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dedylja [7]
3 years ago
15

Write the quadratic equation in general form. (x - 3)^ 2 = 0

Mathematics
2 answers:
algol [13]3 years ago
5 0
The answer is:  x² – 6x + 9 = 0  .
_____________________________________________________
Explanation:
________________________________________________________

Given:  (x – 3)² = 0 ;  write as: general form:  "ax² + bx + c = 0";  a ≠ 0 .
<span>
Note:  </span>(x – 3)² = (x – 3)(x – 3) = x² – 3x – 3x + 9 = x² – 6x + 9 ;
___________________________________________________
Rewrite: (x – 3)²  =  0 ;  →
           as:   x² – 6x + 9 = 0  ; which is our answer.
____________________________________________
→   x² – 6x + 9 = 0  ; is in "general form", or "standard equation format"; that is: " ax² + bx + c = 0 ";  (a ≠ 0) ;
             → in which: 
   a =  1 (implied coefficient, since anything multiplied by "1" is that same                                                                                                                    value);
   b = -6; 
   c =  9
_______________________________________________________
Kisachek [45]3 years ago
5 0
Easy
expand
(x-3)^2=0
(x-3)(x-3)
foil
first: x time x=x²
outter: -3 times x=-3x
inner:x times -3=-3x
last: -3 times -3=9
add them
x²-3x-3x+9=0
x²-6x+9=0
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The computers of nine engineers at a certain company are to be replaced. Four of the engineers have selected laptops and the oth
Gala2k [10]

Answer:

(a) There are 70 different ways set up 4 computers out of 8.

(b) The probability that exactly three of the selected computers are desktops is 0.305.

(c) The probability that at least three of the selected computers are desktops is 0.401.

Step-by-step explanation:

Of the 9 new computers 4 are laptops and 5 are desktop.

Let X = a laptop is selected and Y = a desktop is selected.

The probability of selecting a laptop is = P(Laptop) = p_{X} = \frac{4}{9}

The probability of selecting a desktop is = P(Desktop) = p_{Y} = \frac{5}{9}

Then both X and Y follows Binomial distribution.

X\sim Bin(9, \frac{4}{9})\\ Y\sim Bin(9, \frac{5}{9})

The probability function of a binomial distribution is:

P(U=k)={n\choose k}\times(p)^{k}\times (1-p)^{n-k}

(a)

Combination is used to determine the number of ways to select <em>k</em> objects from <em>n</em> distinct objects without replacement.

It is denotes as: {n\choose k}=\frac{n!}{k!(n-k)!}

In this case 4 computers are to selected of 8 to be set up. Since there cannot be replacement, i.e. we cannot set up one computer twice or thrice, use combinations to determine the number of ways to set up 4 computers of 8.

The number of ways to set up 4 computers of 8 is:

{8\choose 4}=\frac{8!}{4!(8-4)!}\\=\frac{8!}{4!\times 4!} \\=70

Thus, there are 70 different ways set up 4 computers out of 8.

(b)

It is provided that 4 computers are randomly selected.

Compute the probability that exactly 3 of the 4 computers selected are desktops as follows:

P(Y=3)={4\choose 3}\times(\frac{5}{9})^{3}\times (1-\frac{5}{9})^{4-3}\\=4\times\frac{125}{729}\times\frac{4}{9}\\  =0.304832\\\approx0.305

Thus, the probability that exactly three of the selected computers are desktops is 0.305.

(c)

Compute the probability that of the 4 computers selected at least 3 are desktops as follows:

P(Y\geq 3)=1-P(Y

Thus, the probability that at least three of the selected computers are desktops is 0.401.

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