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8090 [49]
3 years ago
10

A rectangle is a quadrilateral with four right angles and congruent diagonals. To prove that the points A(-4, 52), B(3, 92), C(4

, 1), D(-3, -1) graphed on the coordinate plane form a rectangle, Janet calculated the diagonals of the quadrilateral in order to show congruence. What is the length of diagonal AC?
Select one:
A. √2474
B. 8.0
C. √66
D. √2654
Mathematics
1 answer:
solong [7]3 years ago
7 0

Answer:

D. \sqrt {2665}

Step-by-step explanation:

We have been given the points A (-4, 52), B (3, 92), C (4, 1) and D (-3, -1).

Length of the diagonal AC can be calculated from the distance between two points formula or we can also use Pythagoras theorem to calculate the length of the diagonal. But to calculate the length of the diagonal from pythagoras theorem we need to calculate the length of the sides AB and BC, therefore, we will use distance formula to calculate the length of diagonal AC, directly.

Co-ordinates of point A is (-4, 52) and C is (4, 1), using the distance formula we get,

d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}

d=\sqrt{(1-52)^2+(4-(-4))^2}

d=\sqrt{8^2+(-51)^2}

d= \sqrt{64+2601}

d=\sqrt{2665}

Therefore, the length of diagonal AC is \sqrt{2665}, the closest option is option D.

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100?

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4 0
3 years ago
It is said that sufferers of a cold virus experience symptoms for 7 days. However, the amount of time is actually a normally dis
AlexFokin [52]

Answer:

a) 0.18% of cold sufferers experience fewer than 4 days of symptoms

b) 64.40% of cold sufferers experience symptoms for between 7 and 10 days.

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 7.5, \sigma = 1.2

a. What proportion of cold sufferers experience fewer than 4 days of symptoms?

This is the pvalue of Z when X = 4. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{4 - 7.5}{1.2}

Z = -2.92

Z = -2.92 has a pvalue of 0.0018.

So 0.18% of cold sufferers experience fewer than 4 days of symptoms.

b. What proportion of cold sufferers experience symptoms for between 7 and 10 days?

This is the pvalue of Z when X = 10 subtracted by the pvalue of Z when X = 7. So

X = 10

Z = \frac{X - \mu}{\sigma}

Z = \frac{10 - 7.5}{1.2}

Z = 2.08

Z = 2.08 has a pvalue of 0.9812.

X = 7

Z = \frac{X - \mu}{\sigma}

Z = \frac{7 - 7.5}{1.2}

Z = -0.42

Z = -0.42 has a pvalue of 0.3372.

So 0.9812 - 0.3372 = 0.644 = 64.40% of cold sufferers experience symptoms for between 7 and 10 days.

8 0
3 years ago
AM I RIGHT??????????
Delicious77 [7]
I’m pretty sure it’s 13. Def not 10
4 0
3 years ago
Read 2 more answers
Is the ratio $81 in 9 hours equivalent to $63 in 7 hours
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Yes they are equivalent because their ratio is 9
81/9= 9
63/7=9
3 0
3 years ago
If the ratio of the purple flowers to black flowers is 4 to 8 and there are a total of 108 flowers how many of the flowers are p
FinnZ [79.3K]
Purple flowers: black flowers = 4:8 = 108

4 + 8 = 12

108 / 12 = 9. 

9 x 4 = 36. 

36 of the flowers are purple. 
7 0
4 years ago
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