Answer:
<h2>

</h2>
Option D is the correct option.
Step-by-step explanation:
Given,
A ( 4, 5 ) , B ( 2 , 2 ) , C ( 4 , 2 )
Let,
A ( 4 , 5 ) → ( x1 , y1 )
B ( 2 , 2 ) → ( x2 , y2 )
Now, finding the length of AB
Use the distance formula to find the length of AB

plug the values

Calculate the difference

Evaluate the power

Add the numbers

Hope this helps..
Best regards!!
Explanation:
For a quadratic equation in standard form with real coefficients:

The quadratic formula giving its solutions is ...

The quantity under the radical is called the discriminant. If we let d represent it, then ...
d = b²-4ac
and there are three possibilities:
- d < 0. The solutions involve the square root of a negative number, so both are complex. They are conjugates of each other.
- d = 0. There is one real solution. It has multiplicity 2.
- d > 0. There are two distinct real roots.
If the coefficients of the quadratic are rational, the roots will be irrational if and only if d is not a perfect square.
_____
The above formula still applies when coefficients are complex or irrational (or both). In the case of complex coefficients, the description of the number of roots is accurate, but their description as real or complex may not apply.
_____
<u>Examples</u>:
(x -1)² +1 = 0 = x² -2x +2 . . . . d = (-2)²-4(1)(2) = -4; roots are x = 1 ± i
(x-2)² = 0 = x² -4x +4 . . . . . . d = (-4)² -4(1)(4) = 0; roots are x = 2 (twice)
(x+3)² -4 = x² +6x +5 . . . . . . d = 6² -4(1)(5) = 16; roots are x = -5 and x = -1
Commutative Property.
It cannot be multiplication property because it would have to be live 5 x 1 = 5. For multiplication property the answer has to be the same as the number you used to get the answer. Does that make sense? I can send you a pic if you need it. I might be wrong because I just learned it now so I could give you an answer but from the example I got it has to be like 25x1=25, 100x1=100 something like that
Answer:
The minimum sample size required is 207.
Step-by-step explanation:
The (1 - <em>α</em>) % confidence interval for population mean <em>μ</em> is:

The margin of error of this confidence interval is:

Given:

*Use a <em>z</em>-table for the critical value.
Compute the value of <em>n</em> as follows:
![MOE=z_{\alpha /2}\frac{\sigma}{\sqrt{n}}\\3=2.576\times \frac{29}{\sqrt{n}} \\n=[\frac{2.576\times29}{3} ]^{2}\\=206.69\\\approx207](https://tex.z-dn.net/?f=MOE%3Dz_%7B%5Calpha%20%2F2%7D%5Cfrac%7B%5Csigma%7D%7B%5Csqrt%7Bn%7D%7D%5C%5C3%3D2.576%5Ctimes%20%5Cfrac%7B29%7D%7B%5Csqrt%7Bn%7D%7D%20%5C%5Cn%3D%5B%5Cfrac%7B2.576%5Ctimes29%7D%7B3%7D%20%5D%5E%7B2%7D%5C%5C%3D206.69%5C%5C%5Capprox207)
Thus, the minimum sample size required is 207.
Is that the full question? I simplified it to 2x^2 -5x +18 when you plug x+3 in for the variable (x) in the expression. I’m honestly not sure when to go from there. Hope that helps with something. Sorry I couldn’t do more