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Pavlova-9 [17]
3 years ago
5

Side AB of parallelogram ABCD has endpoints at (-1,6) and (6,9). What is the slope of the opposite side, CD?

Mathematics
1 answer:
Butoxors [25]3 years ago
8 0

Answer:

3/7

Step-by-step explanation:

Opposite sides on a parallelogram are parallel, and parallel lines have the same slope, so once we find the slope of AB, we'll know the slope of CD. Point A is (-1,6) and point B is (6,9), so the slope of AB (and by extension, CD) is

\dfrac{9-6}{6-(-1)}=\dfrac{3}{7}

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7(x + 4) + 5(x-6) please expand and simplify
Neporo4naja [7]

Answer:

12x − 2

Step-by-step explanation:

7(x+4)+5(x−6)

Distribute:

=(7)(x) + (7)(4) + (5)(x) + (5)(−6)

=7x + 28 + 5x − 30

Combine Like Terms:

=7x + 28 + 5x − 30

=(7x+5x) + (28−30)

= 12x − 2

8 0
3 years ago
Read 2 more answers
The Town of Hertfordshire clerk knows that 23% of dogs in the town have completed emotional support training. Hertfordshire plan
Nataly_w [17]

Answer:

95.64% probability that under 30% of the dogs are emotional support trained

Step-by-step explanation:

For each dog, there are only two possible outcomes. Either they have completed emotional support training, or they have not. So we use the binomial probability distribution to solve this problem.

However, we are working with samples that are considerably big. So i am going to aproximate this binomial distribution to the normal.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed samples can be 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.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

In this problem, we have that:

\mu = E(X) = np = 100*0.23 = 23

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{100*0.23*0.77} = 4.21

What is the probability that under 30% of the dogs are emotional support trained?

30% of 100 is 0.3*100 = 30

So this is the pvalue of Z when X = 30.

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

Z = \frac{30 - 23}{4.1}

Z = 1.71

Z = 1.71 has a pvalue of 0.9564.

So there is a 95.64% probability that under 30% of the dogs are emotional support trained

5 0
3 years ago
Which property is demonstrated below? n•1=n
Vinvika [58]

Answer:

Step-by-step explanation:

That'd be the Identity Property of Multiplication.

3 0
3 years ago
Add 5x+4y;3x-7y;-4x+8y​
viktelen [127]

The answer is 4x + 5y.

Here, what needs to be done is to combine like terms.

  • 5x + 4y + 3x - 7y - 4x + 8y
  • 5x + 3x - 4x + 4y + 8y - 7y
  • 4x + 5y
4 0
2 years ago
You buy 21 lbs of cucumbers which are 92% water. A few days later they’re 85% water. How much do they weigh then?
IrinaK [193]
To solve this, you must find the initial weight of the cucumber. To do this, you must divide the weight by the percentage of water and multiply it by 100.

(21/92)×100=22.83lbs.

Then, you multiply it by 85% and divide it by 100. Or simply multiply it by 0.85.

22.83×0.85=19.41lbs.

3 0
3 years ago
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