Answer:
4
Step-by-step explanation:
20×25 = 500
20 guest
25 dollars per guest
75s+200= 500
75s = 300
S = 4
They can afford to buy 4 cases of snacks and stay within their budget.
Answer:
13 in
Step-by-step explanation:
It’s a right triangle, so use the Pythagorean Theorem.
12²+5²=c²
144+25=c²
169=c²
√169=c
13=c
Simplifying
8a + 12b = 92
Solving
8a + 12b = 92
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-12b' to each side of the equation.
8a + 12b + -12b = 92 + -12b
Combine like terms: 12b + -12b = 0
8a + 0 = 92 + -12b
8a = 92 + -12b
Divide each side by '8'.
a = 11.5 + -1.5b
Simplifying
a = 11.5 + -1.5b
Answer:
The solution is 
Step-by-step explanation:
From the question we are told that
The function is ![f(x) = 4 + x^2 + tan [\frac{ \pi x}{2} ]](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%204%20%2B%20%20x%5E2%20%20%2B%20tan%20%5B%5Cfrac%7B%20%5Cpi%20x%7D%7B2%7D%20%5D)
, -1 < x < 1 a = 4
Here we are told find 
Let equate
So
![4 + x^2 + tan[\frac{\pi x }{2} ] = 4](https://tex.z-dn.net/?f=4%20%2B%20%20x%5E2%20%20%2B%20tan%5B%5Cfrac%7B%5Cpi%20x%20%7D%7B2%7D%20%5D%20%3D%20%204)
![x^2 + tan[\frac{\pi x }{2} ] = 0](https://tex.z-dn.net/?f=x%5E2%20%20%2B%20tan%5B%5Cfrac%7B%5Cpi%20x%20%7D%7B2%7D%20%5D%20%20%3D%20%200)
For the equation above to be valid x must be equal to 0
Now when x = 0
![f(0) = 4+0^2 + tan [\frac{ \pi * 0}{2} ]](https://tex.z-dn.net/?f=f%280%29%20%3D%204%2B0%5E2%20%2B%20tan%20%5B%5Cfrac%7B%20%5Cpi%20%2A%200%7D%7B2%7D%20%5D)
=> 
=> 
Differentiating f(x)
Now
since
We have
Now
Answer:
Step-by-step explanation:
Step 1: 6(x^2-1) [(6x-1)/(6(x+1)]
Step 2: [6(X+1) (X-1) (6X-1)] / 6(X+1)
Explanation: Factor out the (x^2-1)
Step 3: (6X-1) (X-1)
Explanation: Cancel out common terms on the top and the bottom of the fraction.
Step 4: 6X^2 - 6X-X+1
Explanation: Multiply out and Simplify
Answer: 6X^2 - 7x+1
