Answer:
10x + 15y ≥ 500
x + y ≤ 50
![y\geq \frac{x}{2}](https://tex.z-dn.net/?f=y%5Cgeq%20%5Cfrac%7Bx%7D%7B2%7D)
Step-by-step explanation:
Let, the number of t-shirts = x and number of sweatshirts = y.
It is given that, at most 50 items are to be sold.
Thus, x + y ≤ 50.
Also, the number of sweatshirts to be sold is at least half the number of t-shirts.
Thus, ![y\geq \frac{x}{2}](https://tex.z-dn.net/?f=y%5Cgeq%20%5Cfrac%7Bx%7D%7B2%7D)
Further, it is given that the profit on t-shirts is $10 and on sweatshirts is $15 with the minimum total profit is $500.
So, we get 10x + 15y ≥ 500.
Hence, the system of inequality is given as:
10x + 15y ≥ 500
x + y ≤ 50
![y\geq \frac{x}{2}](https://tex.z-dn.net/?f=y%5Cgeq%20%5Cfrac%7Bx%7D%7B2%7D)
They all have 4 sides, there are 2 shorter sides and 2 longer sides and the two short sides are parallel to each other, and the two long sides are parallel to each other.
Step-by-step explanation:
For a rational function, we cannot values in the domain that will make the denominator 0.
So set the denominator =0
![{x}^{2} - 1 = 0](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20-%201%20%3D%200)
![{x}^{2} = 1](https://tex.z-dn.net/?f=%20%7Bx%7D%5E%7B2%7D%20%20%3D%201)
![x = 1](https://tex.z-dn.net/?f=x%20%3D%201)
or
![x = - 1](https://tex.z-dn.net/?f=x%20%3D%20%20-%201)
So the answer is (-1,1)
Answer:
there are two solutions:
a)
, and
b) ![y=\frac{-6-2\sqrt{6} }{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-6-2%5Csqrt%7B6%7D%20%7D%7B5%7D)
Step-by-step explanation:
In the equation:
, since a perfect square with the unknown "y" is isolated on the left of the equal sign, we start by applying the square root on both sides of the equality, and then on isolating the unknown:
![(5y+6)^2=24\\\sqrt{(5y+6)^2} =+/-\sqrt{24} \\(5y+6)=+/-\sqrt{6*4} \\(5y+6)=+/-2\sqrt{6}\\5y=-6+/-2\sqrt{6}\\y=\frac{-6+/-2\sqrt{6} }{5}](https://tex.z-dn.net/?f=%285y%2B6%29%5E2%3D24%5C%5C%5Csqrt%7B%285y%2B6%29%5E2%7D%20%3D%2B%2F-%5Csqrt%7B24%7D%20%5C%5C%285y%2B6%29%3D%2B%2F-%5Csqrt%7B6%2A4%7D%20%5C%5C%285y%2B6%29%3D%2B%2F-2%5Csqrt%7B6%7D%5C%5C5y%3D-6%2B%2F-2%5Csqrt%7B6%7D%5C%5Cy%3D%5Cfrac%7B-6%2B%2F-2%5Csqrt%7B6%7D%20%7D%7B5%7D)
Therefore there are two solutions:
a)
, and
b) ![y=\frac{-6-2\sqrt{6} }{5}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7B-6-2%5Csqrt%7B6%7D%20%7D%7B5%7D)