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inn [45]
3 years ago
9

Complex root of x^2+3x+9=0

Mathematics
1 answer:
Luden [163]3 years ago
6 0

\text{Quadratic formula}

ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\x_1=\dfrac{-b-\sqrt\Delta}{2a};\ x_2=\dfrac{-b+\sqrt\Delta}{2a}

-----------------------------------------------------------------------

x^2+3x+9=0\\\\a=1;\ b=3;\ c=9\\\\\Delta=3^2-4(1)(9)=9-36=-27\\\\\sqrt\Delta=\sqrt{-27}=\sqrt{(27)(-1)}=\sqrt{27}\cdot\sqrt{-1}=\sqrt{9\cdot3}i=\sqrt9\cdot\sqrt3i=3\sqrt3i

x_1=\dfrac{-3-3\sqrt3i}{2(1)}=-\dfrac{3}{2}-\dfrac{3\sqrt3}{2}i\\\\x_2=\dfrac{-3+3\sqrt3i}{2(1)}=-\dfrac{3}{2}+\dfrac{3\sqrt3}{2}i


i=\sqrt{-1}

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A rectangular auditorium seats 1344 people. The number of seats in each rows exceeds the number of rows by 20. Find the number o
Tasya [4]
Let the number of rows be x

rows = x
seats in each row = x + 20

total seats = 1344
x (x + 20) = 1344
x^2 + 20x - 1344 = 0
(x + 48)(x - 28) = 0
x = -48  (rejected, answer cannot be negative) or x = 28

Therefore,
x = 28 
x + 20 = 48


Check:
Row = 28
Numbers of seat per row = 28 + 20 = 48
28 x 48 = 1344 (Correct)
 
Ans:There are 48 seats per row 
8 0
3 years ago
Use the information given to answer the question. Vanessa and Moe record their quiz scores in music class for a semester. The do
Lorico [155]

Answer:

Vanessa records a total of <u>11</u> quiz scores

Moe records a total of <u>10</u> quiz scores

According to the data, Vanessa's mean score is 80

According to the data, Vanessa's median score is 85

The range of Moe's quiz score is 45

The interquartile range of Moe's quiz score is 16.25

Step-by-step explanation:

Vanessa's score is given in the dot plot

Moe's scores are; 75, 80, 90, 90, 95, 55, 100, 95, 85, 85

1) The number of quiz scores Vanessa records is given by the number of dots on the dot plot, n = 11 dots ≡ 11 quiz scores

2) The number of quiz scores Moe records is given by the number of data points, n = 10 data points ≡ 10 quiz scores

3) Vanessa's mean score = ∑x_i/n

∑x_i/n = (60 + 2× 65 + 75 + 4 × 85 + 2 × 90 +95)/11 = 80

Vanessa's mean score = 80

4) Vanessa's median score is the (11 + 1)/2 th score = Her 6th score = 85

Vanessa's median score = 85

5) The range of Moe's score = Her largest score - Her least score = 100 - 55 = 45

The range of Moe's score = 45

6) Sorting Moe's scores gives;

75, 80, 90, 90, 95, 55, 100, 95, 85, 85

55, 75, 80, 85, 85, 90, 90, 95, 95, 100

The first quartile, Q₁ = 11/4th score = 2.75th score = 75 + 0.75 × 5 = 78.75

The 3rd quartile, Q₃ = The 3/4×11 score = 8.25th score = 95 + 0.25 ×0 = 95

The interquartile range, I = Q₃ - Q₁ = 95 - 78.75 = 16.25

The interquartile range of Moe's quiz score = 16.25.

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2 years ago
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Answer:

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Step-by-step explanation:

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Step by step explanation:

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Answer:

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Step-by-step explanation:

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