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mr_godi [17]
3 years ago
12

Which equation has the solutions x = -3 ± √3i/2 ?

Mathematics
1 answer:
Maurinko [17]3 years ago
6 0

Answer:Answer is option C : [x^{2} + 3x + 3 ] =0

Note:  None of options matches with given question.

instead of "-3" , there should be "-\frac{3}{2}".

Step-by-step explanation:

Note:  None of options matches with given question.

instead of "-3" , there should be "\frac{3}{2}".  

Here, First thing you have to observe the nature of roots.

∴ x = -\frac{3}{2}+\frac{\sqrt{3}}{2}i and x = -\frac{3}{2}-\frac{\sqrt{3}}{2}

∴ [ x+(\frac{3}{2}-\frac{\sqrt{3}}{2}i) ][ x+(\frac{3}{2}+\frac{\sqrt{3}}{2}i) ]=0

∴ [ x^{2} + x(\frac{3}{2}+\frac{\sqrt{3}}{2}i)+ x(\frac{3}{2}-\frac{\sqrt{3}}{2}i) + (\frac{3}{2}-\frac{\sqrt{3}}{2}i)(\frac{3}{2}+\frac{\sqrt{3}}{2}i) ]=0

∴ [x^{2} + \frac{3}{2}x + \frac{\sqrt{3}}{2}ix + \frac{3}{2}x - \frac{\sqrt{3}}{2}ix + (3-\frac{\sqrt{3}}{2}i)(3+\frac{\sqrt{3}}{2}i) ] =0

∴ [x^{2} + 3x + (\frac{3}{2}-\frac{\sqrt{3}}{2}i)(\frac{3}{2}+\frac{\sqrt{3}}{2}i) ] =0

∴ [x^{2} + 3x + \frac{9}{4} - (\frac{\sqrt{3}}{2}i)(\frac{\sqrt{3}}{2}i) ] =0

∴ [x^{2} + 3x + \frac{9}{4} - (\frac{3}{4}) i^{2} ] =0

∴ [x^{2} + 3x + \frac{9}{4} + (\frac{3}{4}) ] =0

∴ [x^{2} + 3x + \frac{12}{4} ] =0  

∴ [x^{2} + 3x + 3 ] =0  

Thus, Answer is option C : <em>[x^{2} + 3x + 3 ] =0  </em>

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Can you help me with number 6? <br> Confused abit <br> Please
Sunny_sXe [5.5K]

You can see the three diagram attached. Each link is labeled with the probability: you have probability 1/6 that a six is rolled, and 5/6 that it is not rolled.


To answer the questions, find the path that brings you to the desired outcome, and multiply all the labels you meet.


First question:

To get three sixes, you have to choose the left path at each roll. The probability is always 1/6, so the answer is


\frac{1}{6} \times \frac{1}{6} \times \frac{1}{6} = \frac{1}{6^3}


Second question:

To get no sixes, you have to choose the right path at each roll. The probability is always 5/6, so the answer is


\frac{5}{6} \times \frac{5}{6} \times \frac{5}{6} = \frac{5^3}{6^3}


Third question:

To get exactly one six, it can either be the first, second or third roll.


In all cases, you have to choose the left path once and the right path twice: left-right-right mean that you get the six in the first roll, right-left-right means that you get the six in the second roll, right-right-left means that you get the six in the third roll.


In every case, the left turn has probability 1/6, and the right turn has probability 5/6. The probability of each combination is thus


\frac{1}{6} \times \frac{5}{6} \times \frac{5}{6} = \frac{5^2}{6^3}


And since there are three of these combinations, The answer is


3\frac{5^2}{6^3}


Fourth question:

Since the question suggests to use what we already achieved, let's do it: having at least one six is the complementary event of having no sixes at all. If an event has probability p, its complementary has probability 1-p. So, since the probability of no sixes is known, the probability of at least one six is


1 - \frac{5^3}{6^3}

4 0
3 years ago
Question 4 (1 point)
mrs_skeptik [129]

Answer:

(C)y=0

Step-by-step explanation:

An exponential function of the form f(x) = a (b^x) + c always has a horizontal asymptote at y = c.

Given our function y=4^x

Comparing with the form,  f(x) = a (b^x) + c, we observe that c=0.

Therefore, the exponential function has an <u>asymptote at y=0.</u>

The correct option is C.

7 0
3 years ago
Dora has 10 seashells and plans to add 2 shells every week. Jerri has 4 seashells and plans to add 5 shells every week. Which sy
Mariulka [41]

Answer:

Let x represents the week and y represents the seashells

As per the statement:

Dora has 10 seashells and plans to add 2 shells every week.

"2 shells every week" means 2x

⇒y = 10 + 2x

It is also given, Jerri has 4 seashells and plans to add 5 shells every week.

"5 shells every week" means 2x

⇒ y = 4 + 5x

The system of equation would be used:

y = 10 + 2x

y = 4 + 5x

Since, the girls have the same number of seashells

⇒10 + 2x = 4 + 5x

Subtract 4 from both sides we get;

6 + 2x = 5x

Subtract 2x from both sides we get;

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Divide by 3 both sides we have;

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Therefore, the number of weeks would it be before the girls have the same number if seashells is, 2 weeks.

3 0
3 years ago
Find the length of x
IRISSAK [1]
To solve you insert into proportions, then cross-multiply and simplify.
But first, add 5 and 6 to get the full side length of the bigger triangle

\frac{x}{5}  x  \frac{5.5}{11}

11x = 27.5
x = 2.5

Hope this helps!
3 0
3 years ago
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nydimaria [60]
Answer:Benjamin’s age = 30 and David’s age = 6

Explanation:

Let x be the age of Benjamin
Let y be the age of David

x + y = 36

And 2x + 2y = 72

If we plug 30 for x and 6 for y we get:

30 + 6 = 36
36 = 36

2(30) + 2(6) = 72
60 + 12 = 72
72 = 72

=

5 0
3 years ago
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