“Just follow your heart to find the answer” -someone
If 5x - 17 ≥ 0, then |5x - 17| = 5x - 17 and the equation reduces to
-8 - 2 (5x - 17) = -14
-8 - 10x + 34 = -14
-10x = -40
x = 4
If 5x - 17 < 0, then |5x - 17| = -(5x - 17) = -5x + 17 and we have
-8 - 2 (-5x + 17) = -14
-8 + 10x - 34 = -14
10x = 28
x = 2.8
Answer:
p(x) = f(x) - g(x) = -0.04x² + 20.96x - 71
Explanation:
The sales are given by f(x) = 24.96x and the cost are represented by g(x) = 0.04x² + 4x + 71.
Then, the profit is equal to
p(x) = f(x) - g(x)
p(x) = 24.96x - (0.04x² + 4x + 71)
p(x) = 24.96x - 0.04x² - 4x - 71
p(x) = -0.04x² + 20.96x - 71
Therefore, the answer is
p(x) = f(x) - g(x) = -0.04x² + 20.96x - 71
so we know that 24% of the students buy their lunch at the cafeteria, and 190 students brownbag.
well, 100% - 24% = 76%, so the remainder of the students, the one that is not part of the 24% is 76%, and we know that's 190 of them.
since 190 is 76%, how much is the 24%?
![\bf \begin{array}{ccll} amount&\%\\ \cline{1-2} 190&76\\ x&24 \end{array}\implies \cfrac{190}{x}=\cfrac{76}{24}\implies 4560=76x \\\\\\ \cfrac{4560}{76}=x\implies 60=x \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{total amount of students}}{190+60\implies 250}](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Bccll%7D%20amount%26%5C%25%5C%5C%20%5Ccline%7B1-2%7D%20190%2676%5C%5C%20x%2624%20%5Cend%7Barray%7D%5Cimplies%20%5Ccfrac%7B190%7D%7Bx%7D%3D%5Ccfrac%7B76%7D%7B24%7D%5Cimplies%204560%3D76x%20%5C%5C%5C%5C%5C%5C%20%5Ccfrac%7B4560%7D%7B76%7D%3Dx%5Cimplies%2060%3Dx%20%5C%5C%5C%5C%5B-0.35em%5D%20~%5Cdotfill%5C%5C%5C%5C%20%5Cstackrel%7B%5Ctextit%7Btotal%20amount%20of%20students%7D%7D%7B190%2B60%5Cimplies%20250%7D)
The equation of direct variation is,

Substitute the values of <em>y</em> and <em>x</em>.

So, the obtained equation will be <em>y</em>=1.35(x).
Let's check with the values of <em>x</em>.
1) If <em>x</em>=4

2) If <em>x</em>=2

3) If <em>x</em>=-2