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gavmur [86]
3 years ago
13

Find an equation for the line perpendicular to 4x+12y=72 and goes through the point (-9,6)

Mathematics
1 answer:
il63 [147K]3 years ago
7 0

Answer:

Step-by-step explanation:

Given the equation

4x+12y=72

The equation of a line can written as

y=mx+c

Where m is the slope

And c is the intercept on y axis

Then, we need to write the equation given in the form of equation of a line (y=mx+c), by making y subject of the formula

4x+12y=72

12y=-4x+72

Divide through by 12

y=-4x/12 + 72/12

y=-⅓x+6

Then, comparing with equation of a line shows that

m=-⅓ and c=6

So we need to get another linen that is perpendicular to this line and passes through the point (-9,6)

The slope of the line perpendicular to another line is given as

m1=-1/m2

Then, m1=-1÷-⅓

Then, the slope of the perpendicular line is 3

Then, m=3

So apply this to equation of the line

y=mx+c

Then, y=3x+c

So to know c, we will insert the point given(-9,6), x=-9 and y=6

y=3x+c

6=3(-9)+c

6=-27+c

Then, c=6+27

c=33

Then, the equation of line becomes

y=3x+33

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Step-by-step explanation:

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The functions f(x) and g(x) are described using the following equation and table: f(x) = −6(1.05)x x g(x) −4 −9 −2 −6 0 −3 2 2 W
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Based on our examination of the y-intercepts, we can deduce that the y-intercept of function f(x) is equivalent to two times the y-intercept of function g. (x)

<h3>What is the examination of the y-intercept?</h3>

The value of the function at the point where the value of x is equal to zero is known as the y-intercept.

f(x)=-6(1.05)^x

Considering x

x=0

f(0)=-6(1.05)^0

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Therefore, the y-intercept is point (0,-6)

Generally, the equation for the function of the y-intercept of g(x) is  mathematically given as

From table

at x=0

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brainly.com/question/14180189

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3 years ago
If there are 17 green marbles in a jar of 65 marbles, what is the probability of drawing 2 green marbles at random without repla
erastovalidia [21]

Answer:

Option b) \frac{17}{260}

Step-by-step explanation:

We are given the following information in the question:

Total number of marbles = 65

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We have to find the probability of drawing 2 green marbles at random without replacement.

Formula:

Probability = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}

\text{P(Drawing 2 green marbles at random without replacement)} = \\\text{Probability of drawing }1^{st} \text{ green marble}\times \text{Probability of drawing }2^{nd} \text{ green marble}

\text{Probability of drawing }1^{st} \text{ green marble} = \displaystyle\frac{17}{65}\\\\\text{Probability of drawing }2^{nd} \text{ green marble} = \displaystyle\frac{16}{64}

\text{P(Drawing 2 green marbles at random without replacement)} =\displaystyle\frac{17}{65}\times \frac{16}{64}=\frac{17}{260}

Option b) \frac{17}{260}

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