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Lesechka [4]
3 years ago
10

Which line is perpendicular to the line y=-1/3x-2 and passes through point (1,4)

Mathematics
2 answers:
xxMikexx [17]3 years ago
4 0

Answer:

Option 3)  y = 3x+1

Step-by-step explanation:

<u><em>Given equation is:</em></u>

y = -\frac{1}{3} x -2

Perpendicular => <u><em>It will have a slope of negative reciprocal to this slope</em></u>

So the  ⊥ line has a slope = m =  3

Now,

Point = (x,y) = (1,4)

So, x = 1, y = 4

<u><em>Putting this in slope intercept form to get b</em></u>

=> y = mx+b

=> 4 = (3)(1) + b

=> b = 4-3

=> b = 1

<u><em>Now, Putting m and b in the slope intercept form to get the required equation:</em></u>

=> y = 3x+1

murzikaleks [220]3 years ago
4 0

Answer:

<h2>y=3x+1</h2>

Option C is the correct option.

Given that,

y =  -  \frac{1}{3} x - 2

Which is in the standard form

y = mx + c

where, m= slope

c=y- intercept

m1 =  -  \frac{1}{3}

Slope of perpendicular lines is the product of slope is -1.

m1.m2 =  - 1 \\  -  \frac{1}{3}  \times m2 =  - 1 \\ m2 =  \frac{ - 1}{ \frac{ - 1}{3} }  \\ m2 = 3

Then, y=3x+c------> equation (i)

(X,y)=(1,4) ---- given

c=4-3x

c=4-3(1)

c=4-3

c=1

Put this in equation (i) we get,

<h2>y=3x+1</h2>

This is the required equation of the line.

Hope this helps...

Good luck on your assignment..

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The sum of w and 54 is equal to s. Let s = 72. Which equation can be used to find the value of w? A. w – 54 = 72 B. w – 72 = 54
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W + 54 = s

w + 54 = 72

Answer: C

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7 0
3 years ago
Which equation best represents the situation?
Gennadij [26K]
It is A because
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The volume of a spherical sculpture is 256 ft³. Rhianna wants to estimate the surface area of the sculpture. To do the estimate,
Brrunno [24]

Answer:

192 ft^2

Step-by-step explanation:

Given that

Volume of spherical sculpture = 256 ft³

\pi is used as 3.

To find:

Surface area of sculpture = ?

Solution:

First of all, let us learn about the formula for Volume and Surface Area of Sphere:

1. Volume =\frac{4}{3}\pi r^3

2. Surface\ Area = 4\pi r^2

Given volume is 256 ft³.

256 = \dfrac{4}{3}\pi r^3\\\Rightarrow 256 = \dfrac{4}{3}\times 3 r^3\\\Rightarrow 256 = 4 r^3\\\Rightarrow r^3=64\\\Rightarrow \bold{r = 4\ ft}

Now, let us put r = 4 in the formula of Surface Area to find the value of Surface Area:

Surface\ Area = 4\pi 4^2 = 4 \times 3 \times 16 = \bold{192\ ft^2}

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3 0
3 years ago
Acertijo.
Cerrena [4.2K]

La edad de cada uno de los integrantes del acertijo es:

  • <u>Luisa = 3 años </u>
  • <u>Juan = 6 años </u>
  • <u>Carmen = 8 años</u>

<em>Cálculo por medio de ecuaciones y el </em><em>método de igualación</em>.

Haciendo uso de la información brindada en el ejercicio, se procede a formular variables con las cuales se calcularán las ecuaciones, por lo tanto:

  • <em>X = Edad de Luisa</em>
  • <em>Y = Edad de Juan</em>
  • <em>Z = Edad de Carmen</em>

Con el enunciado: <em>"Luisa es 3 años más joven que su hermano Juan"</em> se crea la primera ecuación:

  • 1. Y = X + 3

Con el enunciado: <em>"Su hermana Carmen es 2 años mayor que Juan"</em>, se crea la segunda ecuación:

  • 2. Z = Y + 2

Y con el enunciado: <em>"Juan tiene el doble de edad que Luisa"</em>, se crea la tercera ecuación:

  • 3. X = \frac{Y}{2}

Ahora, utilizando el método de igualación, se reemplaza la <em>tercera ecuación en la primera</em>:

  • Y = X + 3
  • Y = (\frac{Y}{2}) + 3

Y se procede a sumar:

  • Y = (\frac{Y}{2}) + 3
  • Y = \frac{Y+6}{2}

El dividendo se pasa al otro lado de la igualdad a multiplicar:

  • 2Y = Y + 6

Y la variable "Y" que está sumando, se pasa al otro lado de la igualdad a restar:

  • 2Y - Y = 6
  • <u>Y = 6</u>

Con el valor de Y (edad de Juan) <em>se calcula X con la tercera ecuación</em>:

  • X = \frac{Y}{2}
  • X = \frac{6}{2}
  • <u>X = 3</u>

Una vez calculado el valor de X (edad de Luisa), se procede a <em>calcular el valor de Z con la segunda ecuación</em>:

  • Z = Y + 2
  • Z = 6 + 2
  • <u>Z = 8</u>

Por lo tanto, se calcula que <u>la edad de Luisa es 3 años, la edad de Juan es 6 años y la edad de Carmen es 8 años</u>.

Más información sobre ecuaciones:

brainly.com/question/15415929?referrer=searchResults

8 0
3 years ago
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