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3 years ago

A parallelogram has consecutive vertices A (-2,0), P (0,-2) and C (2,4). Find the fourth vertex.

Mathematics

2 answers:

nordsb [41]3 years ago

8 0

Let the fourth vertex be D(a,b)
Now equate the midpoint of AC and PD.
After equating you will find x=0 and y=6

GrogVix [38]3 years ago

5 0

One way to do this is to find the equations of the lines parallel to AP and PC which pass through the points C and A respectively . Then solve the 2 equations for x and y.

equation of line parallel to AP

y - y1 = m (x - x1)
m = -(-2) / -2 = -1

point C is (2,4)

y - 4 = -1(x - 2)

y = -x + 6 equation (1)

equation of the line parallel to pc:-

slope m = 6/2 = 3

y - 0 = 3(x - (-2)

y = 3x + 6 equation (2)

solving (1) and (2):-

- x + 6 = 3x + 6
x = 0

and y = 3(0) + 6 = 6

So the fourth vertex is at (0,6)

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3 years ago

A seed company planted a floral mosaic of a national flag. The perimeter of the flag is 2,340 ft Determine the flag's width and

netineya [11]

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Step-by-step explanation:

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3 years ago

A person calls people to ask if they would like to extend their automobile insurance beyond the normal3years. The probability th

Sonbull [250]

Using the binomial distribution, it is found that there is a 0.0231 = 2.31% probability that the first person to say yes will occur with the seventh customer.

For each person, there are only two possible outcomes, either they say yes, or they say no. The probability of a person saying yes is independent of any other person, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

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

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

The parameters are:

x is the number of successes.
n is the number of trials.
p is the probability of a success on a single trial.

In this problem:

The probability that the seventh person is the first to say yes is P(X = 0) when n = 6(first six say no) multiplied by 0.37(probability the seventh say yes).
37% say yes, hence $p = 0.37$

Then:

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

$P(X = 0) = C_{6,0}.(0.37)^{0}.(0.63)^{6} = 0.0625$

$p = 0.37(0.0625) = 0.0231$

0.0231 = 2.31% probability that the first person to say yes will occur with the seventh customer.

A similar problem is given at brainly.com/question/24863377

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2 years ago

If<br>A = i +3j -2K and B=4i-2j+4k<br>Find (2A+B).(A-2B)

Marizza181 [45]

GIVEN :

a = 1/√10 ( 3i + k) and

b = 1/7 ( 2i + 3j - 6k)

TO FIND :

( 2a- b) . [ ( a x b ) x ( a + 2b)]

SOLUTION :

◆Going with the equation given,

( 2a - b) . [ ( a x b ) x ( a + 2b)]

= (2a - b) [( a×b×a) + 2(a×b)×b]

◆BAC - CAB RULE,

A×B×C = B( A.B ) - C(A.B )

= (2a- b ) [ (b (a.a ) - a (a.b ) + 2b ( a.b) -2b (a.b]

Solving further

= (2a - b )(b - 2a)

= -4a.a -b.b

=-5.

Answer:

( 2 - b) . [ ( a x b ) x ( a + 2b)] = -5

Hoped I helped

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