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3 years ago

Points A(-2, 4), B(1, 3), C(4, -1) and D form a parallelogram. What are the coordinates of D?

2 answers:

8 0

Let point A(-2,4) = A (X1,Y1)
point B( 1,3 )= B (X2,Y2)
point C(4,-1) = C (X3,Y3)
and point D(?, ?) = D (X4,Y4) We have to find this point

To find X4 we have to use the formula:
X2-X1=X3-X4

Now just plug in the numbers that correspond to the letters provided:
(1)-(-2)=(4)-(X4) ----> we don't know what X4 is yet, so we have to solve for it!
1+2=4-X4
3=4-X4
3-4=-X4
-1=-X4 divide both sides by -1
X4=1

Now we have to find Y4 using this formula:
Y2-Y1=Y3-Y4

Therefore,
(3)-(4)=(-1)-(Y4)
-1=-1-Y4
-1+1=-Y4
0=-Y4
So,
Y4=0

Now we have found the coordinates of the point D, which is (1,0)

Hope this helped!

Basile [38]3 years ago

3 0

Answer: d- (1,0)

Step-by-step explanation:

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3 years ago

A marketing researcher wants to find a 96% confidence interval for the mean amount those visitors spend per person per day while

ki77a [65]

Answer:

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Step-by-step explanation:

Notation

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$\mu$ population mean (variable of interest)

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n represent the sample size

ME = 4 the margin of error desired

Solution to the problem

When we create a confidence interval for the mean the margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (a)

And on this case we have that ME =4 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 96% of confidence interval now can be founded using the normal distribution. The significance is $\alpha=1-0.96 =0.04$ . And in excel we can use this formula to find it:"=-NORM.INV(0.02;0;1)", and we got $z_{\alpha/2}=2.054$ , replacing into formula (b) we got:

$n=(\frac{2.054(12)}{4})^2 =37.97 \approx 38$

So then the minimum sample to ensure the condition given is n= 38

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3 years ago