Your total profit is $13,000. First you bought the 200 items for $20 each. That costs $4,000. Then you sold $50 of the items at $100 each. That’s $5,000. So already you’re in the green. You’ve already made $1,000 profit. Then you sold the rest of the items at a 20% discount. 150 items multiplied by $80 is $12,000. $12,000 plus the $1,000 equals $13,000 total.
Answer:
The given expressions simplifies to tan (4x).
Step-by-step explanation:
Here, the given expression is : 
By TRIGONOMETRIC IDENTITY:
Putting this identity here, and taking A = 9 x, B = 5 x, we get
= tan(4x)
Hence, the given expressions simplifies to tan (4x).
Answer:
1250 m²
Step-by-step explanation:
Let x and y denote the sides of the rectangular research plot.
Thus, area is;
A = xy
Now, we are told that end of the plot already has an erected wall. This means we are left with 3 sides to work with.
Thus, if y is the erected wall, and we are using 100m wire for the remaining sides, it means;
2x + y = 100
Thus, y = 100 - 2x
Since A = xy
We have; A = x(100 - 2x)
A = 100x - 2x²
At maximum area, dA/dx = 0.thus;
dA/dx = 100 - 4x
-4x + 100 = 0
4x = 100
x = 100/4
x = 25
Let's confirm if it is maximum from d²A/dx²
d²A/dx² = -4. This is less than 0 and thus it's maximum.
Let's plug in 25 for x in the area equation;
A_max = 25(100 - 2(25))
A_max = 1250 m²
Answer: Yes, the point (3,4) is a solution to the system.
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Proof of this:
Replace x with 3 and y with 4 in the first equation
x+y = 7
3+4 = 7
7 = 7
This confirms the first equation. Repeat for the second equation
x-2y = -5
3-2(4) = -5
3 - 8 = -5
-5 = -5
We get true equations for both when we plug in (x,y) = (3,4). This confirms it is a valid solution to the system of equations. It turns out it's the only solution to this system of equations. Visually, the two lines cross at the single location (3,4).
