General Idea:
Domain of a function means the values of x which will give a DEFINED output for the function.
Applying the concept:
Given that the x represent the time in seconds, f(x) represent the height of food packet.
Time cannot be a negative value, so
The height of the food packet cannot be a negative value, so
We need to replace 
for f(x) in the above inequality to find the domain.
![-15x^2+6000\geq 0 \; \; [Divide \; by\; -15\; on\; both\; sides]\\ \\ \frac{-15x^2}{-15} +\frac{6000}{-15} \leq \frac{0}{-15} \\ \\ x^2-400\leq 0\;[Factoring\;on\;left\;side]\\ \\ (x+200)(x-200)\leq 0](https://tex.z-dn.net/?f=%20-15x%5E2%2B6000%5Cgeq%200%20%5C%3B%20%5C%3B%20%20%5BDivide%20%5C%3B%20by%5C%3B%20-15%5C%3B%20on%5C%3B%20both%5C%3B%20sides%5D%5C%5C%20%5C%5C%20%5Cfrac%7B-15x%5E2%7D%7B-15%7D%20%2B%5Cfrac%7B6000%7D%7B-15%7D%20%5Cleq%20%5Cfrac%7B0%7D%7B-15%7D%20%5C%5C%20%5C%5C%20x%5E2-400%5Cleq%200%5C%3B%5BFactoring%5C%3Bon%5C%3Bleft%5C%3Bside%5D%5C%5C%20%5C%5C%20%28x%2B200%29%28x-200%29%5Cleq%200%20)
The possible solutions of the above inequality are given by the intervals ![(-\infty , -2], [-2,2], [2,\infty )](https://tex.z-dn.net/?f=%20%28-%5Cinfty%20%2C%20-2%5D%2C%20%5B-2%2C2%5D%2C%20%5B2%2C%5Cinfty%20%29%20)
. We need to pick test point from each possible solution interval and check whether that test point make the inequality 
true. Only the test point from the solution interval [-200, 200] make the inequality true.
The values of x which will make the above inequality TRUE is 
But we already know x should be positive, because time cannot be negative.
Conclusion:
Domain of the given function is 
12 x 6 x 3 =216. He can dress himself up in 216 different ways.
I hope this helps!
Answer:
The answer is a
Step-by-step explanation:
Answer:
Prime.
Step-by-step explanation:
First let's multiply our outer coefficients in this case 1 and 8, so we have 1x8=8. Now the point of this is to get the factors of 8 and see if we can get that middle term -7. Factors of 8 are 1x8, 2x4 and that's it. From there I notice that -8+1 = -7 and so:
Notice that the (x-8) and (x+8) are not the same factors, therefore the factors are not any of those answer choices and so it's prime. You can calculate the factors by using the quadratic formula, however I think that is beyond the scope of this question.
Answer:
14.125
Step-by-step explanation:
You combine the two equations and get
8x - 23
and since they're in a 90 degree angle you do
8x - 23 = 90
add 23 to both sides
8x =113
divide 113 by 8 and you get 14.125 and if you plug it in for both x's you get 24.625 + 65.375 you get an even 90
