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3 years ago

X^3 - 8 = x - 2 Solve the equation for all values of x

1 answer:

8 0

X³-8=x-2: Original equation.
x³-x-6=0: Subtract x and add 2 to both sides.
(x-2)(x²+2x+3): Factor the equation
x-2=0; x²+2x+3=0: Separate the expressions into equations
x=2: Add 2 to both sides
x²+2x+3=0: Quadratic Formula
x= 2, -2+√-8,-2-√-8
 2 2

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PLEASE ANSWER ASAP!!! SHOW ALL THE STEPS.

fenix001 [56]

Answer:

For the first question $x = 4\\ y = -1$ and

For the second question $x = 0.5\\ y = -1$

Step-by-step explanation:

Given:

x - 3y = 7

3x + 3y = 9

8x+ 3y = 1

4x + 2y = 0

Elimination method :

In the elimination method we need to make the coefficient of x or the coefficient of y same in both the equation so by adding or subtracting we can eliminate the x term or the y term.

Then substitute that values which you will get on eliminating in any equation you will get the corresponding value.

For the first question, the y coefficient is same hence by adding both the equation we can eliminate 3y term. so on solving we get

$(x - 3y) + (3x + 3y) = 7 + 9\\4x = 16\\x = \frac{16}{4}\\x = 4$

Now substitute X equal to 4 in equation x -3y = 7 we get

$4 - 3y = 7\\-3y = 7 - 4\\-3y = 3\\y = \frac{3}{-3}\\ y = -1\\$

This way we have x is equal to 4 and y is equal to -1 for question number 1.

For the second question, we will make X coefficient same in the second equation that is multiplying by 2 to the equation 4x + 2y = 0 then we get

$8x + 4y = 0\\$

Now the coefficient of x term become same now we will subtract the two equations that is 8x + 3y = 1 and 8x + 4y =0 we get

$(8x + 3y) - (8x + 4y) = 1 - 0\\3y - 4y = 1\\ -y = 1\\y = -1$

Now substitute y equal to -1 in equation 8x +3y = 1 we get

$8x + 3\times -1 = 1\\8x - 3 = 1\\8x = 1 + 3\\8x = 4\\x = \frac{4}{8}\\ x = 0.5\\$

This way we have x is equal to 0.5 and y is equal to -1 for question number 2.

3 0

3 years ago

He Mercedes S-Class luxury vehicle depreciates by 32.4% after just one year. The starting price in 2015 was $70,000.

kumpel [21]

the depreciation amount after one year for the Mercedes S-Class vehicle is $22,680 .

Step-by-step explanation:

Here we have , he Mercedes S-Class luxury vehicle depreciates by 32.4% after just one year. The starting price in 2015 was $70,000. We need to find What is the depreciation amount after one year for the Mercedes S-Class vehicle. Let's find out:

The starting price in 2015 was $70,000 , let's find price after one year i.e. in 2016 when Mercedes S-Class luxury vehicle depreciates by 32.4% ,According to question following equation is framed as :

⇒ $Price - \frac{Price(32.4)}{100}$

⇒ $70,000 - \frac{70,000(32.4)}{100}$

⇒ $70,000 - 700(32.4)$

⇒ $70,000 - 22,680$

⇒ $\$47,320$

Therefore , the depreciation amount after one year for the Mercedes S-Class vehicle is $22,680 .

4 0

3 years ago

Solving radical equation

Darya [45]

$\bf \sqrt{k-9}-\sqrt{k}=-1\implies \sqrt{k-9}=\sqrt{k}-1\impliedby \textit{squaring both sides}
\\\\\\
(\sqrt{k-9})^2=(\sqrt{k}-1)^2\implies k-9=(\sqrt{k}-1)(\sqrt{k}-1)\impliedby \textit{FOIL}
\\\\\\
k-9=k-2\sqrt{k}+1\implies -10=-2\sqrt{k}\implies \cfrac{-10}{-2}=\sqrt{k}
\\\\\\
\sqrt{\cfrac{-10}{-2}}=k$