Answer:
x + y = 50 (1) and 2x + 3y = 115 (2); x = 35, y = 15
Step-by-step explanation:
Since x represents the number of 2 point shots and y represents the number of 3 point shots. If the total number of shots is 50, then x + y = 50 (1)
Also, the total 2 point shots is number of 2 point shots × points per shot = 2x and the total 3 point shots is number of 3 point shots × points per shot = 3y. Since the total number of points is 115, then
2x + 3y = 115 (2)
So, the system of equations are
x + y = 50 (1) and 2x + 3y = 115 (2)
We can solve for x and y by substituting x = 50 - y into (2)
So, 2(50 - y) + 3y = 115
100 - 2y + 3y = 115
100 + y = 115
y = 115 - 100
y = 15
So, x = 50 - y
= 50 - 15
= 35
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)
Answer:
x = 2/3 or x = -1
Step-by-step explanation by completing the square:
Solve for x:
3 x^2 + x - 2 = 0
Divide both sides by 3:
x^2 + x/3 - 2/3 = 0
Add 2/3 to both sides:
x^2 + x/3 = 2/3
Add 1/36 to both sides:
x^2 + x/3 + 1/36 = 25/36
Write the left hand side as a square:
(x + 1/6)^2 = 25/36
Take the square root of both sides:
x + 1/6 = 5/6 or x + 1/6 = -5/6
Subtract 1/6 from both sides:
x = 2/3 or x + 1/6 = -5/6
Subtract 1/6 from both sides:
Answer: x = 2/3 or x = -1
Answer:
-8 and 1
Step-by-step explanation:
Answer:
Excuse me, wrong answer did not mean to type that. It would be C.
Step-by-step explanation:
This is because C. y - 5 = -2 (x+9) is an inequality. But, because of the slope of -2 passing through the point (-5, 9), it would be x - 9. So, C.
