Answer: 7
Step-by-step explanation:
f(x) 3x+1
f(2) = 3(2) +1
f(2) = 6+1
= 7
Given:
The limit problem is:
To find:
The limit of the function by using direct substitution.
Solution:
We have,
Applying limit, we get
Therefore, the correct option is D.
That's the second one,
180 - x = r
Whenever two lines cross we get congruent opposite angles and supplemental adjacent angles, i.e. they add to 180 degrees.
The first one is almost right; we have r+y+z=180 and r+x=180 so x=y+z not quite what was written.
Intersection of the first two lines:
Multiply the first equation by 4 and the second by 5:
Subtract the two equations:
Plug this value for y in one of the equation, for example the first:
So, the first point of intersection is 
We can find the intersection of the other two lines in the same way: we start with
Use the fact that x and y are the same to rewrite the second equation as
And since x and y are the same, the second point is 
So, we're looking for a line passing through and . We may use the formula to find the equation of a line knowing two of its points, but in this case it is very clear that both points have the same coordinates, so the line must be 
In the attached figure, line 
is light green, line 
is dark green, and their intersection is point A.
Simiarly, line 
is red, line 
is orange, and their intersection is B.
As you can see, the line connecting A and B is the red line itself.
9514 1404 393
Answer:
(c) (3, 3)
Step-by-step explanation:
Point E partitions both the x-distance and the y-distance in the ratio 2 : 1. That is, for either the x-coordinates or the y-coordinates, ...
CE : ED = 2 : 1
Try the answers with the x-coordinates.
CE : ED = (1 -(-1)) : (5 - 1) = 2 : 4 . . . . incorrect
CE : ED = (-3 -(-1)) : (5 -(-3)) = -2 : 8 . . . . incorrect
CE : ED = (3 -(-1)) : (5 -3) = 4 : 2 = 2 : 1 . . . . correct
CE : ED = (-1 -(-1)) : (5 -(-1)) = 0 : 6 . . . . incorrect
The only viable choice is (3, 3).
_____
<em>Alternate solution</em>
For a partitioning of m : n, the desired point is ...
E = (n×C +m×D)/(m+n)
For partitioning of 2 : 1, the desired point is ...
E = (1×(-1, -3) + 2×(5, 6))/(2+1) = (-1+10, -3 +12)/3
E = (3, 3)
