Answer:The line goes through the points (4,-3) and (0,-2), so its gradient is (-2-(-3))/(0-4) = -1/4. The y-intercept is -2 because f(0)=-2. So the equation of the line is y = -1/4 x - 2.This can be represented by the linear function f(x) = (-1/4)x - 2. The composite function ff is given by ff(x) = f(-1/4 x - 2) = (-1/4)((-1/4)x - 2) - 2 = x/16 - 3/2.HOPE'S THIS HELP'S
<span>Width = 6
Length = 30
We know the perimeter of a rectangle is simply twice the sum of it's length and width. So we have the expression:
72 = 2*(L + W)
And since we also know for this rectangle that it's length is 6 more than 4 times it's width, we have this equation as well:
L = 6 + 4*W
So let's determine what the dimensions are. Since we have a nice equation that expresses length in terms of width, let's substitute that equation into the equation we have for the perimeter and solve. So:
72 = 2*(L + W)
72 = 2*(6 + 4*W + W)
72 = 2*(6 + 5*W)
72 = 12 + 10*W
60 = 10*W
6 = W
So we now know that the width is 6. And since we have an expression telling us the length when given the width, we can easily determine the length. So:
L = 6 + 4*W
L = 6 + 4*6
L = 6 + 24
L = 30
And now we know the length as well.</span>
The correct answer is is the option B . X>0
Hopefully this help you
Answer:
C. -11,325
Step-by-step explanation:
- To know the answer, is convenient to replace some values of "n" in the sum
![\sum_{(n=1)}^{150}[-1-(n-1)]](https://tex.z-dn.net/?f=%5Csum_%7B%28n%3D1%29%7D%5E%7B150%7D%5B-1-%28n-1%29%5D)
.
- The result would appear after adding up every value of the expression when n=1,2,3.....,150.
- When n=1, the expression takes the value of (-1):
![[-1-(1-1)]= (-1)-0=-1](https://tex.z-dn.net/?f=%5B-1-%281-1%29%5D%3D%20%28-1%29-0%3D-1)
. - When n=2, the expression takes the value of (-2):
![[-1-(2-1)]=-1-1=-2](https://tex.z-dn.net/?f=%5B-1-%282-1%29%5D%3D-1-1%3D-2)
. - Following this way, for every n, we will obtain -n, then, the sum will be:
. This sum can actually be expressed as 
, which is the result of solving the initial expression of the sum 
. - Finally, the sum of n=-1 to n=-150 equals -11,325.
