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2 years ago

Find the distance between Line L and Point P if Line L contains the points

Mathematics

1 answer:

svet-max [94.6K]2 years ago

3 0

Answer:

(b) 4.2

Step-by-step explanation:

The distance from a point to a line can be found using the formula. To use it, we need the equation of the line in general form.

We notice that the coordinates of the given points have the same y/x = 2/3 ratio. This means they lie on the line y = 2/3x. The equation for that line, written in general form is ...

y = 2/3x

3y = 2x

2x -3y = 0 . . . . . . general form equation for the line through the points.

The formula for the distance from (x, y) to the line ax+by+c=0 is ...

d = |ax +by +c|/√(a²+b²)

The distance from (x, y) to our line is given by the formula ...

d = |2x -3y|/√(2² +(-3)²)

d = |2x -3y|/√13

For point P(9, 11), the distance to the line is ...

d = |2·9 -3·11|/√13 = |18 -33|/√13 = 15/√13 ≈ 4.2

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How do I confirm that f and g are inverses?

Anestetic [448]

Answer:

see explanation

Step-by-step explanation:

To show f and g are inverses we require to show that

f(g(x)) = x and g(f(x)) = x

f(g(x))

= f(6x - 4)

= $\frac{6x-4+4}{6}$ = $\frac{6x}{6}$ = x

-----------------------------------------------------------------------------

g(f(x))

= g( $\frac{x+4}{6}$ )

= ( 6 × $\frac{x+4}{6}$ ) - 4

= x + 4 - 4 = x

-------------------------------------------------

Hence f and g are inverses

4 0

3 years ago

Please help solve 6x < 42

tensa zangetsu [6.8K]

6x<42

Divide 6 by both sides

x<7

7 0

3 years ago

A paint can has a radius of 4 inches and a height of 15 inches. What is the volume of the paint can? Round to the nearest tenth.

Hunter-Best [27]

Answer:

753.6

Step-by-step explanation:

3.14x4²x15

$\pi$ r^2x15

3 0

3 years ago

Read 2 more answers

According to a 2010 study conducted by the Toronto-based social media analytics firm Sysomos, 71% of all tweets get no reaction.

klemol [59]

Answer:

a) the expected number of tweets with no reaction is 71 tweets

b) the variance is 20.59 tweets² ( ≈ 21 tweets )and the standard deviation is

4.537 tweets (≈ 5 tweets)

Step-by-step explanation:

we can use the binomial probability distribution

P(x, N, p ) = N!/[(N-x)!x!] * p^x * (1-p)^(N-x)

where

x = number of successful events

N = population total

p = probability for success for every individual and independent event

P = probability for x successful events

in our case p = 71% = 71/100 (probability of a tweet without reaction) , N = 100 tweets

a) the expected number of tweets

E(x) = N* p = 100 tweets * 71/100 = 71 tweets

b) the variance is

V(x) = N * p * (1-p)

V = 100 * 71/100 * (1-71/100) = 71* 29/100 = 20.59 tweets² ( units of variance are [N²] )

the standard deviation is

s = √V = √20.59 tweets² = 4.537 tweets

6 0

3 years ago

If the perimeter of a circular ground is 308 M find its radius

crimeas [40]

Answer:

Correct option is

49m

The circumference of a circular field is 308m

Therefore, 2πr=308

⇒r=

2×22

308×7

⇒r=49m

Step-by-step explanation:

here you go

3 0

2 years ago

Read 2 more answers