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2 years ago

Express the radical using the imaginary unit i

Mathematics

1 answer:

diamong [38]2 years ago

6 0

Answer:

$i$ $\sqrt{30}$

Step-by-step explanation:

$\sqrt{-30}$

= $\sqrt{30 * -1}$

= $\sqrt{30} * \sqrt{-1}$ Separate the two numbers into 2 radicals.

= $i\sqrt{30}$ Simplify, knowing that $i = \sqrt{-1}$ .

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Write this equation in vertex form. y = x^2 -12x +20

kotegsom [21]

Answer:

$y = (x-6) ^ 2 -16$

Step-by-step explanation:

The vertex form for a quadratic equation has the following form:

$y = (x-h) ^ 2 + k$

Where the vertice of the equation is the point (h, k)

To transform the equation $y = x ^ 2 -12x +20$ in its vertex forms we must find its vertex.

Be a quadratic equation of the form:

$ax ^ 2 + bx + c$

Where a, b and c are real numbers, then the vertex of the equation will be:

$x = - \frac{b}{2a}$

For the given equation:

$b = -12\\a = 1$

Therefore the vertice is:

$x = - \frac{-12}{2(1)}\\\\x = 6$

Now we substitute x = 6 into the equation and find the value of k.

$y = (6) ^ 2 -12 (6) +20\\\\y = -16 = k$

Therefore the vertice is: (6, -16)

And the equation is:

$y = (x-6) ^ 2 -16$

8 0

2 years ago

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Find the missing side. Round to the nearest tenth.

Firdavs [7]

Answer: 23.7

Step-by-step explanation:

Let's calculate the acute angle at the base of the triangle:

180° - 90° - 40° = 50°

Find side x:

$\dfrac{sin \: 90^{o} }{31} =\dfrac{sin \: 50^{o} }{x}\\\\sin \: 90^{o} \cdot x=sin \: 50^{o} \cdot 31\\\\sin \: 90^{o} =1\\sin \: 50^{o} \approx 0.766\\1 \cdot x =0.766 \cdot 31\\x=23.746\\23.746 \approx 23.7$

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2 years ago

Select the correct answer.

-Dominant- [34]

Answer:

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Step-by-step explanation:

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2 years ago

Nia plans to put enough money in the bank each week for 100 weeks so that the amount in the bank is always proportional to the w

garri49 [273]

Answer:

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Step-by-step explanation:

2 1/2 times the week

8 x 2.5 = 20

12 x 2.5 = 30

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3 years ago

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If a radius of a circle is perpendicular to a chord, then it _____ that chord.

labwork [276]

The answer is b. There is a proof, but it is easily got by proving the other cases wrong.

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3 years ago

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