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2 years ago

Which is equivalent to 5 Square root of 1215^x

Mathematics

2 answers:

tia_tia [17]2 years ago

8 0

Answer:

$(3\sqrt[5]{5} )^{x}$

Step-by-step explanation:

Given that

$\sqrt[5]{1215^{x} }$

=> $1215^{\frac{x}{5} }$ Using radical rule

=> $(3*3*3*3*3*5)^{\frac{x}{5} }$

=> $(3^{5} * 5 )^{\frac{x}{5} }$

=> $(3^{5*\frac{1}{5} } * 5 )^{x}$

=> $(3*5^{\frac{1}{5} } )^{x}$

=> $(3\sqrt[5]{5} )^{x}$

drek231 [11]2 years ago

3 0

Answer:

$5\sqrt{1215^{x}}\Rightarrow 45\sqrt{15^{x}}\:\:or\:\:45*15^{\frac{x}{2}}$

Step-by-step explanation:

1) Performing Prime Factorization

$\\1215|3\\405|3\\135|3\\45|3\\15|3\\5|5\\1\Rightarrow 3^{2}*3^{3}*5$

2) Simplifying

$5\sqrt{3^{2}*3^{2}*3*5}\Rightarrow 5*9\sqrt{15^{x}}\Rightarrow 45\sqrt{15^{x}}$

3) Rewriting it as a power, where the denominator is the index, and the numerator is the exponent:

$45\sqrt{15^{x}}\:\:=\:\:45*15^{\frac{x}{2}}$

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Write the monomial in standard form. name it's coefficient and identify its degree.

Hunter-Best [27]

Answer:

$Standard\ Form = {3n^2} m^{-2}$

Step-by-step explanation:

Given

$\frac{2}{3m^2n} * 4.5n^3$

Required

Write in Standard Form

To start with; the two monomials have to be multiplied together;

$\frac{2}{3m^2n} * 4.5n^3$

$Standard\ Form = \frac{2 * 4.5n^3}{3m^2n}$

Split the numerator and the denominator

$Standard\ Form = \frac{2 * 4.5 * n^3}{3 * m^2 * n}$

Multiply Like terms

$Standard\ Form = \frac{9 * n^3}{3 * m^2 * n}$

Divide 9 by 3 to give 3

$Standard\ Form = \frac{3 * n^3}{m^2 * n}$

Divide n³ by n to n²

$Standard\ Form = \frac{3 * n^2}{m^2 }$

Split fraction

$Standard\ Form = {3 * n^2} * \frac{1}{m^2 }$

From laws of indices;

$\frac{1}{a^n} = a^{-n}$

$Standard\ Form = {3 * n^2} * \frac{1}{m^2 }$ becomes

$Standard\ Form = {3 * n^2} * m^{-2}$

Multiply all together

$Standard\ Form = {3n^2} m^{-2}$

5 0

3 years ago

What are the exact solutions of x2 − 5x − 1 = 0 using x equals negative b plus or minus the square root of the quantity b square

geniusboy [140]

Answer:

$x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}$

Step-by-step explanation:

So the question here is asking you to use the quadratic formula which is expressed as: $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\$

A quadratic can generally be expressed as: $y=ax^2+bx+c$

So using the equation you gave: $0=x^2-5x-1$

We can identify the following values: a=1, b=-5, c=-1

Btw the equation explicitly write "1" as the coefficient of x, but since it's not provided it's implied that it's 1.

So plugging in the known values, we get the following equation:

$x=\frac{5\pm\sqrt{(-5)^2-4(1)(-1)}}{2(1)}\\\\x=\frac{5\pm\sqrt{25+4}}{2}\\\\x=\frac{5\pm\sqrt{29}}{2}\\\\x=2.5+\frac{\sqrt{29}}{2}\\\\x=2.5-\frac{\sqrt{29}}{2}$

The last step just consists of taking the + and - solution, and since it asks for exact solutions you leave the 29 under the radical, and you don't approximate. There is no further simplification that can be done here.

5 0

1 year ago

Please help me IDk this at all!!!!

jasenka [17]

It would help if you find common denominator... 12
so 1/3 times 4 both the numerator and denominator
4/12

and 3/4 times by 3 both the numerator and denominator
9/12

the recipe calls for 4/12 cup of oil and you have 9/12

two batches would be 8/12 cups of oil, you have 9/12 that is just enough for the recipe for two batches...

now to simplify it again, 1/3 + 1/3 = 2/3 and 2/3 is less than 3/4
the answer would be the upper right

3 0

3 years ago

Read 2 more answers

Which inequality statement describes the two numbers on a number line? "16 and a number 10 units to the left of 16" A) 6 > 16

Ivenika [448]

The answer is c because the two numbers on a number line 16 will be greater then 10

4 0

3 years ago

Hannah is a photographer who specializes in portraits. This morning, she soent four hours doing graduation portrait sessions. In

FromTheMoon [43]

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2 years ago