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Sindrei [870]
1 year ago
8

Factor the polynomial expression 3x² + 2.

Mathematics
1 answer:
mel-nik [20]1 year ago
5 0

Answer:

\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}

Step-by-step explanation:

Setting the expression equal to zero to find the roots,

3x^2 +2=0\\\\3x^2 =-2\\\\x^2 =-\frac{2}{3}\\\\x=\pm i\sqrt{\frac{2}{3}}

This means that

3x^2 +2=\boxed{\left(x+i\sqrt{\frac{2}{3}}i \right)\left(x-i\sqrt{\frac{2}{3}}i \right)}

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Solve y = x + 6 for X.<br> x= y + 6<br> x= -y + 6<br> x = y - 6<br> x= -y - 6
damaskus [11]

Answer:

x=y-6

Step-by-step explanation:

First, flip the equation.

x+6=y

Finally, add -6 to both sides.

x+6+−6=y+−6

x=y−6

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2 years ago
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An umbrella is made by stitching 10 triangular pieces of clothes of 2 different colors, each piece measuring 9 cm, 40 cm and 41
malfutka [58]

Answer:

See below in bold.

Step-by-step explanation:

The triangular piece of cloth is a right triangle because 41^2 = 40^2 + 9^2 (By the Pythagoras theorem).

So the area of one piece = 1/2 * 9 * 40  cm^2.

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= 1800 cm^2.

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3 0
3 years ago
What is the equation of the quadratic graph with a focus of (4, −3) and a directrix of y = −6?
Artyom0805 [142]

Answer:

y=\frac{1}{6} (x-4)-\frac{9}{2}

Step-by-step explanation:

∵ The quadratic equation form is :

y = [1/2(b - k)] (x - a)² + (b + k)/2

Where (a , b) is the focus and directrix y = k

∵ The focus is (4 , -3) and directix is y = -6

∵ y=\frac{1}{2(-3-(-6))} (x-4)^{2}+\frac{(-3)+(-6)}{2}

∴ y=\frac{1}{6} (x - 4)^{2}+\frac{-9}{2}

∴ y=\frac{1}{6} (x-4)-\frac{9}{2}

another way:

Assume that (x , y) is the general point on the parabola

∵ The distance between the directrix and (x , y) = the distance between the focus and (x , y)

By using the distance rule:

∵ (y - -6)² = (x - 4)² + (y - -3)² ⇒ (y + 6)² = (x - 4)² + (y + 3)

∴ y² + 12y + 36 = (x - 4)² + y² + 6y + 9

∴ 12y - 6y = (x - 4)² + 9 - 36

∴ 6y = (x - 4)² - 27 ⇒ ÷ 6

∴ y = 1/6 (x - 4)² - 9/2

4 0
3 years ago
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4vir4ik [10]

Answer: i don't need the money but i can try to help you

Step-by-step explanation:

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2 years ago
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guajiro [1.7K]

Answer:

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Step-by-step explanation:

3/5 + 1/10

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