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jarptica [38.1K]
3 years ago
12

Complete the square to transform the quadratic equation into the form (x – p)2 = q.

Mathematics
1 answer:
ryzh [129]3 years ago
7 0

The transformed equation is:

(x-3)^2 = 23

Step-by-step explanation:

We have to convert the equation in the form

(x-p)^2 = q

Given equation is:

x^2-6x-8 = 6

Adding 8 on both sides

x^2-6x-8+8 = 6+8\\x^2-6x = 14

In the given equation

a = x

b= ?

So,

2.x.b = 6x\\b =\frac{6x}{2x}\\b = 3\\

So 3^2 will be added on both sides

(x)^2-6x+ (3) = 14+ (3)^2\\(x-3)^2 = 14+9\\(x-3)^2 = 23

Hence,

The transformed equation is:

(x-3)^2 = 23

Keywords: Quadratic equation, transformation

Learn more about quadratic equation at:

  • brainly.com/question/5248692
  • brainly.com/question/5223123

#LearnwithBrainly

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Using the Pythagorean identity,

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A random sample of 25 glass sheets is obtained and their thicknesses are measured. The sample mean is x= 3.54 mm and sample stan
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Answer: (3.46, 3.62)

Step-by-step explanation:

The formula to find the confidence interval for population mean is given :-

\overline{x}\ \pm\ t_{\alpha/2}\dfrac{s}{\sqrt{n}}

, where n = sample size.

t_{\alpha/2} = Two-tailed t-value for significance level of (\alpha) and degree of freedom df= n-1.

s = sample standard deviation.

As per given , we have

\overline{x}= 3.54 mm

s= 0.20 mm

n= 25

Significance level =\alpha=1-0.95=0.05

Since population standard deviation is not given , it means the given problem has t- distribution.

Two-tailed t-value for significance level of (0.05) and degree of freedom df= 24:

t_{\alpha/2\ ,df}=t_{0.025,\ 24}=2.0639

95% Confidence interval for population mean:

3.54\ \pm\ (2.0639)\dfrac{0.20}{\sqrt{25}}

=3.54\ \pm\ (2.0639)\dfrac{0.20}{5}

=3.54\ \pm\ (2.0639)(0.04)

=3.54\ \pm\ 0.082556

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Hence, the 95% two-sided confidence interval for the mean glass thickness = (3.46, 3.62)

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3 years ago
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