Factor. x2−6x+8 Enter your answer in the boxes.

Mathematics

2 answers:

LUCKY_DIMON [66]3 years ago

7 0

Answer:
The factored form is: (x-2)(x-4) = 0

Explanation:
To factor an expression, we need to get its solutions.

The standard form of the quadratic equation is:
ax² + bx + c = 0

The given equation is:
x² - 6x + 8 = 0

By comparison:
a = 1
b = -6
c = 8

Now, to get the roots, we will substitute with the values of a, b and c in the quadratic formula shown in the attached image.

This will give us:
either x = $\frac{6+ \sqrt{(-6)^2-4(1)(8)} }{2(1)} = 4$
This means that the first factor is (x-4)

or x = $\frac{6- \sqrt{(-6)^2-4(1)(8)} }{2(1)} = 2$
This means that the second factor is (x-2)

Based on the above, the factored form would be:
(x-4)(x-2) = 0

Hope this helps :)

avanturin [10]3 years ago

5 0

Answer:

(x-2)(x-4)

Step-by-step explanation:

x^2 -6x +8

We need to find numbers that add to -6 but multiply 8. We know that 4 and 2 multiply to 8 but they do not add to -6. -4 and -2 add to -6 and -4 times -2 equal 8. Therefore the factored form of x^2 -6x + 8 is (x-2)(x-4).

Hope this helps:))) Hva e a good day

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(1 point) Suppose we want a 95% confidence interval for the average amount spent on books by freshmen in their first year at col

Ne4ueva [31]

Answer:

a) $n=(\frac{1.960(16)}{5})^2 =39.33 \approx 40$

So the answer for this case would be n=40 rounded up to the nearest integer

b) For this case if we see the formula for the margin of error

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

We can see that the margin of error is inversely proportional to the sample size so if we want a samller margin of error we need a LARGER sample

Answer: LARGER

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean

$\sigma=16$ represent the population standard deviation

n represent the sample size

Solution to the problem

Part a

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =5 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got $z_{\alpha/2}=1.960$ , replacing into formula (b) we got: