Mathematics, 23.08.2020 01:01 fatimah89

$\sqrt{24n^3}$ (simplify radical) please show work

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Answer from: aria0826

The answer is

$2n \sqrt{6n}$

Step-by-step explanation:

$\sqrt{24 {n}^{3} }$

First of all factor out the perfect square out.

In this question the perfect squares are 4 and x²

So we have

$\sqrt{4 \times {n}^{2} \times 6n}$

Separate the radicals

That's

$\sqrt{4} \times \sqrt{ {n}^{2} } \times \sqrt{6n}$

Simplify

$\sqrt{4} = 2 \\ \sqrt{ {n}^{2} } = n$

So we have

$2 \times n \times \sqrt{6n}$

We have the final answer as

$2n \sqrt{6n}$

Hope this helps

Answer from: Quest

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

$4/2 = 2\\7/3.5=2\\8/4=2\\10/5=2$

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

$y=\frac{x}{2}$

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

Answer from: Quest

answer: b. f(x) = (x + 2)^3 (x^2 - 7x + 3)^4

step-by-step explanation:

polynomials always have as many roots as their order. this is a 4th order polynomial- hence 4 roots!

complex roots of polynomials always come in pairs. the quadratic equation has the "+/-" in that will alwaysgenerate m+ni amd m-ni, so 7-2i must be a root of this polynomial equation.

the order of the numerator and denominator are both 2. so the horizontal asymptote is y=a2/b2 =7

verticle asymptotes are the forbidden x-values. f(x) becomes undefined at x=-3 because this value will cause a zero denominator.

a graph of r(x) will have vertical asymptotes at ±1 because these values will make the denominator zero. so the domain of the function cannot include ±1.

you 're wlecome! : )

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