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3 years ago

Solve this quadratic equation by completing the square.

Mathematics

1 answer:

nadya68 [22]3 years ago

3 0

Answer:

$x=-3+\sqrt{27}\\ x=-3-\sqrt{27}$

Step-by-step explanation:

Let's find our C value for the quadratic equation.

$(\frac{6}{2})^{2} = 9$

That is our C. Since we added 9 to one side, we have to do the same to the other. We get:

$x^{2} +6x + 9 = 18 + 9\\x^{2} +6x + 9 = 27$

Now, lets form the left side as a binomial squared.

$(x+3)^{2} = 27$

Let's square both sides now:

$x+3 = (+/-)\sqrt{27}$

Now, we subtract 3 from both sides to isolate the variable, X:

$x= -3(+/-)\sqrt{27}$

This means that the answers are:

$x=-3+\sqrt{27}\\ x=-3-\sqrt{27}$

I do not understand your answers though. Answer A makes no sense, answer B is 221, answer C is 115, and answer D also does not make sense. If you could clarify this portion, maybe I can help you find your alphabetic answer

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Determine the common ratio and find the next three terms of the geometric sequence t8, t5, t2

attashe74 [19]

The common ratio of the given geometric sequence is the number that is multiplied to the first term in order to get the second term. Consequently, this is also the number multiplied to the second term to get the third term. This cycle goes on and on until a certain term is acquired. In this item, the common ratio r is,

r = t⁵/t⁸ = t²/t⁵

The answer, r = t⁻³.

The next three terms are,

n₄ = (t²)(t⁻³) = t⁻¹
n₅ = (t⁻¹)(t⁻³) = t⁻⁴
n₆ = (t⁻⁴)(t⁻³) = t⁻⁷

The answers for the next three terms are as reflected above as n₄, n₅, and n₆, respectively.

3 0

3 years ago

Read 2 more answers

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Liula [17]

The answer for this problem is b

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2 years ago

The rates of on-time flights for commercial jets are continuously tracked by the U.S. Department of Transportation. Recently, So

tatyana61 [14]

Answer:

The probability that at least 13 flights arrive late is 2.5196 $\times 10^{-6}$ .

Step-by-step explanation:

We are given that Southwest Air had the best rate with 80 % of its flights arriving on time.

A test is conducted by randomly selecting 18 Southwest flights and observing whether they arrive on time.

The above situation can be represented through binomial distribution;

$P(X = x) = \binom{n}{r}\times p^{r} \times (1-p)^{n-r} ; x = 0,1,2,3,.........$

where, n = number of trials (samples) taken = 18 Southwest flights

r = number of success = at least 13 flights arrive late

p = probability of success which in our question is probability that

flights arrive late, i.e. p = 1 - 0.80 = 20%

Let X = Number of flights that arrive late.

So, X ~ Binom(n = 18, p = 0.20)

Now, the probability that at least 13 flights arrive late is given by = P(X $\geq$ 13)

P(X $\geq$ 13) = P(X = 13) + P(X = 14) + P(X = 15) + P(X = 16) + P(X = 17) + P(X = 18)

= $\binom{18}{13}\times 0.20^{13} \times (1-0.20)^{18-13}+ \binom{18}{14}\times 0.20^{14} \times (1-0.20)^{18-14}+ \binom{18}{15}\times 0.20^{15} \times (1-0.20)^{18-15}+ \binom{18}{16}\times 0.20^{16} \times (1-0.20)^{18-16}+ \binom{18}{17}\times 0.20^{17} \times (1-0.20)^{18-17}+ \binom{18}{18}\times 0.20^{18} \times (1-0.20)^{18-18}$

= $\binom{18}{13}\times 0.20^{13} \times 0.80^{5}+ \binom{18}{14}\times 0.20^{14} \times 0.80^{4}+ \binom{18}{15}\times 0.20^{15} \times 0.80^{3}+ \binom{18}{16}\times 0.20^{16} \times 0.80^{2}+ \binom{18}{17}\times 0.20^{17} \times 0.80^{1}+ \binom{18}{18}\times 0.20^{18} \times 0.80^{0}$