For this case we define the following variables:
x: Number of party dresses
y: Number of suits
You have 30 hours per week to cut, that is, the first equation is given by:
![3x + 3y = 30\\](https://tex.z-dn.net/?f=3x%20%2B%203y%20%3D%2030%5C%5C)
It is also known that 25 hours per week are available for sewing, that is:
![2x + 3y = 25\\](https://tex.z-dn.net/?f=2x%20%2B%203y%20%3D%2025%5C%5C)
It has a system of two equations with two unknowns, solving we have:
![3x + 3y = 30\\\\2x + 3y = 25\\](https://tex.z-dn.net/?f=3x%20%2B%203y%20%3D%2030%5C%5C%5C%5C2x%20%2B%203y%20%3D%2025%5C%5C)
Multiplying the second equation by -1:
![3x + 3y = 30\\\\-2x-3y = -25\\](https://tex.z-dn.net/?f=3x%20%2B%203y%20%3D%2030%5C%5C%5C%5C-2x-3y%20%3D%20-25%5C%5C)
Adding up:
![x + 0 = 5\\\\x = 5\\](https://tex.z-dn.net/?f=x%20%2B%200%20%3D%205%5C%5C%5C%5Cx%20%3D%205%5C%5C)
Substituting x in the first equation:
![3 * 5 + 3y = 30\\\\15 + 3y = 30\\](https://tex.z-dn.net/?f=3%20%2A%205%20%2B%203y%20%3D%2030%5C%5C%5C%5C15%20%2B%203y%20%3D%2030%5C%5C)
Clearing and:
![3y = 30-15\\\\3y = 15\\](https://tex.z-dn.net/?f=3y%20%3D%2030-15%5C%5C%5C%5C3y%20%3D%2015%5C%5C)
![y = \frac{15}{3}\\\\y = 5\\](https://tex.z-dn.net/?f=y%20%3D%20%5Cfrac%7B15%7D%7B3%7D%5C%5C%5C%5Cy%20%3D%205%5C%5C)
Thus, per week, the designer can produce 5 party dresses and 5 suits working at her maximum capacity.
Answer:
5 Party dresses
5 Suits
For y=x^2-6x-11
complete the square
so roots
set y=0
0=x^2-6x-11
group x terms
0=(x^2-6x)-11
take 1/2 of linear coefient (-6) and square it
-6/2=-3, (-3)^2=9
add positive and neative to inside of parenthasees
0=(x^2-6x+9-9)-11
complete square
0=((x-3)^2-9)-11
expand
0=(x-3)^2-9-11
0=(x-3)^2-20
add 20 to both sides
20=(x-3)^2
sqrt both sides
remember positive and negative roots
+/-2√5=x-3
add 3 to both sides
3+/-2√5=x
so
x=3+2√5 and 3-2√5
I hope this helps you
(2-5i)(2+5i)
2.2+2.5i-2.5i-5.5.I.I
4-25.i^2
4-25. (-1)
4+25
29
Answer:
110
Step-by-step explanation: