A rectangular patio has a length of (3x-6) and a width of 5x, find the perimeter in simplest form

3x ^2 - 9 x y ^2+ 12 X ^3Y^2

shepuryov [24]

$\huge \boxed{\mathfrak{Question} \downarrow}$

$3 x ^ { 2 } y - 9 x y ^ { 2 } + 12 x ^ { 3 } y ^ { 2 }$

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$3 x ^ { 2 } y - 9 x y ^ { 2 } + 12 x ^ { 3 } y ^ { 2 }$

Factor out $3$ .

$3\left(x^{2}y-3xy^{2}+4x^{3}y^{2}\right)$

Consider $x^{2}y-3xy^{2}+4x^{3}y^{2}$ . Factor out $xy$ .

$xy\left(x-3y+4x^{2}y\right)$

Rewrite the complete factored expression.

$\boxed{ \boxed{ \bf \: 3xy\left(x-3y+4x^{2}y\right) }}$

4 0

3 years ago

It is given that 2(3 + x) = 6 + 2x. This is an example of the ___________ property.

Reptile [31]

Answer:

Distributive Property

Step-by-step explanation:

Here is the problem:

2(3 + x)

Here is the answer 6 + 2x

Method to solve it:

a(b+c) = ab + ac

Let's substitute numbers for letters:

2(3 + x)

2*3 = 6

2 * x = 2x

=

6 + 2x

Best Of Luck,

- I.A. -

4 0

3 years ago

Find the distance between a point (– 2, 3 – 4) and its image on the plane x+y+z=3 measured parallel to a line

Ber [7]

Answer:

The distance is:

$\displaystyle\frac{3\sqrt{142}}{10}$

Step-by-step explanation:

We re-write the equation of the line in the format:

$\displaystyle\frac{x+2}{3}=\frac{y+\frac{3}{2}}{2}=\frac{z+\frac{4}{3}}{\frac{5}{3}}$

Notice we divided the fraction of y by 2/2, and the fraction of z by 3/3.

In that equation, the director vector of the line is built with the denominators of the equation of the line, thus:

$\displaystyle\vec{v}=\left< 3, 2, \frac{5}{3}\right>$

Then the parametric equations of the line along that vector and passing through the point (-2, 3, -4) are:

$x=-2+3t\\y=3+2t\\\displaystyle z=-4+\frac{5}{3}t$

We plug them into the equation of the plane to get the intersection of that line and the plane, since that intersection is the image on the plane of the point (-2, 3, -4) parallel to the given line:

$\displaystyle x+y+z=3\to -2+3t+3+2t-4+\frac{5}{3}t=3$

Then we solve that equation for t, to get:

$\displaystyle \frac{20}{3}t-3=3\to t=\frac{9}{10}$

Then plugging that value of t into the parametric equations of the line we get the coordinates of the intersection:

$\displaystyle x=-2+3\left(\frac{9}{10}\right)=\frac{7}{10}\\\displaystyle y=3+2\left(\frac{9}{10}\right)=\frac{24}{5} \\\displaystyle z=-4+\frac{5}{3}\left(\frac{9}{10}\right)=-\frac{5}{2}$

Then to find the distance we just use the distance formula:

$\displaystyle d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2+(z_1-z_2)^2}$

So we get:

$\displaystyle d=\sqrt{\left(-2-\frac{7}{10}\right)^2+\left(3-\frac{24}{5}\right)^2+\left(-4 +\frac{5}{2}\right)^2}=\frac{3\sqrt{142}}{10}$

3 0

3 years ago

Suppose you want to play four music CDs at your party. How many different orders can you

joja [24]

24 <span>different orders can you </span>choose to play them so that will be the best answer

8 0

4 years ago

the basketball team sold t shirts and hats as a fundrasier they sold a total of 23 items and made a profit of 246 the made a pro

Gnesinka [82]

s - the number of the t-shirts;

h - the number of hats:

The system of equations:

s + h = 23

10 s + 12 h = 246

--------------------------

s = 23 - h

10 * ( 23 - h ) + 12 h = 246

230 - 10 h + 12 h = 246

2 h = 246 - 230

2 h = 16

h = 16 : 2

h= 8

s = 23 - 8

s = 15

Answer: The basketball team sold 15 t-shirts and 8 hats.

mark me as brainliest answer

6 0

3 years ago