each system have? circle and line

Identify each equation as an ellipse or a hyperbola. $$\frac{x^{2}}{36}+\frac{y^{2}}{4}=1$$

Is the equation of a circle a function? Explain your answer.

Solve the system of equations. $$\begin{aligned} x+6 y+3 z &=4 \\ 2 x+y+2 z &=3 \\ 3 x-2 y+z &=0 \end{aligned}$$

Solve the exponential equation algebraically. Then check using a graphing calculator. $$2^{x}=32$$

Solve. $$\frac{1}{3}-\frac{5}{6}=\frac{1}{x}$$

Write an equivalent expression without negative exponents. $$\frac{1}{(5.9)^{-4}}$$

If a rational inequality contains a \(\leq\) or \(\geq\) symbol, will the endpoints of the solution set always be included? Explain your answer.

If a nonlinear system consists of equations with the following graphs, a) sketch the different ways in which the graphs can intersect. b) make a sketch in which the graphs do not intersect. c) how many possible solutions can each system have? parabola and line

Identify each equation as an ellipse or a hyperbola. $$\frac{x^{2}}{9}-\frac{y^{2}}{25}=1$$

Solve the system of equations. $$\begin{aligned} x-y+2 z &=-3 \\ x+2 y+3 z &=4 \\ 2 x+y+z &=-3 \end{aligned}$$

Solve the exponential equation algebraically. Then check using a graphing calculator. $$2^{2 x}=8$$

Solve. $$\frac{x+2}{4}-\frac{x-1}{5}=15$$

Write an equivalent expression without negative exponents. $$\frac{x^{-5}}{y^{-4}}$$

If a nonlinear system consists of equations with the following graphs, a) sketch the different ways in which the graphs can intersect. b) make a sketch in which the graphs do not intersect. c) how many possible solutions can each system have? parabola and ellipse

Identify each equation as an ellipse or a hyperbola. $$\frac{(y-3)^{2}}{4}-\frac{(x+5)^{2}}{9}=1$$

Identify the center and radius of each circle and graph. $$(x+2)^{2}+(y-4)^{2}=9$$

Solve the system of equations. $$\begin{aligned} x+y+z &=6 \\ 2 x-y-z &=-3 \\ x-2 y+3 z &=6 \end{aligned}$$

Solve the exponential equation algebraically. Then check using a graphing calculator. $$3^{7 x}=27$$

Solve. $$\frac{t+1}{3}-\frac{t-1}{2}=1$$

Write an equivalent expression without negative exponents. $$\frac{a^{-2}}{b^{-8}}$$

If a nonlinear system consists of equations with the following graphs, a) sketch the different ways in which the graphs can intersect. b) make a sketch in which the graphs do not intersect. c) how many possible solutions can each system have? ellipse and hyperbola

Identify each equation as an ellipse or a hyperbola. $$\frac{(x-4)^{2}}{16}+\frac{(y-1)^{2}}{9}=1$$

Identify the center and radius of each circle and graph. $$(x+1)^{2}+(y+3)^{2}=25$$

Solve the system of equations. $$\begin{aligned} x+2 y-z &=5 \\ 2 x-4 y+z &=0 \\ 3 x+2 y+2 z &=3 \end{aligned}$$

Solve the exponential equation algebraically. Then check using a graphing calculator. $$2^{x}=33$$

Solve. $$\frac{1}{2}+\frac{2}{x}=\frac{1}{3}+\frac{3}{x}$$

Write an equivalent expression without negative exponents. $$\frac{m^{-1} n^{-12}}{t^{-6}}$$

If a nonlinear system consists of equations with the following graphs, a) sketch the different ways in which the graphs can intersect. b) make a sketch in which the graphs do not intersect. c) how many possible solutions can each system have? parabola and hyperbola

Identify each equation as an ellipse or a hyperbola. $$16 x^{2}-y^{2}=16$$

Identify the center and radius of each circle and graph. $$(x-5)^{2}+(y-3)^{2}=1$$

Solve the system of equations. $$\begin{aligned} 2 x+3 y-z &=1 \\ x+2 y+5 z &=4 \\ 3 x-y-8 z &=-7 \end{aligned}$$

Solve the exponential equation algebraically. Then check using a graphing calculator. $$2^{x}=40$$

Solve. $$\frac{1}{t}+\frac{1}{2 t}+\frac{1}{3 t}=5$$

Write an equivalent expression without negative exponents. $$\frac{x^{-9} y^{-17}}{z^{-11}}$$

Identify each equation as an ellipse or a hyperbola. $$4 x^{2}+25 y^{2}=100$$

Identify the center and radius of each circle and graph. $$x^{2}+(y-5)^{2}=9$$

Solve the system of equations. $$\begin{aligned} x+2 y-z &=-8 \\ 2 x-y+z &=4 \\ 8 x+y+z &=2 \end{aligned}$$

Solve the exponential equation algebraically. Then check using a graphing calculator. $$5^{4 x-7}=125$$

Solve. $$\frac{5}{3 x+2}=\frac{3}{2 x}$$

Simplify. 23^{0}

Solve each quadratic inequality. Graph the solution set and write the solution in interval notation. $$x^{2}+6 x-7 \geq 0$$

Solve each system. $$\begin{aligned} x^{2}+4 y &=8 \\ x+2 y &=-8 \end{aligned}$$

Identify each equation as an ellipse or a hyperbola. $$\frac{x^{2}}{25}+y^{2}=1$$

Identify the center and radius of each circle and graph. $$(x+3)^{2}+y^{2}=4$$