Book edition 6th

Author(s) Sullivan

Pages 1200 pages

ISBN 9780321795465

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Short Answer

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$y = \sqrt{4 - x^{2}}; y = 2 x + 4$

he graph of the system of equations $y = \sqrt{4 - x^{2}}; y = 2 x + 4$ is:

The points of intersection are $(- \frac{6}{5}, \frac{8}{5}), (- 2, 0)$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given

The system of non-linear equation:

$y = \sqrt{4 - x^{2}}; y = 2 x + 4$

To graph the equation and to find the point of intersection.

Step 2. Graph the equations

Graph the equations in the same plane.

Step 3. To find the point of intersection.

Equate both the equations,

$\sqrt{4 - x^{2}} = 2 x + 4$

Squaring on both sides, we get,

$4 - x^{2} = {(2 x + 4)}^{2} 4 - x^{2} = 4 x^{2} + 16 x + 16 5 x^{2} + 16 x + 12 = 0$

Step 4. Solve the equations

$5 x^{2} + 16 x + 12 = 0 (5 x + 6) (x + 2) = 0 x = - \frac{6}{5}, - 2$

The value of $x$ is $- \frac{6}{5}, - 2$

Step 5. Find y

When

$x = - \frac{6}{5}, y = 2 x + 4 = 2 (- \frac{6}{5}) + 4 = - \frac{12}{5} + 4 = \frac{8}{5}$

When $x = - 2,$

$y = 2 x + 4 = 2 (- 2) + 4 = 0$

The point of intersections are $(- \frac{6}{5}, \frac{8}{5}), (- 2, 0)$

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Precalculus Enhanced with Graphing Utilities

Answers without the blur.

Short Answer

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$y = \sqrt{4 - x^{2}}; y = 2 x + 4$

Step by Step Solution

Step 1. Given

Step 2. Graph the equations

Step 3. To find the point of intersection.

Step 4. Solve the equations

Step 5. Find y

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Precalculus Enhanced with Graphing Utilities

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Short Answer

In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.y=4-x2;y=2x+4

Step by Step Solution

Step 1. Given

Step 2. Graph the equations

Step 3. To find the point of intersection.

Step 4. Solve the equations

Step 5. Find y

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In Problems 5–24, graph each equation of the system. Then solve the system to find the points of intersection.
$y = \sqrt{4 - x^{2}}; y = 2 x + 4$