Answer:
-2
Assumption:
Find the value of x such that
.
Step-by-step explanation:
![(f+g)(x)=0](https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D0)
![f(x)+g(x)=0](https://tex.z-dn.net/?f=f%28x%29%2Bg%28x%29%3D0)
![(x^2-2x)+(6x+4)=0](https://tex.z-dn.net/?f=%28x%5E2-2x%29%2B%286x%2B4%29%3D0)
Combine like terms:
![x^2+4x+4=0](https://tex.z-dn.net/?f=x%5E2%2B4x%2B4%3D0)
This is not too bad too factor on the left hand side since 2(2)=4 and 2+2=4.
![(x+2)(x+2)=0](https://tex.z-dn.net/?f=%28x%2B2%29%28x%2B2%29%3D0)
![(x+2)^2=0](https://tex.z-dn.net/?f=%28x%2B2%29%5E2%3D0)
So we need to solve:
![x+2=0](https://tex.z-dn.net/?f=x%2B2%3D0)
Subtract 2 on both sides:
![x=-2](https://tex.z-dn.net/?f=x%3D-2)
Let's check:
![(f+g)(-2)](https://tex.z-dn.net/?f=%28f%2Bg%29%28-2%29)
![f(-2)+g(-2)](https://tex.z-dn.net/?f=f%28-2%29%2Bg%28-2%29)
![((-2)^2-2(-2))+(6(-2)+4)](https://tex.z-dn.net/?f=%28%28-2%29%5E2-2%28-2%29%29%2B%286%28-2%29%2B4%29)
![(4+4)+(-12+4)](https://tex.z-dn.net/?f=%284%2B4%29%2B%28-12%2B4%29)
![(8)+(-8)](https://tex.z-dn.net/?f=%288%29%2B%28-8%29)
![0](https://tex.z-dn.net/?f=0)
0 was the desired output of
.
Answer:
a
Generally given that the number of cups of blue to that of red paint is 3: 1 then the Lara mixed 3 cups of blue paint with 1 cup of red paint
b
The number is ![x= \frac{1}{3}](https://tex.z-dn.net/?f=x%3D%20%20%5Cfrac%7B1%7D%7B3%7D)
c
The price is ![P = \$ 8](https://tex.z-dn.net/?f=P%20%20%3D%20%5C%24%208%20)
Step-by-step explanation:
From the question we are told that
The ratio of the number of cups of blue paint to the number of cups of red paint is ![r = 3: 1](https://tex.z-dn.net/?f=r%20%20%3D%20%203%3A%201)
Generally given that the number of cups of blue to that of red paint is 3: 1 then the Lara mixed 3 cups of blue paint with 1 cup of red paint
Given that 1 cup of red paint => 3 cups of blue paint
x cup of red paint => 1 cup of blue paint
So
![x= \frac{1 * 1}{3}](https://tex.z-dn.net/?f=x%3D%20%20%5Cfrac%7B1%20%2A%20%201%7D%7B3%7D)
=> ![x= \frac{1}{3}](https://tex.z-dn.net/?f=x%3D%20%20%5Cfrac%7B1%7D%7B3%7D)
Generally the unit price of a cup of blue paint is mathematically represented as
![P = \frac{48}{6}](https://tex.z-dn.net/?f=P%20%20%3D%20%20%5Cfrac%7B48%7D%7B6%7D)
=> ![P = \$ 8](https://tex.z-dn.net/?f=P%20%20%3D%20%5C%24%208%20)
(8.4 / 6) + 3.2
Hope this helps :)