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Wittaler [7]
2 years ago
15

Could someone explain why the value of x is (-2).​

Mathematics
2 answers:
irina [24]2 years ago
8 0

Answer:

x=-2

Step-by-step explanation:

<u>Given equation</u>:

2x^3+16=0

To <u>solve</u> for the <u>unknown variable x</u>, apply <u>arithmetic operations</u> to <u>isolate the variable</u>.

Subtract 16 from both sides:

\implies 2x^3+16-16=0-16

\implies 2x^3=-16

Divide both sides by 2:

\implies \dfrac{2x^3}{2}=\dfrac{-16}{2}

\implies x^3=-8

Take the cube root of both sides:

\implies \sqrt[3]{x^3}=\sqrt[3]{-8}

\implies x=-2

When taking the <u>cube root of a negative number</u>, the result will be negative.  To understand why, examine what happens when we cube a negative number.

When a number is cubed, it is multiplied by itself, then by itself again.

When multiplying a <u>negative number</u> by another <u>negative number</u>, the result is always positive.

When multiplying a <u>positive number</u> by a <u>negative number</u>, the result is always negative.

Therefore:

\begin{aligned}\implies (-2)^3 &= -2 \cdot -2 \cdot -2\\ & = 4 \cdot -2\\& = -8\end{aligned}

So if -8 is cube rooted, the result is -2.

Artyom0805 [142]2 years ago
6 0

Answer:

x = -2

Step-by-step explanation:

2x^3 +16 = 0

We are solving for x

Subtract 16 from each side

2x^3 +16- 16 = 0-16

2x^3 = -16

Divide each side by 2

(2x^3 ) /2 = -16/2

x^3 = -8

Take the cube root of each side

\sqrt[3]{x^3} = \sqrt[3]{-8}

x = -2

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I have X, I just need Y.
GarryVolchara [31]

I'm getting x = 9.3223 which rounds to 9.32. Nice work.

Once you know the value of x, you can use the law of sines to find the value of y

sin(A)/a = sin(B)/b

sin(y)/7 = sin(70)/x

sin(y)/7 = sin(70)/9.3223

sin(y) = 7*(sin(70)/9.3223)

sin(y) = 0.70560358983312

y = arcsin(0.70560358983312)

y = 44.8783278056846

<h3>y = 44.88 approximately</h3>

------------------------------

If you must use the law of cosines, then here's how you could do it

c^2 = a^2 + b^2 - 2*a*b*cos(C)

7^2 = x^2 + 9^2 - 2*x*9*cos(y)

7^2 = (9.3223)^2 + 9^2 - 2*9.3223*9*cos(y)

49 = 86.90527729+81-167.8014cos(y)

49 = 167.90527729-167.8014cos(y)

-167.8014cos(y) = 49-167.90527729

-167.8014cos(y) = -118.90527729

cos(y) = -118.90527729/(-167.8014)

cos(y) = 0.708607182598

y = arccos(0.708607182598)

y = 44.8782954209662 ... this is slightly different from before due to rounding error

<h3>y = 44.88 approximately</h3>
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3 years ago
Which of the following are endpoints of the segments shown in the picture? Check all that apply.
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Someone please answer 28 points please answer with the right facts and the explanation thank you
Otrada [13]

Answer:

The transformation

(x,y) \rightarrow (x-5,-y+1)

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Step-by-step explanation:

Let us take point Z on the XYZ triangle and see what sequence of transformations we have to apply to map it into the point Z''.

Now Z = (-2, 2) and Z'' = (-7, -1).

The x-coordinate goes from -2 ⇒ -7.

The y-coordinate goes from 2 ⇒  -1.

The x-coordinate is just shifted by -5; thus, x \rightarrow x-5, and the y-coordinate first transforms as y \rightarrow -y, and is then shifted by 1; thus, it transforms as y \rightarrow -y+1.

So we have the full transformation

(x,y) \rightarrow (x-5,-y+1)

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Step-by-step explanation:

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