5s=13 what is the answer

What is the factored form of this expression? 27m^3 +125n^3

ddd [48]

Answer:

$\left(3m+5n\right)\left(9m^2-15mn+25n^2\right)$

Step-by-step explanation:

$27m^3+125n^3=\left(3m\right)^3+\left(5n\right)^3$

Apply sum of cubes formula: $x^3+y^3=\left(x+y\right)\left(x^2-xy+y^2\right)$

$\left(3m\right)^3+\left(5n\right)^3=\left(3m+5n\right)\left(3^2m^2-3m\times 5n+5^2n^2\right)$

$\left(3m+5n\right)\left(9m^2-15mn+25n^2\right)$

5 0

2 years ago

Read 2 more answers

Which is a correct step in solving the following equation for g?

OleMash [197]

1. -2g = 1.75 -4
-g = -2.25/2
g = 1.12

8 0

3 years ago

Radical form of f(x)=3+2 in X

kondor19780726 [428]

The answer would be -17 because i know

6 0

3 years ago

An opaque cylindrical tank with an open top has a diameter of 3.25 m and is completely filled with water. When the afternoon Sun

kicyunya [14]

Answer:

10.69

Step-by-step explanation:

We must first know that the angle of refraction is given by the following equation:

n_water * sin (A_water) = n_air * sin (A_air)

where n is the refractive index, for water it is 1.33 and for air it is 1.

The angle (A) in the air is 22.8 °, and that of the water is unknown.

Replacing these values we have to:

1.33 * sin (A_water) = 1 * 0.387

sin (A_water) = 1 * 0.387 / 1.33

A_water = arc sin (0.2907) = 16.9 °

now for the tank depth:

h = D / tan (A_water)

D = 3.25

Replacing

h = 3.25 / tan 16.9 °

h = 10.69

Therefore the depth is 10.69 meters.

6 0

2 years ago

The prices of commodities X,Y,Z are respectively x, y, z, rupees per unit. Mr. A purchases 4 units of Z and sells 3 units of X a

liubo4ka [24]

Answer:

$(x,y,z)=(1477, 1464, 1437)$

Step-by-step explanation:

Consider the selling of the units positive earning and the purchasing of the units negative earning.

Mr. A purchases 4 units of Z and sells 3 units of X and 5 units of Y
Mr.A earns Rs6000

So, the equation would be

$3x + 5y - 4z = 6000$

Mr. B purchases 3 units of Y and sells 2 units of X and 1 units of Z
Mr B neither lose nor gain meaning he has made 0₹

hence,

$2x - 3y + z = 0$

Mr. C purchases 1 units of X and sells 4 units of Y and 6 units of Z
Mr.C earns 13000₹

therefore,

$- x + 4y + 6z = 13000$

Thus our system of equations is

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

<u>Solving </u><u>the </u><u>system </u><u>of </u><u>equations</u><u>:</u>

we will consider elimination method to solve the system of equations. To do so ,separate the equation in two parts which yields:

$\begin{cases}3x + 5y - 4z = 6000\\2x - 3y + z = 0\end{cases}\\\begin{cases}2x - 3y + z = 0\\ - x + 4y + 6z = 13000\end{cases}$

Now solve the equation accordingly:

$\implies\begin{cases}11x-7y=6000\\-13x+22y=13000\end{cases}$

Solving the equation for x and y yields:

$\implies\begin{cases}x= \dfrac{223000}{151}\\\\y= \dfrac{221000}{151}\end{cases}$

plug in the value of x and y into 2x - 3y + z = 0 and simplify to get z. hence,

$\implies z= \dfrac{217000}{151}$

Therefore,the prices of commodities X,Y,Z are respectively approximately 1477, 1464, 1437

6 0

2 years ago