Answer:
![-\frac{x^2y^2}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7Bx%5E2y%5E2%7D%7B2%7D)
Step-by-step explanation:
We have an extremely large equation and are asked to divide it, so let's solve it step-by-step :
Remove the parenthesis to make it easier to read :
![\frac{-3x^3 *2x^3y^4z *3z^2}{4x^3z*3yz*3xyz}](https://tex.z-dn.net/?f=%5Cfrac%7B-3x%5E3%20%2A2x%5E3y%5E4z%20%2A3z%5E2%7D%7B4x%5E3z%2A3yz%2A3xyz%7D)
Multiply the numerators :
![\frac{-18x^6y^4z^3}{4*3*3x^3yyzzz}](https://tex.z-dn.net/?f=%5Cfrac%7B-18x%5E6y%5E4z%5E3%7D%7B4%2A3%2A3x%5E3yyzzz%7D)
Multiply the denominators :
![\frac{-18x^6y^4z^3}{36x^4y^2z^3}](https://tex.z-dn.net/?f=%5Cfrac%7B-18x%5E6y%5E4z%5E3%7D%7B36x%5E4y%5E2z%5E3%7D)
Apply the negative rule :
![-\frac{18x^6y^4z^3}{36x^4y^2z^3}](https://tex.z-dn.net/?f=-%5Cfrac%7B18x%5E6y%5E4z%5E3%7D%7B36x%5E4y%5E2z%5E3%7D)
Cancel the common factor which is 18 :
![-\frac{x^6y^4z^3}{2x^4y^2z^3}](https://tex.z-dn.net/?f=-%5Cfrac%7Bx%5E6y%5E4z%5E3%7D%7B2x%5E4y%5E2z%5E3%7D)
Apply the addition exponent rule :
![\frac{y^4z^3x^{6-4} }{2y^2z^3}](https://tex.z-dn.net/?f=%5Cfrac%7By%5E4z%5E3x%5E%7B6-4%7D%20%7D%7B2y%5E2z%5E3%7D)
Subtract :
![\frac{x^2y^4z^3 }{2y^2z^3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2y%5E4z%5E3%20%7D%7B2y%5E2z%5E3%7D)
Apply the rule for y :
![\frac{x^2y^{4-2} z^3 }{2z^3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2y%5E%7B4-2%7D%20z%5E3%20%7D%7B2z%5E3%7D)
Subtract :
![\frac{x^2y^2z^3 }{2z^3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%5E2y%5E2z%5E3%20%7D%7B2z%5E3%7D)
Cancel the common factor of z^3 :
![-\frac{x^2y^2}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7Bx%5E2y%5E2%7D%7B2%7D)
16 is the answer. I can explain if you need
A rug is to fit in a room so that a border of even width is left on all four sides.
If the room is 16 feet by 25 feet and the area of the rug is 220 square feet, how wide will the border
:
Let x = the width of the border around the rug
then
(25-2x) by (16-2x) the dimensions of the rug
:
The area equation
(25-2x)*(16-2x) = 220 sq/ft
FOIL
400 - 50x - 32x + 4x^2 = 220
:
Arrange as a quadratic equation
4x^2 - 82x + 400 - 220 = 0
:
4x^2 - 82x + 180 = 0
Simplify, divide by 2
2x^2 - 41x + 90 = 0
Factor
(2x - 5)(x - 18) = 0
Two solutions
2x = 5
x = 2.5 ft
and
x = 18 ft, obviously this not the solution
;
Border will be 2.5 ft
:
:
Check this by finding the dimension of the rug, and then the area
(25 - 2(2.5))*(16 - 2(2.5)) =
(25 - 5) * (16 - 5) =
20 * 11 = 220
Answer:
=20 apples
Step-by-step explanation:
90+70+140=300
300 crates in total
300÷15=20
Answer:
Step-by-step explanation:
Q1: 4=10x+5
4-5=10x
-1=10x
-1/10=10x/10=-0.1
Q2:s=3w+2x
s-3w=2x
s-3w/2=2x/2.