For a function to begin to qualify as differentiable, it would need to be continuous, and to that end you would require that 
is such that
Obviously, both limits are 0, so 
is indeed continuous at 
.
Now, for to be differentiable everywhere, its derivative 
must be continuous over its domain. So take the derivative, noting that we can't really say anything about the endpoints of the given intervals:
and at this time, we don't know what's going on at , so we omit that case. We want to be continuous, so we require that
from which it follows that 
.
Answer:
The number would be 22.
Step-by-step explanation:
In order to solve for the number, we need to make both statements into numerical statements.
Fifteen more than four times a number = 15 + 4x
difference between 191 and four times the number = 191 - 4x
Now we set them equal to each other.
15 + 4x = 191 - 4x -----> Add 4x to each side
15 + 8x = 191 ------> Subtract 15 from both sides
8x = 176 -------> Divide by 8
x = 22
Answer:
15;9;-8
Step-by-step explanation:
1. 5/3x-3=2/3x+12
x=15 once you combine like terms
2. 5x+35-3x+12=7x+2
2x+47=7x+2
5x=45
x=9
3. 12x+20-3=9x-7
12x+17=9x-7
3x=-24
x=-8
Answer:
3x + 1y = $163
2x + 3y =$174
Step-by-step explanation:
Adult tickets to space amusement park cost x dollars children’s tickets cost y dollars.
Henson family bought 3 adults and 1 child's tickets for $163
x + y = 163
3x + 1y = 163
The Garcia family bought 2 adults and 3 child’s ticket for $174.
x + y = $174
2x + 3y = $174
Therefore the equations representing both families cost are
Henson family
3x + 1y = $163
Garcia family
2x + 3y = $174
Two triangles are similar if and only if all corresponding angles are equal (congruence), even if the corresponding sides are equal or not, therefore the answer is true because ΔJKL and ΔRST are similar and the statement above demands that "it must be", namely, this is a sufficient condition.
