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neonofarm [45]
3 years ago
14

Solve the quadratic equation by completing the square.

Mathematics
1 answer:
nikklg [1K]3 years ago
6 0

Answer:

x = - 1 + 2i,  \:  \:  - 1 - 2i

Step-by-step explanation:

{x}^{2}  + 2x + 5 = 0 \\  \\  {x}^{2}  + 2x + 1 + 4 = 0 \\  \\  {x}^{2}  + 2x + 1 =  - 4 \\  \\  {(x + 1)}^{2}  =  - 4 \\  \\ (x + 1) =  \pm \sqrt{ - 4} \\  \\ x + 1 =  \pm 2i \\  \\ x =   - 1\pm 2i  \\  \\ x =  - 1 + 2i, \:  \: x =  - 1 - 2i \\  \\ x = - 1 + 2i,  \:  \:  - 1 - 2i

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The population correlation coefficient is significant if the correlation is closer to 1, less significant is closer to zero, and not significant at all if the correlation coefficient is zero.

  • Correlation coefficients are used in determining the significance of a population and the strength of the relationship <u>between two variables. </u>

  • This relationship can either be strong, weak, or not exist.

  • The correlation coefficient can have values between 0 and 1 inclusive.  The population correlation coefficient is significant if the correlation is closer to 1, less significant is closer to zero, and not significant at all if the correlation coefficient is zero.

Learn more on correlation here: brainly.com/question/13879362

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3 years ago
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4 years ago
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Velocity is given as 80 feet per second, so replace V with 80.

The rocket is launched from the ground so the initial height is 0, so replace h with 0


The formula now becomes" h(t) = -16t^2 + 80t +0


To find the maximum we need to find the coordinates of the vertex by finding the axis of symmetry:

-b/2a = -80/(2*-16) = -80/-32 = 2.5

This represents the amount of time for the rocket to reach maximum height.

So we now replace t in the equation with 2.5 and solve for the height:

h(2.5) = -16(2.5)^2 + 80(2.5)

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4 0
3 years ago
A triangle has two sides measuring 16 and 21. The included angle is 116°. What is the length of the side opposite the 116° angle
Crank

Answer:

Length of the side opposite to angle 116^{\circ} is 31.49

Step-by-step explanation:

Included angle can be defined as the angle in between two sides of the triangle.

So angle 116^{\circ} is in between sides 16 and 21.

Refer to the attachment for triangle diagram.

To find the length of opposite side, use cosine rule as follows

a^{2}=b^{2}+c^{2}-2\:b\:c\cos\left(A\right)

From the diagram, b = 21,c = 16,\angle A=116^{\circ}

Substituting the values in the formula,

a^{2}=\left(21\right)^{2}+\left(16\right)^{2}-2\left(21\right)\left(16\right)\cos\left(116\right)

Simplifying,

a^{2}=441+256-225792\left(-0.44\right)

a^{2}=991.59

Taking square root on both sides,

\sqrt{a^{2}}=\sqrt{991.59}

a=31.49

Therefore length of third side is 31.49

7 0
3 years ago
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