Answer:
-56
Step-by-step explanation:
Hello!
Let's create an equation to figure out what the middle integer really is.
Creating an equation:
n + (n + 1) + (n + 2) = -168 (This is true because we must account for the <em>consecutive integers </em>part.)
Simplifying:
3n + 3 = -168
Subtracting:
3n = -171
Dividing:
n = -57
Now, we plug-and-chug:
-57, -56, -54 (this is because we accounted for adding <em>positive </em>one.)
Thus, the middle integer is 
.
Check:
We can see if we are correct by adding up -57, -56, -54.
(-57) + (-56) + (-54) = -168
So we are correct!
Hope this helps!
Answer:
Step-by-step explanation:
Hello, when you have an equation like y = ax+b you know that this is a line.
In this example, the function is defined in two different intervals.
For x < 1 this is the line y = 4 + x
and for x>=1 this is the line y = 4 - 2x
At the frontier, x= 1, we have 4+1=5 on one side and 4-2=2 on the other side, we we expect a "jump" in the graph.
Except that "jump"you just have to draw lines, so if you have two points you can draw them right.
For x<1, the line is passing by (-4,0) and (0,4)
And you have to stop for x<1 so the point (1,5) is not on the graph.
for x>=1 the points (1,2) and (2,0) are on the graph and we just have to draw the line.
I attached the graph.
Thanks
The given plane has normal vector
Scaling <em>n</em> by a real number <em>t</em> gives a set of vectors that span an entire line through the origin. Translating this line by adding the vector <2, 1, 1> makes it so that this line passes through the point (2, 1, 1). So this line has equation
This line passes through (2, 1, 1) when <em>t</em> = 0, and the line intersects with the plane when
which corresponds the point (3, -1, 1) (simply plug <em>t</em> = 1 into the coordinates of 
).
So the distance between the plane and the point is the distance between the points (2, 1, 1) and (3, -1, 1):
