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4 years ago

The line parallel to x-3y=-12 that passes through (-3,4)

2 answers:

4 0

X-3y=12
3y=x-12
y=1/3x-4
parallel means same gradient, which is 1/3.
Use formula y-y1=m(x-x1), m=gradient and y1 is y coordinate of point and x1 is x coordinate of point.
y-4=1/3[x-(-3)]
y-4=x/3+1
y=x/3+5

romanna [79]4 years ago

4 0

Answer:

-3y = -x - 12

3y = x + 12

y = (1/3)x + 4

y - 4 = (1/3)(x + 3)

y - 4 = (1/3)x + 1

y= (1/3)x+5

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Solve 1-12 or any of them please.

ladessa [460]

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2. y = -x + 4
3. y = 1/3x +1
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5. y = 1/7x + 2
6. y = -4x + 2.75
7. y = 3x + 5
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3 0

4 years ago

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Solve the system of equations by the addition method.<br> 1 - 3x = -5y - 8<br> 6x<br> 3y = -5

Advocard [28]

$-3x = -5y -8~~~....(i) \\\\6x -3y = -5 ~~......(ii)\\\\\text{Multiply equation (i) by 2 and do (i) + (ii):}\\\\2 \cdot (-3x) + 6x -3y = 2(-5y-8) + (-5)\\\\\implies -6x +6x -3y = -10y -16 -5 \\\\\implies -3y = -10y -21\\\\\implies -3y +10y =-21\\\\\implies 7y = -21 \\\\\implies y = -\dfrac{21} 7 = -3\\\\\text{Substitute}~y =-3~ \text{in equation (ii):} \\\\6x - 3(-3) = -5\\\\\implies 6x +9 = -5\\\\\implies 6x = -5 -9 = -14\\\\\implies x = -\dfrac{14}6 = - \dfrac{7}3\\$

$\text{Hence}~ (x,y) = \left(-\dfrac 73, -3 \right)$

3 0

3 years ago

Find the distance between the point (3, 5) and a line with the equation 5 x - 3 y + 10 = 0

timama [110]

The distance between the point (3, 5) and a line with the equation 5x – 3y + 10 = 0 will be 10 / √(34) units.

<h3>What is the distance between a point and a line?</h3>

Let (x₁, y₁) be the point and ax + by + c = 0 be the line.

Then the distance between a point and a line will be

$\rm d = \dfrac{|ax_1 + by_1 + c|}{\sqrt{a^2 + b^2}}$

The point (3, 5) and a line with the equation 5x – 3y + 10 = 0.

Then the distance between them will be

$\rm d = \dfrac{|5 *3 - 3 *5 + 10|}{\sqrt{5^2 + (-3)^2}}\\d = \dfrac{10 }{\sqrt{34}} \ units$

Learn more about the distance between a point and a line here;

brainly.com/question/11558698

#SPJ1

7 0

2 years ago

Astronomers treat the number of stars in a given volume of space as a Poisson random variable. The density in the Milky Way Gala

umka21 [38]

Answer:

a) 0.264

b) 48 cubit light-years

Step-by-step explanation:

For calculating a) What is the probability of 3 or more stars in 16 cubic light years?

λ= 1 star/16 cubic light-years

t= measure t in units of 16 cubic light years.

E(Y) = λ t = (1/16)(16) = 1 star

P(X>=2) = 1 - P(X<2)

= 1 - [e^-1 + (e^-1)(1)/1!]

= 0.264

P(X≥1) = 1 - P(X=0)

= 1 - e^-μ

0.95 = 1 - e^-μ

e^-μ = 1 - 0.95

e^-μ = 0.05

ln(e^-μ) = ln(0.05)

-μ = -3

μ = 3

Therefore 3 x 16 = 48 cubic light years of space

4 0

4 years ago

At which root does the graph of f(x) = (x – 5)3(x + 2)2 touch the x axis?

LuckyWell [14K]

We have that
f(x) = (x – 5)³(x + 2)²

we know that
<span>the roots can touch or cross the x axis

</span>The way you can tell if the graph is going to cross the x-axis or just touch the x-axis is by looking at the power of the factor.

(x - 5)³ has a power of 3 which is an ODD number. An ODD power means that the graph will cross through the x-axis.

(x + 2)² has a power of 2 which is an EVEN number. An EVEN power means that the graph will touch the x-axis.

therefore

the answer is
<span>the graph of f(x) touch the x axis for the root x=-2
</span>
see the attached figure

5 0

3 years ago

Read 2 more answers