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Diano4ka-milaya [45]
1 year ago
5

consider the line 4x+9y=-8find the equation of the line that is perpendicular to this line and passes through the point (-2, -2)

find the equation of the line that is parallel of this line and passes through the point (-2, -2)
Mathematics
1 answer:
levacccp [35]1 year ago
8 0
\begin{gathered} \text{The equation of the line is,} \\ 4x+9y=-8 \\ 9y=-4x-8 \\ y=-\frac{4}{9}x-\frac{8}{9} \\ \text{The slope is}\Rightarrow m=-\frac{4}{9} \\ perpendicular\text{ slope}\Rightarrow m^{\prime}=\frac{9}{4} \\ 1. \\ x_1=-2,y_1=-2 \\ So,\text{ the perpendicular equation of line is} \\ y-y_1=m^{\prime}(x-x_1) \\ y+2=\frac{9}{4}(x+2) \\ 4y+8=9x+18 \\ 4y=9x+10 \\ y=\frac{9}{4}x+\frac{5}{2}(\text{Ans)} \\ 2. \\ The\text{ parallel equation is,} \\ y-y_1=m(x-x_1) \\ y+2=-\frac{4}{9}(x+2) \\ 9y+18=-4x-8 \\ 9y=-4x-26 \\ y=-\frac{4}{9}x-\frac{26}{9}(\text{Ans)} \end{gathered}

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3 years ago
La edad de juan es un año menos que la tercera parte de la edad de la madre. si dentro de 5 años, la edad de la madre sera 10 añ
koban [17]

Usando un sistema de ecuaciones, se encuentra que Juan tiene 12 años e su madre tiene 39 años.

<h3>¿Qué es un sistema de ecuaciones?</h3>

Un sistema de ecuaciones es cuando dos o más variables están relacionadas y las ecuaciones se construyen para encontrar los valores de cada variable.

En este problema, las variables son:

  • Variable x: Edad de Juan.
  • Variable y: Edad de su madre.

La edad de juan es un año menos que la tercera parte de la edad de la madre, por eso:

x = \frac{y}{3} - 1

Dentro de 5 años, la edad de la madre sera 10 años mas que el doble de juan, por eso:

y + 5 = 2(x + 5) + 10

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Como x = \frac{y}{3} - 1:

y + 5 = \frac{2y}{3} + 18

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y = 39

x = \frac{y}{3} - 1 = \frac{39}{3} - 1 = 13 - 1 = 12

Juan tiene 12 años e su madre tiene 39 años.

Puede-se aprender más a cerca de sistema de ecuaciones en brainly.com/question/20178040

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Step-by-step explanation:

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As the ratio is 9:2 we can find:

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What is the solution of the proportion 5/8=b/12
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Answer:

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Step-by-step explanation:

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