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faltersainse [42]
2 years ago
8

Solve for the roots in simplest form by completing the square x^2-12x+20=0

Mathematics
1 answer:
Alex17521 [72]2 years ago
5 0

Answer:

x = 10 or x = 2

Step-by-step explanation:

Solve for x:

x^2 - 12 x + 20 = 0

Hint: | Solve the quadratic equation by completing the square.

Subtract 20 from both sides:

x^2 - 12 x = -20

Hint: | Take one half of the coefficient of x and square it, then add it to both sides.

Add 36 to both sides:

x^2 - 12 x + 36 = 16

Hint: | Factor the left hand side.

Write the left hand side as a square:

(x - 6)^2 = 16

Hint: | Eliminate the exponent on the left hand side.

Take the square root of both sides:

x - 6 = 4 or x - 6 = -4

Hint: | Look at the first equation: Solve for x.

Add 6 to both sides:

x = 10 or x - 6 = -4

Hint: | Look at the second equation: Solve for x.

Add 6 to both sides:

Answer: x = 10 or x = 2

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A random sample of 85 sixth-graders in a large city take a course designed to improve scores on a reading comprehension test. Ba
BartSMP [9]

Answer:

12.6 < \mu < 14.8

For this case we can find the margin of error like this:

ME= \frac{14.8-12.6}{2}= 1.1

Since we need to divide the width of the interval by 2.

And now with the margin of error we can find the sample mean with any of the two following ways:

12.6 +1.1=13.7

14.8-1.1=13.7

So for this case the correct answer would be:

A. Sample Mean = 13.7; Margin of Error = 1.1

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  

The margin of error is the range of values below and above the sample statistic in a confidence interval.  

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  

Solution to the problem

The confidence interval for the mean is given by the following formula:  

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}} (1)  

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:  

df=n-1=85-1=84

We know that the confidence interval is given by:

12.6 < \mu < 14.8

For this case we can find the margin of error like this:

ME= \frac{14.8-12.6}{2}= 1.1

Since we need to divide the width of the interval by 2.

And now with the margin of error we can find the sample mean with any of the two following ways:

12.6 +1.1=13.7

14.8-1.1=13.7

So for this case the correct answer would be:

A. Sample Mean = 13.7; Margin of Error = 1.1

3 0
2 years ago
CAN SOMEONE HELP ME PLEASE WILL MARK BRANLIST
olga2289 [7]

Answer:

36x

Step-by-step explanation:

6x=6x=12x

12-6.4=18x

5.5--2.1=6x

12x+18x+6x=36x

3 0
3 years ago
Complete the table to describe the model. The model will have a verbal description, a division expression, and a fraction.
NARA [144]

Answer:

what I dont even know whT your talking about. could you please explain your question a bit more?? then maybe I could help you out

5 0
3 years ago
Please help with solving
Makovka662 [10]
N.O = 4
N is midpoint of M.0
Meaning M.N also has to be 4
4+4= 8
N.P = 6
0.P = 2
8+ 2 = 10

4 0
2 years ago
A tourist standing on the New York City coast sees the Statue of Liberty, which is 305 feet tall. She must tilt her head 9 degre
mixer [17]

Given:

Height of the Statue of Liberty = 305 feet

Angle of elevation = 9 degrees

To find:

The between the tourist and the Statue of Liberty.

Solution:

Using the given information, draw a figure as shown below.

In a right triangle,

\tan \theta=\dfrac{Perpendicular}{Base}

In the triangle ABC,

\tan 9^\circ=\dfrac{305}{x}

x=\dfrac{305}{\tan 9^\circ}

x=1925.6942

x\approx 1926

Therefore, the tourist is standing 1926 feet from the Statue of Liberty.

4 0
2 years ago
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