We have
f(x)=<span>−x</span>²<span>+ 5x + 6
g(x)=</span><span>3x − 2
we know that
f(x)=g(x)
the solution is the intersection both graphs
using a graph tool
see the attached figure
the solution are the points(4,10)and(-2,-8)</span>
Answer:
<h3>
There is a constant of variation in the equation and it is 750. This means that the amount olivia earns increases by $750 every week.</h3>
Step-by-step explanation:
Given the equation y = 750x which represents the number of dollars y Olivia earns in x weeks, from the equation, it can be inferred that the number of dollars olivia earns is DIRECTLY PROPORTIONAL to the number of weeks. This relationship is therefore a direct variation.
In direct variation, increase in a variable will lead to corresponding increase in the other variable and vice versa by a factor known as the constant of variation.
For example if y is directly proportional to x, it is written mathematically as shown;



where k is the constant of proportionality.
comparing the general expression above with the equation in question,
y = 750x
k = 750
Therefore we can conclude that there is a constant of variation in the equation and it is 750. This means that the amount olivia earns increases by $750 every week.
Yes they are that’s correct
Lets start by factoring the 216 into its smaller parts.
![\sqrt[3]{2 * 2 * 2 * 3 * 3 * 3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%20%2A%202%20%2A%202%20%2A%203%20%2A%203%20%2A%203%7D)
From here, we can separate the three 2s and the three 3s into two separate radicals.
![\sqrt[3]{2*2*2} * \sqrt[3]{3*3*3}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B2%2A2%2A2%7D%20%2A%20%20%5Csqrt%5B3%5D%7B3%2A3%2A3%7D%20)
Since we have three copies of the same number in each, the answer to the cube root is the number we have the copies of.
![\sqrt[3]{2*2*2} * \sqrt[3]{3*3*3} = 2 * 3](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B2%2A2%2A2%7D%20%2A%20%20%5Csqrt%5B3%5D%7B3%2A3%2A3%7D%20%3D%202%20%2A%203)
Finally, we just need to multiply out what remains to find the solution.

So, the final answer is 6.