Step-by-step explanation:
A rational function the ratio of two polynomial functions, where the polynomial in the denominator is not equal to zero.
Answer:
![6x^2+5x-6=(3x-2)(2x+3)](https://tex.z-dn.net/?f=6x%5E2%2B5x-6%3D%283x-2%29%282x%2B3%29)
Step-by-step explanation:
<u>Given expression</u>:
![6x^2+5x-6](https://tex.z-dn.net/?f=6x%5E2%2B5x-6)
To factor a quadratic in the form
, first find two numbers that multiply to
and sum to
:
![\implies ac=6 \cdot -6=-36](https://tex.z-dn.net/?f=%5Cimplies%20ac%3D6%20%5Ccdot%20-6%3D-36)
![\implies b=5](https://tex.z-dn.net/?f=%5Cimplies%20b%3D5)
Two numbers that multiply to -36 and sum to 5 are: 9 and -4
Rewrite b as the sum of these two numbers:
![\implies 6x^2+9x-4x-6](https://tex.z-dn.net/?f=%5Cimplies%206x%5E2%2B9x-4x-6)
Factorize the first two terms and the last two terms separately:
![\implies 3x(2x+3)-2(2x+3)](https://tex.z-dn.net/?f=%5Cimplies%203x%282x%2B3%29-2%282x%2B3%29)
Factor out the common term (2x + 3):
![\implies (3x-2)(2x+3)](https://tex.z-dn.net/?f=%5Cimplies%20%283x-2%29%282x%2B3%29)
Therefore:
![6x^2+5x-6=(3x-2)(2x+3)](https://tex.z-dn.net/?f=6x%5E2%2B5x-6%3D%283x-2%29%282x%2B3%29)
The ratio of apple to orange juice is 28:12
This can be simplified to 7:3
Hope this helps :)
The answer is 78.99%, So rounded up to 79%
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