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kaheart [24]
3 years ago
15

place the following steps in order to complete the square and solve for the quadratic equation, x squared -6x +7=0

Mathematics
1 answer:
BlackZzzverrR [31]3 years ago
4 0
To solve the quadratic by complete square method we proceed as follows:
x²-6x+7=0
this can be written as:
x²-6x=-7
but
c=(-b/2a)^2
c=(-(-6)/2)^2=9
next we add 9 on both sides of our expression to get:
x²-6x+9=-7+9
x²-6x+9=2
factoring out the LHS we get:
(x-3)(x-3)=2
(x-3)²=2
getting the square root of both sides we obtain:
x-3=+/-√2
hence:
x=3+/-√2
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Answer:

B) 0.287

Step-by-step explanation:

For each Coffeeton resident, there are only two possible outcomes. Either they recognize the brand name, or they do not. The probability of a resident recognizing the brand name is independent of other residents. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

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This means that p = 0.53

Find the probability that exactly 4 of the 7 Coffeeton residents recognize the brand name.

This is P(X = 4) when n = 7. So

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 4) = C_{7,4}.(0.53)^{4}.(0.47)^{3} = 0.287

So the anwer is:

B) 0.287

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Answer:

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(3, -4)    Vertex

Step-by-step explanation:

f(x) = x² - 6x + 5

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