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2 years ago

In two or more complete sentences, explain how to solve the cube root equation, .^3√x-1+2=0

Mathematics

1 answer:

Strike441 [17]2 years ago

4 0

Answer:

$x= -7$

Step-by-step explanation:

We need to solve the following root equation:

$\sqrt[3]{x-1} + 2 = 0$

1. First, we need to add minus two to both sides of the equation:

$\sqrt[3]{x-1}= -2$

2. Elevate each side of the equation to the power of 3:

$x-1= -8$

3. Solve for 'x':

$x= -8 + 1$

$x= -7$

Therefore, the result is:

$x= -7$ ✔️

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Rationalize the denominator of $\frac{5}{2+\sqrt{6}}$. The answer can be written as $\frac{A\sqrt{B}+C}{D}$, where $A$, $B$, $C$

horrorfan [7]

Answer:

$A +B+C+D = 3$ is the correct answer.

Step-by-step explanation:

Given:

$\frac{5}{2+\sqrt{6}}$

To find:

$A+B+C+D = ?$ if given term is written as following:

$\frac{A\sqrt{B}+C}{D}$

Solution:

We can see that the resulting expression does not contain anything under $\sqrt$ (square root) so we need to rationalize the denominator to remove the square root from denominator.

The rule to rationalize is:

Any term having square root term in the denominator, multiply and divide with the expression by changing the sign of square root term of the denominator.

Applying this rule to rationalize the given expression:

$\dfrac{5}{2+\sqrt{6}} \times \dfrac{2-\sqrt6}{2-\sqrt6}\\\Rightarrow \dfrac{5 \times (2-\sqrt6)}{(2+\sqrt{6}) \times (2-\sqrt6)} \\\Rightarrow \dfrac{10-5\sqrt6}{2^2-(\sqrt6)^2}\ \ \ \ \ (\because \bold{(a+b)(a-b)=a^2-b^2})\\\Rightarrow \dfrac{10-5\sqrt6}{4-6}\\\Rightarrow \dfrac{10-5\sqrt6}{-2}\\\Rightarrow \dfrac{-5\sqrt6+10}{-2}\\\Rightarrow \dfrac{5\sqrt6-10}{2}$

Comparing the above expression with:

$\frac{A\sqrt{B}+C}{D}$

A = 5, B = 6 (Not divisible by square of any prime)

C = -10

D = 2 (positive)

GCD of A, C and D is 1.

So, $A +B+C+D = 5+6-10+2 = \bold3$

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3 years ago

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gavmur [86]

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3 years ago

What is the sum of 1/4 and 3/8

kupik [55]

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3 years ago

While mining, Jason found a large metal bar that weighed 24 ounces. Jason was also able to determine that the bar had 6 ounces o

tino4ka555 [31]

25% 6 divided by 24 will give you the percentage of copper in the bar

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3 years ago

- 5.8c + 4.2 - 3.1 + 1.4c − 5.8c + 4.2 − 3.1 + 1.4c

Cerrena [4.2K]

Answer:

-8.8c + 2.2 OR SOLVED c = 0.25

Step-by-step explanation:

Step 1: Combine like terms

- 5.8c + 4.2 - 3.1 + 1.4c − 5.8c + 4.2 − 3.1 + 1.4c

-8.8c + 2.2

Step 2: If needed solve for c

-8.8c + 2.2 - 2.2 = 0 - 2.2

-8.8c / -8.8 = -2.2 / -8.8

c = 0.25

Answer: -8.8c + 2.2 OR SOLVED c = 0.25

8 0

2 years ago

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