Exam 11: Nonlinear Functions, Conic Sections, and Nonlinear Systems

Solve the problem by using a nonlinear system. -The area of a rectangular rug is $252 \mathrm{ft}^{2}$ and its perimeter is 64 feet. Find the dimensions of the rug.

(Multiple Choice)

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Question 81

Evaluate the expression. -[[-18]]

(Multiple Choice)

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Question 82

Describe the graph of the solution set of the following inequality: $x<-y^{2}-8$

(Essay)

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Question 83

Graph the inequality. - $y^2-16 \leq -4x^2$ $Graph the inequality. - y^2-16 \leq -4x^2$

(Multiple Choice)

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Question 84

Graph the system of inequalities. - $3x - 2y \leq 6$ $x - 1 \geq 0$ $Graph the system of inequalities. - 3x - 2y \leq 6 x - 1 \geq 0$

(Multiple Choice)

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Question 85

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - $y^{2}=128-x^{2}$

(Multiple Choice)

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Question 86

Choose the inequality that matches the graph. -

(Multiple Choice)

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Question 87

The graph of the equation $\frac{x}{16}+\frac{y}{25}=1$ is an ellipse.

(True/False)

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Question 88

The circle with equation $(x+7)^{2}+(y+5)^{2}=49$ has center at $(7,5)$ .

(True/False)

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Question 89

Graph the inequality. - $25 y^{2}-16 x^{2} \geq 400$ $Graph the inequality. - 25 y^{2}-16 x^{2} \geq 400$

(Multiple Choice)

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Question 90

The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one of the solutions. Find the other solution. - $The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one of the solutions. Find the other solution. - y=x^{2}+2 \mathrm{x}-\mathrm{y}=-4$ $y=x^{2}+2$ $\mathrm{x}-\mathrm{y}=-4$

(Multiple Choice)

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Question 91

Graph. - $25 x^{2}+49 y^{2}=1225$ $Graph. - 25 x^{2}+49 y^{2}=1225$

(Multiple Choice)

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Question 92

The hyperbola shown in the calculator-generated graph was graphed in function mode with a square viewing window. What are the two functions $y_{1}$ and $y_{2}$ that were used to obtain the graph whose equation is given? - $\frac{y^{2}}{25}-\frac{x^{2}}{9}=1$ $The hyperbola shown in the calculator-generated graph was graphed in function mode with a square viewing window. What are the two functions y_{1} and y_{2} that were used to obtain the graph whose equation is given? - \frac{y^{2}}{25}-\frac{x^{2}}{9}=1$

(Multiple Choice)

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Question 93

Graph the hyperbola. - $\frac{x^{2}}{9}-\frac{y^{2}}{25}=1$ $Graph the hyperbola. - \frac{x^{2}}{9}-\frac{y^{2}}{25}=1$

(Multiple Choice)

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Question 94

Choose the equation that matches the graph. -

(Multiple Choice)

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Question 95

Graph the function. Give the domain and range. - $f(x)=|x-6|-5$

(Multiple Choice)

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Question 96

Graph the circle. - $x^{2}+y^{2}+2 x+8 y+8=0$ $Graph the circle. - x^{2}+y^{2}+2 x+8 y+8=0$

(Multiple Choice)

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Question 97

The circle with equation $x^{2}+y^{2}=25$ has center at $(5,5)$ .

(True/False)

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Question 98

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $x^{2}+4 x y+2 y^{2}=1$ $x^{2}-4 x y-2 y^{2}=1$

(Multiple Choice)

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Question 99

Describe the graph of the solution set of the following inequality: $y>-x^{2}+9$

(Essay)

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Question 100

Showing 81 - 100 of 233

Solve the problem by using a nonlinear system. -The area of a rectangular rug is $252 \mathrm{ft}^{2}$ and its perimeter is 64 feet. Find the dimensions of the rug.

Evaluate the expression. -[[-18]]

Describe the graph of the solution set of the following inequality: $x<-y^{2}-8$

Graph the inequality. - $y^2-16 \leq -4x^2$ $Graph the inequality. - y^2-16 \leq -4x^2$

Graph the system of inequalities. - $3x - 2y \leq 6$ $x - 1 \geq 0$ $Graph the system of inequalities. - 3x - 2y \leq 6 x - 1 \geq 0$

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - $y^{2}=128-x^{2}$

Choose the inequality that matches the graph. -

The graph of the equation $\frac{x}{16}+\frac{y}{25}=1$ is an ellipse.

The circle with equation $(x+7)^{2}+(y+5)^{2}=49$ has center at $(7,5)$ .

Graph the inequality. - $25 y^{2}-16 x^{2} \geq 400$ $Graph the inequality. - 25 y^{2}-16 x^{2} \geq 400$

Graph. - $25 x^{2}+49 y^{2}=1225$ $Graph. - 25 x^{2}+49 y^{2}=1225$

Graph the hyperbola. - $\frac{x^{2}}{9}-\frac{y^{2}}{25}=1$ $Graph the hyperbola. - \frac{x^{2}}{9}-\frac{y^{2}}{25}=1$

Choose the equation that matches the graph. -

Graph the function. Give the domain and range. - $f(x)=|x-6|-5$

Graph the circle. - $x^{2}+y^{2}+2 x+8 y+8=0$ $Graph the circle. - x^{2}+y^{2}+2 x+8 y+8=0$

The circle with equation $x^{2}+y^{2}=25$ has center at $(5,5)$ .

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $x^{2}+4 x y+2 y^{2}=1$ $x^{2}-4 x y-2 y^{2}=1$

Describe the graph of the solution set of the following inequality: $y>-x^{2}+9$

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Further Topics in Algebra

Appendices

Filters

Exam 11: Nonlinear Functions, Conic Sections, and Nonlinear Systems

Solve the problem by using a nonlinear system. -The area of a rectangular rug is 252ft2252 \mathrm{ft}^{2}252ft2 and its perimeter is 64 feet. Find the dimensions of the rug.

Evaluate the expression. -[[-18]]

Describe the graph of the solution set of the following inequality: x<−y2−8x<-y^{2}-8x<−y2−8

Graph the inequality. - y2−16≤−4x2y^2-16 \leq -4x^2y2−16≤−4x2

Graph the system of inequalities. - 3x−2y≤63x - 2y \leq 63x−2y≤6 x−1≥0x - 1 \geq 0x−1≥0

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - y2=128−x2y^{2}=128-x^{2}y2=128−x2

Choose the inequality that matches the graph. -

The graph of the equation x16+y25=1\frac{x}{16}+\frac{y}{25}=116x​+25y​=1 is an ellipse.

The circle with equation (x+7)2+(y+5)2=49(x+7)^{2}+(y+5)^{2}=49(x+7)2+(y+5)2=49 has center at (7,5)(7,5)(7,5) .

Graph the inequality. - 25y2−16x2≥40025 y^{2}-16 x^{2} \geq 40025y2−16x2≥400

The graphing calculator screen shows the graphs of the two given functions, and the display gives the coordinates of one of the solutions. Find the other solution. - y=x2+2y=x^{2}+2y=x2+2 x−y=−4\mathrm{x}-\mathrm{y}=-4x−y=−4

Graph. - 25x2+49y2=122525 x^{2}+49 y^{2}=122525x2+49y2=1225

The hyperbola shown in the calculator-generated graph was graphed in function mode with a square viewing window. What are the two functions y1y_{1}y1​ and y2y_{2}y2​ that were used to obtain the graph whose equation is given? - y225−x29=1\frac{y^{2}}{25}-\frac{x^{2}}{9}=125y2​−9x2​=1

Graph the hyperbola. - x29−y225=1\frac{x^{2}}{9}-\frac{y^{2}}{25}=19x2​−25y2​=1

Choose the equation that matches the graph. -

Graph the function. Give the domain and range. - f(x)=∣x−6∣−5f(x)=|x-6|-5f(x)=∣x−6∣−5

Graph the circle. - x2+y2+2x+8y+8=0x^{2}+y^{2}+2 x+8 y+8=0x2+y2+2x+8y+8=0

The circle with equation x2+y2=25x^{2}+y^{2}=25x2+y2=25 has center at (5,5)(5,5)(5,5) .

Solve the system by the elimination method or a combination of the elimination and substitution methods. - x2+4xy+2y2=1x^{2}+4 x y+2 y^{2}=1x2+4xy+2y2=1 x2−4xy−2y2=1x^{2}-4 x y-2 y^{2}=1x2−4xy−2y2=1

Describe the graph of the solution set of the following inequality: y>−x2+9y>-x^{2}+9y>−x2+9

Review of the Real Number System

Linear Equations, Inequalities, and Applications

Linear Equations, Graphs, and Functions

Systems of Linear Equations

Exponents, Polynomials, and Polynomial Functions

Factoring

Rational Expressions and Functions

Roots, Radicals, and Root Functions

Quadratic Equations, Inequalities, and Functions

Inverse, Exponential, and Logarithmic Functions

Further Topics in Algebra

Appendices

Filters

Solve the problem by using a nonlinear system. -The area of a rectangular rug is $252 \mathrm{ft}^{2}$ and its perimeter is 64 feet. Find the dimensions of the rug.

Describe the graph of the solution set of the following inequality: $x<-y^{2}-8$

Graph the inequality. - $y^2-16 \leq -4x^2$ $Graph the inequality. - y^2-16 \leq -4x^2$

Graph the system of inequalities. - $3x - 2y \leq 6$ $x - 1 \geq 0$ $Graph the system of inequalities. - 3x - 2y \leq 6 x - 1 \geq 0$

Identify the graph of the equation as a parabola, hyperbola, ellipse, or circle. - $y^{2}=128-x^{2}$

The graph of the equation $\frac{x}{16}+\frac{y}{25}=1$ is an ellipse.

The circle with equation $(x+7)^{2}+(y+5)^{2}=49$ has center at $(7,5)$ .

Graph the inequality. - $25 y^{2}-16 x^{2} \geq 400$ $Graph the inequality. - 25 y^{2}-16 x^{2} \geq 400$

Graph. - $25 x^{2}+49 y^{2}=1225$ $Graph. - 25 x^{2}+49 y^{2}=1225$

Graph the hyperbola. - $\frac{x^{2}}{9}-\frac{y^{2}}{25}=1$ $Graph the hyperbola. - \frac{x^{2}}{9}-\frac{y^{2}}{25}=1$

Graph the function. Give the domain and range. - $f(x)=|x-6|-5$

Graph the circle. - $x^{2}+y^{2}+2 x+8 y+8=0$ $Graph the circle. - x^{2}+y^{2}+2 x+8 y+8=0$

The circle with equation $x^{2}+y^{2}=25$ has center at $(5,5)$ .

Solve the system by the elimination method or a combination of the elimination and substitution methods. - $x^{2}+4 x y+2 y^{2}=1$ $x^{2}-4 x y-2 y^{2}=1$

Describe the graph of the solution set of the following inequality: $y>-x^{2}+9$