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Archy [21]
3 years ago
7

In parallelogram ABCD, AE=x^2-6 and CE=5x what is the value of x ? What is AC?

Mathematics
1 answer:
lutik1710 [3]3 years ago
3 0

Answer:

see explanation

Step-by-step explanation:

The diagonals of a parallelogram bisect each other, hence

AE = EC, that is

x² - 6 = 5x ( subtract 5x from both sides )

x² - 5x - 6 = 0 ← in standard form

(x - 6)(x + 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x - 6 = 0 ⇒ x = 6

x + 1 = 0 ⇒ x = - 5

However x > 0 ⇒ x = 6

AC = x² - 6 + 5x = 6² - 6 + 5(6) = 36 - 6 + 30 = 60

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Find the limits<br>The answer is - 3/4
Kipish [7]

Hello from MrBillDoesMath!

Answer:

This is a puzzling one! The answer is indeed -3/4 but I was unable to prove it using mathematics appropriate to the "middle school" level. Sorry I couldn't be more helpful.

(To prove it I generated the first few terms of its Laurent series, a Calculus topic. The first few terms are  -(3/4) + (41/64x) +  and as x approaches  minus infinity the term with "x" in the denominator goes to zero, leaving the constant value -3/4 as the answer. )


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igomit [66]

Answer:

The standard deviation of the load distribution is of 5102.041 pounds.

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

\mu = 20000

Also, the probability that the load is between 10,000 and 30,000 pounds is 0.95.

10,000 pounds and 30,000 pounds are equidistant from the mean. Due to this, and the probability of 0.95 of having a value in this range, 10000 is the (100-95)/2 = 2.5th percentile and 30000 is the (100+95)/2 = 97.5th percentile. Applying one of them, we find the standard deviation.

30,000 is the 97.5th percentile:

This means that when X = 30000, Z has a pvalue of 0.975. So when X = 30000, Z = 1.96. Then

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

1.96 = \frac{30000 - 20000}{\sigma}

1.96\sigma = 10000

\sigma = \frac{10000}{1.96}

\sigma = 5102.041

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Step-by-step explanation:

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