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balu736 [363]
3 years ago
13

Which Quadratic equation is equivalent to (x-4)^2-(x-4)-6=0

Mathematics
2 answers:
Aleksandr-060686 [28]3 years ago
6 0

For this case, we must find the quadratic equation equivalent to:

(x-4) ^ 2- (x-4) -6 = 0

By definition we have to:

(a-b) ^ 2 = a^2-2ab + b ^ 2

So:

(x-4) ^ 2 = x ^ 2-2 (x) (4) + 4 ^ 2 = x ^ 2-8x + 16

So, we have:

- * + = +\\- * - = +

x ^ 2-8x + 16-x + 4-6 = 0

Equal signs add up and the same sign is placed.

Different signs are subtracted and the sign of the major is placed.

x ^ 2-9x + 14 = 0

Answer:

x ^ 2-9x + 14 = 0

MrMuchimi3 years ago
5 0

Answer:

x²-9x+14 is the quadratic equation.

Step-by-step explanation:

We have given the equation:

(x-4)²-(x-4)-6=0

We have to find the quadratic equation equivalent to the given equation.So,

(x-4)²-(x-4)-6=0

As we know that, (a-b)²=a²+b²-2ab  then we get,

x²+16-8x-x+4-6=0

x²-9x+14=0

x²-9x+14 is the quadratic equation equivalent to (x-4)²-(x-4)-6=0

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8.2-2.58\frac{2.2}{\sqrt{18}}=6.86    

8.2+2.58\frac{2.2}{\sqrt{18}}=9.54    

So on this case the 90% confidence interval would be given by (6.86;9.54)    And the error is given by:

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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".

\bar X=8.2 represent the sample mean for the sample  

\mu population mean (variable of interest)

\sigma=2.2 represent the population standard deviation

n represent the sample size  

Solution to the problem

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

\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}   (1)

Since the Confidence is 0.90 or 90%, the value of \alpha=0.1 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.005,0,1)".And we see that z_{\alpha/2}=2.58

Now we have everything in order to replace into formula (1):

8.2-2.58\frac{2.2}{\sqrt{18}}=6.86    

8.2+2.58\frac{2.2}{\sqrt{18}}=9.54    

So on this case the 90% confidence interval would be given by (6.86;9.54)    And the error is given by:

ME= 2.58\frac{2.2}{\sqrt{18}} =1.338

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