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4 years ago

Rationalize the denominator

Mathematics

2 answers:

fenix001 [56]4 years ago

7 0

The fraction is a cubic root, so to rationalize the denominator, you would multiply them by 3.

The answer is b. 3

bearhunter [10]4 years ago

7 0

Answer:

Step-by-step explanation:

There are many ways of seeing this problem. One of them is

cube root(5) / cube root (9) which translates to

cube root(5)/ cube root(3*3)

To rationalize the denominator you need another 3 in the denominator.

Rule: To rationalize anything, you need the power in denominator to be divisible by the power on the denominator. Whatever it takes to get it up to get it to a number that is divisible by the root is what you multiply the denominator by.

So in this case, you need 3 threes in the denominator. You have 2. You need 1 more. If you add 1 more root in the denominator, you must do the same in the numerator.

cube root(5)*cube root (3) / (cube root (3 * 3) * cube root (3) )

cube root (15) / cube root (3 * 3 * 3)

cube root (15) / 3

Answer B is the closest.

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4 years ago

What is eight time the diffrence of a number and 2 is the same as 3 times the sumof the number and 3

ale4655 [162]

eight time the difference of a number and 2 is the same as 3 times the sum of the number and 3

8* (n-2) = 3*(n+3)

distribute

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subtract 3n from each side

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3 years ago

Perform each indicated operation

MissTica

Answer: $\frac{x+6}{x-4}$

Step-by-step explanation:

First you need know some general formuals of factorization such as

$x^3+y^3=(x+y)(x^2-xy+y^2)$ so you have $x^3+64=X^3+4^3=(x+4)(x^2-4x+4^2)$

And, $x^2-y^2=(x-y)(x+y)$ so you have $2x^2-32=2(x^2-16)=2(x^2-4^2)=2(x+4)(x-4)$

If you use them, then you can modify your equations such as

$\frac{x^3+64}{2x^2-32}$ ÷ $\frac{x^2-4x+16}{2x+12}$ = $\frac{(x+4)(x^2-4x+4^2)}{2(x+4)(x-4)}$ ÷ $\frac{x^2-4x+16}{2(x+6)}$ = $\frac{(x+4)(x^2-4x+4^2)}{2(x+4)(x-4)} . \frac{2(x+6)}{{x^2-4x+16}} = \frac{1}{x-4}.\frac{x+6}{1}=\frac{x+6}{x-4}$

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3 years ago

To solve y and x, I am adding a picture

Viktor [21]

Answer:

$x =\sqrt 5$

$y = \sqrt{5$

Step-by-step explanation:

Given

The attached triangle

Required

Solve for x

Considering angle 45 degrees, we have:

$\cos(45) = \frac{y}{\sqrt{10}}$ --- cosine formula i.e. adj/hyp

Solve for y

$y = \sqrt{10} * \cos(45)$

In radical form, we have:

$y = \sqrt{10} * \frac{1}{\sqrt 2}$

$y = \sqrt{10/2}$

$y = \sqrt{5$

To solve for x, we make use of Pythagoras theorem

$x^2 + y^2 = (\sqrt{10})^2$

$x^2 + y^2 =10$

Substitute for y

$x^2 + (\sqrt 5)^2 =10$

$x^2 + 5 =10$

Collect like terms

$x^2 =10-5$

$x^2= 5$

Solve for x

$x =\sqrt 5$

4 0

3 years ago

An equilateral triangle is a triangle with __ congruent side

kupik [55]

Answer:

3 congruent sides

Step-by-step explanation:

When a triangle has three congruent sides, we call the triangle an equilateral triangle. We mark the congruent sides by a slash mark. The angles in an equilateral triangle are always 60°. When a triangle has two congruent sides it is called an isosceles triangle.

5 0

3 years ago

Rationalize the denominator​

Rationalize the denominator