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3 years ago

X^2+6x-6=0 rewritten by completing the square

Mathematics

1 answer:

Pie3 years ago

4 0

Hello from MrBillDoesMath!

Answer:

(x+3)^2 -15 = 0

Discussion:

To complete the square add (and then subtract) the square of one-half the coefficient of x:

x^2 + 6x -6 = 0 =>

-- complete the square part --

x^2 + 6x + (6/2)^2 - (6/2)^2 - 6 = 0 =>

x^2 + 6x + 9 - 9 - 6 = 0 => as 6/2 = 3

(x + 3)^ 2 - 9 - 6 = 0 =>

(x+3)^2 -15 = 0

We can solve this as follows:

(x+3)^2 = 15 take square root of both sides

(x+3) = +\- sqrt(15)

x = -3 +\- sqrt(15)

Thank you,

MrB

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Please please Help me!!!!!

pav-90 [236]

Answer:

19,23

Step-by-step explanation:

9+x-7≥ 21

Combine like terms

2+x≥21

Subtract 2 from each side

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3 years ago

A researcher reports survey results by stating that the standard error of the mean is 25 the population standard deviation is 40

bezimeni [28]

Answer:

a) A sample of 256 was used in this survey.

b) 45.14% probability that the point estimate was within ±15 of the population mean

Step-by-step explanation:

This question is solved using the normal probability distribution and the central limit theorem.

Normal probability distribution

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.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

a. How large was the sample used in this survey?

We have that $s = 25, \sigma = 400$ . We want to find n, so:

$s = \frac{\sigma}{\sqrt{n}}$

$25 = \frac{400}{\sqrt{n}}$

$25\sqrt{n} = 400$

$\sqrt{n} = \frac{400}{25}$

$\sqrt{n} = 16$

$(\sqrt{n})^2 = 16^2[tex][tex]n = 256$

A sample of 256 was used in this survey.

b. What is the probability that the point estimate was within ±15 of the population mean?

15 is the bounds with want, 25 is the standard error. So

Z = 15/25 = 0.6 has a pvalue of 0.7257

Z = -15/25 = -0.6 has a pvalue of 0.2743

0.7257 - 0.2743 = 0.4514

45.14% probability that the point estimate was within ±15 of the population mean

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3 years ago

D’Quan’s grandmother made a quilt for his bed. The quilt is

damaskus [11]

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The total area of the quilt in meters is $4.465m^{2}$
As you're looking for square feet, you've then got to multiply this by 10.764
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Rounded, this is 48.06 square feet.
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3 years ago

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Mrac [35]

Answer:

1/8

Step-by-step explanation:

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2 years ago