Answer:
x=5
Step-by-step explanation:
Answer:
Step-by-step explanation:
The cross section will have the same shape as the base of the pentagonal prism; the dimensions will be proportionally smaller.
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 
Answer:
1)107
2)43
Step-by-step explanation:
Triangles interior angles add up to 180 degrees. In the first one, the first two angles are 31and 42, and if interior angles add up to 180, the equation should be 31+42+x=180 x=107.
Second one is hardes. A square means a right angle, or 90 degrees. 180-90 is 90. Next, we have the two angles x, and x+4 We know that triangles interior angles add up to 180 degrees, so x+x+4+90=180 2x+94=180 2x=86 x=43
Hope this helps :D Please mark brainliest if correct :D
Answer:
y = -15
x = -10
Step-by-step explanation:
1/4x - 1/2 = 5 (1)
3x + 2/3y = -40 (2)
Multiply (1) by 4
1/4x - 1/2 = 5
1/4x * 4 - 1/2y * 4 = 5 * 4
4/4x - 4/2y = 20
x - 2y = 20 (3)
Multiply (2) by 3
3x + 2/3y = -40 (2)
3x * 3 + 2/3y * 3 = -40 * 3
9x + 6/3y = -120
9x + 2y = -120 (4)
x - 2y = 20 (3)
9x + 2y = -120 (4)
Using elimination method, Add (3) and (4)
9x + x = -120 + 20
10x = -100
x = -100/10
x = -10
Substitute x = -10 into (3)
x - 2y = 20 (3)
-10 - 2y = 20
-2y = 20 + 10
-2y = 30
y = 30/-2
y = -15
y = -15
x = -10
