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2 years ago

What are the roots of this quadratic equation?-10x^2+12x-9=0

Mathematics

1 answer:

Ugo [173]2 years ago

7 0

Answer:

Step-by-step explanation:

-10x² + 12x - 9 = 0

Multiply the whole equation by (-1)

10x² - 12x + 9 = 0

a = 10 ; b = -12 ; c = 9

D = b² - 4ac = (-12)² - 4*10*9

= 144 - 360

= -216

√D = √-216 = $\sqrt{2*2 * 3 * 3 * 2 *3 * i^{2}}$

$= 2*3*i*\sqrt{3*2}\\\\= 6i \sqrt{6}$

Roots = $\frac{-b + \sqrt{D}}{2a} ; \frac{-b-\sqrt{D}}{2a}$

$= \dfrac{-[-12]+6i\sqrt{6}}{2*10} \ ; \ \dfrac{-[-12] - 6i\sqrt{6}}{2*10}\\\\= \dfrac{12+6i\sqrt{6}}{20} ; \ \dfrac{12-6i\sqrt{6}}{20}\\\\\\= \dfrac{2*(6+3i\sqrt{6}}{20} ; \ \dfrac{2*(6-3i\sqrt{6}}{20}\\\\=\dfrac{6+3i\sqrt{6}}{10} ; \dfrac{6-3i\sqrt{6}}{10}$

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Nadusha1986 [10]

Answer:

Linear: greater than 2011

Quadratic: lesser than 2011

Cubic: lesser than 2011

Step-by-step explanation:

At x = 2

Linear regression equation:

y = -6777.54(2) + 110001.04

y = 96445.96

More than 2011

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y = 92093.62

lesser than 2011

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3 years ago

Describe the piecewise function below by evaluating the function for given values of the domain

tekilochka [14]

We have a piecewise function.
Therefore, to find the function, we must evaluate each domain separately.
We have then:

For $x \leq -2$ :
The function for this domain is:
$y = -3
$

For $-2 \ \textless \ x \leq 2$ :
The function for this domain is:
$y = mx + b
$
Where,
$b = -3

 m = (y2 - y1) / (x2 - x1)

 m = (1 - (-7)) / (2 - (-2))$
$m = (1 + 7) / (2 + 2)

 m = 8/4

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For $x\ \textgreater \ 2$ :
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3 years ago

Equivalent to 28xy+16x

snow_tiger [21]

Answer:

$4x(7y+4)$

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2 years ago

A candy store called "Sugar" built a giant sugar cube out of wood to hang above the entrance to their store. It took 545454 feet

DedPeter [7]

Answer:

The volume inside the giant sugar cube is 27 cubic feet.

Step-by-step explanation:

It took 54 feet² of material to build the giant sugar cube. That means, the total surface area of the cube is 54 feet²

Formula for surface area of a cube is: $S= 6a^2$ , where $a$ is the length of each edge of the cube.

So, we will get.........

$6a^2=54\\ \\ a^2= \frac{54}{6}=9 \\ \\a= \sqrt{9}= 3$

Now, the volume of the cube will be: $V= a^3= (3)^3 = 27$ feet³

Thus, the volume inside the giant sugar cube is 27 cubic feet.

3 0

2 years ago

Based on historical data, your manager believes that 40% of the company's orders come from first-time customers. A random sample

Vedmedyk [2.9K]

Answer:

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