Skip to main content
Ch. 5 - Systems of Equations and Inequalities
Blitzer - College Algebra 8th Edition
Blitzer8th EditionCollege AlgebraISBN: 9780136970514Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoBlitzer 8th EditionCh. 5 - Systems of Equations and InequalitiesProblema 17
Capitolo 6, Problema 17

Graph each inequality. (x−2)2+(y+1)2<9

Guida verificata passo dopo passo
1
Identify the inequality as representing a circle in the coordinate plane. The general form of a circle's equation is \( (x - h)^2 + (y - k)^2 = r^2 \), where \((h, k)\) is the center and \(r\) is the radius.
Compare the given inequality \( (x - 2)^2 + (y + 1)^2 < 9 \) to the general form. Here, the center is at \( (2, -1) \) and the radius \( r \) is \( \sqrt{9} = 3 \).
Since the inequality is '<' (less than), the graph represents all points inside the circle but not on the boundary. This means the circle itself is not included, so the boundary should be drawn as a dashed curve.
Plot the center point at \( (2, -1) \) on the coordinate plane. Then, using the radius 3, mark points 3 units away from the center in all directions (up, down, left, right) to help sketch the circle.
Shade the interior region of the circle to represent all points \( (x, y) \) that satisfy the inequality \( (x - 2)^2 + (y + 1)^2 < 9 \). This shaded area shows the solution set.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
6m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Graphing Circles

The inequality (x−2)² + (y+1)² < 9 represents all points inside a circle centered at (2, -1) with radius 3. Understanding how to graph circles involves identifying the center and radius from the equation and plotting the circle accordingly.
Video consigliato:
5:18
Circles in Standard Form

Inequalities and Regions

An inequality like (x−2)² + (y+1)² < 9 describes a region inside the circle, not just the boundary. Points satisfying the inequality lie strictly inside the circle, so the graph includes all interior points but excludes the circle itself.
Video consigliato:
6:19
Systems of Inequalities

Coordinate Plane and Plotting Points

Plotting the graph requires familiarity with the coordinate plane, including locating points using (x, y) coordinates. This skill helps in accurately drawing the circle's center and radius, and shading the correct region defined by the inequality.
Video consigliato:
05:10
Graphs & the Rectangular Coordinate System
Pratica correlata
Domanda del libro di testo

Solve each system in Exercises 5–18. {3(2x+y)+5z=−12(x−3y+4z)=−94(1+x)=−3(z−3y)\(\begin{cases}\) 3(2x + y) + 5z = -1 \\ 2(x - 3y + 4z) = -9 \\ 4(1 + x) = -3(z - 3y) \(\end{cases}\)

652
views
Domanda del libro di testo

Write the partial fraction decomposition of each rational expression. x/(x2 +2x -3)

703
views
Domanda del libro di testo

In Exercises 16–24, write the partial fraction decomposition of each rational expression. x/(x - 3)(x + 2)

705
views
Domanda del libro di testo

Write the partial fraction decomposition of each rational expression. 4x2+13x-9/x (x − 1)(x+3)

709
views
Domanda del libro di testo

In Exercises 5–18, solve each system by the substitution method. y = (1/3)x + 2/3 y = (5/7)x - 2

725
views
Domanda del libro di testo

In Exercises 1–18, solve each system by the substitution method. {x+y=1x2+xy−y2=−5\(\begin{cases}\) x + y = 1 \\ x^2 + xy - y^2 = -5 \(\end{cases}\)

624
views