Unit 7, Lesson 9
Modelos matemáticos a partir de sistemas de desigualdades en dos variables
Matemáticas integradas 1
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El organizador de una conferencia necesita al menos 200 libretas para el evento y tiene un presupuesto de \$160 para las libretas. En una tienda se venden libretas en paquetes de 24 y paquetes de 6.
Este sistema de desigualdades representa las restricciones: \(\begin{cases} 24x+6y\geq200\\16x + 5.40y\leq160 \end{cases}\)
Esta es una gráfica incompleta de las desigualdades del sistema, que solo muestra las rectas frontera de las regiones solución.
¿Cuál es la recta frontera de la segunda desigualdad?
A system of inequalities graphed on a coordinate plane, origin O. Horizontal axis, number of large packages, scale from 0 to 12, by 2’s. Vertical axis, number of small packages, scale from 0 to 40, by 4’s. First line starts on vertical axis at approximately 33, goes through approximately 4 comma 18 and ends on the horizontal axis at about 8. Second line starts on vertical axis at approximately 29, goes through approximately 4 comma 18 and ends on the horizontal axis at about 10.
Completa la gráfica para mostrar el conjunto solución del sistema de desigualdades.
Un estilista cobra \$15 por un corte de cabello y \$30 por una coloración de cabello. Un corte de cabello tarda en promedio 30 minutos, mientras que una coloración tarda 2 horas. El estilista trabaja hasta 8 horas en un día y necesita recolectar como mínimo \$150 dólares al día para pagar sus gastos.
Grafica las desigualdades y muestra el conjunto solución.
¿Cuál gráfica muestra la solución de este sistema? \(\begin{cases} y > 3x + 2 \\ \text-4x+3y \leq12 \end{cases}\)
Graph of 2 intersecting lines, origin O. Scale -10 to 8 on both axes. Lines start in lower left and extend to upper right. Solid line passes through negative 6 comma negative 4 and 0 comma 4. Dotted line passes through negative 2 comma negative 4 and 0 comma 2. They intersect around 1 comma 6. The area to the right of the intersection point and below both lines is shaded.
Graph of 2 intersecting lines, origin O. Scale -10 to 8 on both axes. Lines start in lower left and extend to upper right. Solid line passes through negative 6 comma negative 4 and 0 comma 4. Dotted line passes through negative 2 comma negative 4 and 0 comma 2. They intersect around 1 comma 6. The area between the lines above their intersection point is shaded.
Two inequalities graphed on a coordinate plane, origin O, scale from negative 10 to 10 on both axes. The dashed line passes through negative 4 comma negative 10, 0 comma 2, and 2 comma 8. The area below the dashed line starting at the intersection point is shaded. The solid lines passes through negative 6 comma negative 4, 0 comma 4, and 3 comma 8. The area below the solid line until the intersection point is shaded.
Two inequalities graphed on a coordinate plane, origin O, scale from negative 10 to 10 on both axes. The dashed line passes through negative 4 comma negative 10, 0 comma 2, and 2 comma 8. The area below the dashed line is shaded. The solid lines passes through negative 6 comma negative 4, 0 comma 4, and 3 comma 8. The area above the solid line is shaded. The area between and above the point of intersection is not shaded.
Empareja cada desigualdad con la gráfica de su solución.
Gráfica A
Gráfica C
Gráfica D
Gráfica E
\(2x - 5y \geq 20\)
\(5x + 2y \geq 20\)
\(4x - 10y \leq 20\)
\(4x - 5y \geq 20\)
\(2x + 10y \leq 20\)