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katrin [286]
1 year ago
5

If using the method of completing the square to solve the quadratic equation x^2 + 3x +21 =0?

Mathematics
1 answer:
goldfiish [28.3K]1 year ago
8 0

Answer:

x= \dfrac 12 \left( -3 +i5\sqrt 3\right)\\\\x= \dfrac 12 \left( -3 -i5\sqrt 3\right)

Step-by-step explanation:

~~~~~~x^2 +3x +21 = 0\\\\\implies x^2 +3x = -21\\\\\implies x^2 + 2\cdot  \dfrac 32 \cdot x + \left( \dfrac 32 \right)^2 = -21 + \left( \dfrac 32 \right)^2\\\\\implies \left(x + \dfrac 32 \right)^2 = -21+\dfrac 94\\\\\implies \left(x + \dfrac 32 \right)^2 = -\dfrac{75}4\\\\\implies x+ \dfrac 32 = \pm\sqrt{-\dfrac{75}4 \right)\\\\\implies x + \dfrac 32 = \pm i \dfrac{5\sqrt 3}{2}\\\\\implies x = -\dfrac 32 \pm i \dfrac {5\sqrt 3}2\\\\\implies x = \dfrac 12 \left( -3 \pm  i5\sqrt 3\right)

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Answer:

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Step-by-step explanation:

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In which quadrant is the number –14 – 5i located on the complex plane?
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Positive numbers go to the right on the real axis and up on the imaginary axis, and vice versa for negative numbers.

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3 years ago
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ipn [44]

Answer:

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Step-by-step explanation:

7 0
3 years ago
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A university is building a new student center that is two- thirds the distance from the arts center to the residential complex.
Natasha2012 [34]

Answer:

C = (\frac{21}{5},\frac{33}{5})

Step-by-step explanation:

Given

Points: (1, 9) and (9, 3)

Ratio = 2/3

Required

Determine the coordinate of the center

Represent the ratio as ratio

Ratio = 2:3

The new coordinate can be calculated using

C = (\frac{mx_2 + nx_1}{n + m},\frac{my_2 + ny_1}{n + m})

Where

(x_1,y_1) = (1, 9)

(x_2, y_2) = (9, 3)

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Substitute these values in the equation above

C = (\frac{2 * 9 + 3 * 1}{3 + 2},\frac{2 * 3 + 3 * 9}{2 + 3})

C = (\frac{18 + 3}{5},\frac{6 + 27}{5})

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Hence;

<em>The coordinates of the new center is </em>C = (\frac{21}{5},\frac{33}{5})<em></em>

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3 years ago
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when X = 70

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Using the standard distribution tables, proportion is P1 = 0.0228

 

when X = 130

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Using the standard distribution tables, proportion is P2 = 0.9772

 

Therefore the proportion between X of 70 and 130 is:

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P (70<X<130) = 0.9772 - 0.0228

P (70<X<130) = 0.9544

 

Therefore 0.9544 or 95.44% of the test takers scored between 70 and 130.

6 0
3 years ago
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