Answer:
12 Bottles of Lotion
Step-by-step explanation:
If Each bottle uses 1/4 Gallon (0.25 Gallon) then in order to find how many bottles of lotion Jill will be able to make with 3 Gallons, you would need to divide the 3 Gallons by the amount each bottle needs, like so...
3 gallons / 0.25 = # of Bottles
3 gallons / 0.25 = 12 Bottles
After doing this small calculation we can see that from the 3 Gallons Jill will be able to make a total of 12 Bottles of Lotion
Answer:
x = 9
Step-by-step explanation:
Corresponding sides are in proportion, that is
=
( cross- multiply )
8x = 72 ( divide both sides by 8 )
x = 9
Step-by-step explanation:
First let solve the inequality
![5 {x}^{2} + 2x - 3 < 0](https://tex.z-dn.net/?f=5%20%7Bx%7D%5E%7B2%7D%20%20%2B%202x%20-%203%20%3C%200)
Factor by grouping
![5 {x}^{2} + 5x - 3x - 3 < 0](https://tex.z-dn.net/?f=5%20%7Bx%7D%5E%7B2%7D%20%20%2B%205x%20-%203x%20-%203%20%3C%200)
![5x(x + 1) - 3(x + 1)](https://tex.z-dn.net/?f=5x%28x%20%2B%201%29%20-%203%28x%20%2B%201%29)
So the factor are
![(5x - 3)(x + 1)](https://tex.z-dn.net/?f=%285x%20-%203%29%28x%20%2B%201%29)
So the factor are
![x = \frac{3}{5}](https://tex.z-dn.net/?f=x%20%3D%20%20%5Cfrac%7B3%7D%7B5%7D%20)
and
![x = - 1](https://tex.z-dn.net/?f=x%20%3D%20%20-%201)
Solutions to a quadratic can be represented by a absolute value equation because remeber quadratics
creates 2 roots and/or double roots.
The inequality
![|x - b| < c](https://tex.z-dn.net/?f=%20%7Cx%20-%20b%7C%20%20%20%3C%20%20c)
works as
b is the midpoint between 2 roots. And c is the
![|x + b| = c](https://tex.z-dn.net/?f=%20%7Cx%20%2B%20b%7C%20%20%3D%20c)
We know that the midpoint between both roots is-1/5.
so
![|x - ( - \frac{1}{5} )| < c](https://tex.z-dn.net/?f=%20%7Cx%20-%20%28%20-%20%20%5Cfrac%7B1%7D%7B5%7D%20%29%7C%20%20%3C%20c)
![|x + \frac{1}{5} | < c](https://tex.z-dn.net/?f=%20%7Cx%20%2B%20%20%5Cfrac%7B1%7D%7B5%7D%20%7C%20%20%3C%20c)
Let use roots 3/5
![| \frac{3}{5} + \frac{1}{5} | = \frac{4}{5}](https://tex.z-dn.net/?f=%20%7C%20%5Cfrac%7B3%7D%7B5%7D%20%20%2B%20%20%5Cfrac%7B1%7D%7B5%7D%20%7C%20%20%3D%20%20%5Cfrac%7B4%7D%7B5%7D%20)
-1 works as well.
![| - 1 + \frac{1}{5} | = | - \frac{4}{5} | = \frac{4}{5}](https://tex.z-dn.net/?f=%20%7C%20-%201%20%2B%20%20%5Cfrac%7B1%7D%7B5%7D%20%7C%20%20%3D%20%20%20%7C%20%20%20-%20%20%20%5Cfrac%7B4%7D%7B5%7D%20%7C%20%20%3D%20%20%5Cfrac%7B4%7D%7B5%7D%20)
So the absolute value equation is
![|x + \frac{1}{5} | < \frac{4}{5}](https://tex.z-dn.net/?f=%20%7Cx%20%2B%20%20%5Cfrac%7B1%7D%7B5%7D%20%7C%20%20%3C%20%20%5Cfrac%7B4%7D%7B5%7D%20)