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HACTEHA [7]
3 years ago
9

What is the equation of a line perpendicular to y= 3/4x +12 that passes through (12, 3)

Mathematics
1 answer:
ycow [4]3 years ago
4 0

Answer:

y=-4/3x-9

 

=

−

4

3

x

−

9

Step-by-step explanation:

First we need to get the slope of the perpendicular line

The slope of a perpendicular line is equal to the negative inverse of the slope of the given line

y

=

m

x

+

b

y

=

3

4

x

−

2

⇒

m

=

3

4

m

'

=

−

1

m

⇒

m

'

=

−

1

3

4

⇒

m

'

=

−

4

3

Now that we have the slope, we need to find the y-intercept.

To find the y-intercept, we need to plug-in values of  

x

and  

y

that the line passes through

y

'

=

m

'

x

'

+

b

⇒

y

'

=

−

4

3

x

'

+

b

⇒

7

=

−

4

3

(

−

12

)

+

b

⇒

7

=

16

+

b

⇒

b

=

−

9

Therefore, the equation of the line is

y

=

−

4

3

x

−

9

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10 normal six sided dice are thrown.Find the probability of obtaining at least 8 failuresif a success is 5 or 6.
erastova [34]

Answer:

0.2992 = 29.92% probability of obtaining at least 8 failures.

Step-by-step explanation:

For each dice, there are only two possible outcomes. Either a failure is obtained, or a success is obtained. Trials are independent, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

A success is 5 or 6.

A dice has 6 sides, numbered 1 to 6. Since a success is 5 or 6, the other 4 numbers are failures, and the probability of failure is:

p = \frac{4}{6} = 0.6667

10 normal six sided dice are thrown.

This means that n = 10

Find the probability of obtaining at least 8 failures.

This is:

P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)

So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 8) = C_{10,8}.(0.6667)^{8}.(0.3333)^{2} = 0.1951

P(X = 9) = C_{10,9}.(0.6667)^{9}.(0.3333)^{1} = 0.0867

P(X = 10) = C_{10,10}.(0.6667)^{10}.(0.3333)^{0} = 0.0174

Then

P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.1951 + 0.0867 + 0.0174 = 0.2992

0.2992 = 29.92% probability of obtaining at least 8 failures.

8 0
3 years ago
2. Write the equation of a circle that has a diameter of 12 units if its center is at (4,7).
ahrayia [7]

Answer:

The Answer is B

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here diameter = 12, thus radius = 12 ÷ 2 = 6 and (h, k) = (2.5, - 3.5), thus

(x - 2.5)² + (y - (- 3.5))² = 6², that is

(x - 2.5)² + (y + 3.5)² = 36 ← equation of circle

5 0
3 years ago
What is the slope of -9
maksim [4K]

Answer:

Step-by-step explanation:

the slope of -9 is -9/1

5 0
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Mazyrski [523]
The answer to your question is c the rug will cover 14 feet of the floor
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