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Mrac [35]
2 years ago
10

Diagram 5 shows a triangle ABD such that AD = 17 cm, AB = 10 cm and BD = 21 cm. The straight line AC is perpendicular to the str

aight line BD and the value of area of triangle ABD is an integer. Calculate the length of AC, in cm. (4 marks)​

Mathematics
1 answer:
OlgaM077 [116]2 years ago
7 0

Answer:

8

Step-by-step explanation:

100 = x^2 + AC^2

17^2 = AC^2 + (21 - x)^2

289 = AC^2 + 21^2 + x^2 - 2*21*x

289 =<u> AC^2</u> + 441 +<u> x^2</u> - 42x

from 1st equation AC^2 + x^2 = 100

289 = 441 + 100 - 42x

289 = 541 - 42x

42x = 541 - 289 = 252

x = 252/42 = 6

so AC^2 = 100 - 6^2 = 100 - 36 = 64

AC = 8

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Answer:

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And in the figure attached we see the limits with the percentages associated.

Step-by-step explanation:

For this case we know that the random variable of interest is the scores on a test given to all juniors in a school district follows a normal distribution with the following parameters:

X \sim N(\mu= 74, \sigma =8)

For this case we know from the empirical rule that within one deviation from the mean we have approximately 68.2% of the data, within 2 deviations from the mean we have 95% and within 3 deviation 99.7%

We can find the limits and we got:

\mu -\sigma = 66 , \mu +\sigma = 82

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\mu -3\sigma = 50 , \mu +3\sigma = 98

And in the figure attached we see the limits with the percentages associated.

7 0
3 years ago
Given line segment AB, the coordinates of A are (3,-5) and the coordinates midpoint are (5,-1), what are the coordinates for B?
dsp73

Answer:

<h3>           B(7, 3)</h3>

Step-by-step explanation:

Point P(5, -1) being the midpoint of AB means that  x_P-x_A=x_B-x_P

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and   y_P-y_A=y_B-y_P

-1-(-5)=y_B-(-1)\\\\-1+5=y_B+1\\\\y_B=3

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