I believe the answer is:
A. 8/9 n-11/3
Let h be the number of lemonade sold. If the vendor sold 86 items today and h of them are lemonade, then the rest are hot dogs, so he sold 86-h hot dogs.
When you add the number of sold lemonade and hot dogs, then you get 86 items in total:
h+(86-h)=86.
This equation is exactly the same as equation
(86-h)+h=86.
Moreover,
1. if a snack cart sells lemonade for $2, then he gets $2h for h sold lemonade;
2. if a snack cart sells hot dogs for $5, then he gets $5(86-h) for (86-h) sold hot dogs.
In total he gets $330, then
2h+5(86-h)=330.
Both these equations are true, but only first is among given options.
Answer: correct choice is B.
Answer: cos(Θ) = (√15) / 4
Explanation:
The question states:
1) sin(Θ) = 1/4
2) 0 < Θ < π / 2
3) find cos(Θ)
This is how you solve it.
1) Use the fundamental identity (in this part I use α instead of Θ, just for facility of wirting the symbols, but they mean the same for the case).

2) From which you can find:

3) Replace sin(α) with 1/4
=>

=>

4) Given that the angle is in the first quadrant, you know that cosine is positive and the final answer is:
cos(Θ) =

.
And that is the answer.
Answer:
x=1
Step-by-step explanation:
5x + 2 = 3x + 4(2x - 1)
Distribute the 4
5x + 2 = 3x + 8x - 4
Combine like terms
5x + 2 = 11x - 4
Subtract 5x from each side
5x -5x + 2 = 11x - 5x - 4
2 = 6x-4
Add 4 to each side
2+4 = 6x-4+4
6 = 6x
Divide each side by 6
6/6 =6x/6
1= x