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sveta [45]
3 years ago
7

Given that ABCD is a rhombus, what is the value of x?

Mathematics
1 answer:
choli [55]3 years ago
8 0

Answer:

A. 19.5

Step-by-step explanation:

Diagonals of a rhombus intersect at right angles. Therefore the angle opposite to AD = 90°.

Thus:

90° + x + 3x + 12 = 180° (sum of ∆)

Add like terms

102 + 4x = 180

Subtract 102 from each side

4x = 180 - 102

4x = 78

Subdue both sides by 4

x = 19.5

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What is the variance of the following data? If necessary, round your answer to two decimal places. 17, 13, 13, 22, 11, 20
Bond [772]
Variance is the standard deviation squared but we're not going to use that now. Let's first calculate the mean:

mean = (17+13+13+22+11+20)/6 = 16.

Now for each value, let's see how far it is from this mean. We'll square these distances and average them. That's our variance.

17 distance 1 squared = 1
13 distance 3 squared = 9
13 distance 3 squared = 9
22 distance 6 squared = 36
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Now average these outcomes:

variance = (1+9+9+36+25+16)/6 = 16.

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Answer C is your answer.
7 0
4 years ago
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Answer:

4 horses and 8 ducks.

Step-by-step explanation:

Let the number of ducks be d and the number of horses be h.

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2d + 2h = 24

Subtract this equation from the second equation:

4h - 2h = 32 - 24

2h = 8

h = 4.

So there were 4 horses and 12 - 4 = 8 ducks.

4 0
3 years ago
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