The first thing that we want to do is simplify both side of this equation.
2(m-8).
The first thing we have to do, is multiple 2 by m and -8, also called distributing. So, when we do that, we get
2(m-8)=2*m + 2*-8 = 2m-16
4(m+6)
Now, we do the same thing we did for the first parenthesis, and that's multiple 4 by m and 6.
4(m+6)=4*m + 4*6 = 4m+24
Now, we need to get m by itself on one side. So, lets bring the equation from the right to the left
2m-16 = 4m + 24 (bring 4m to the other side by subtracting)
2m-16-4m = 24 (bring -16 to the right by adding)
-2m=24+16
-2m=40 (divide both sides by -2 to get your value for m)
m=40/-2 = -20
So, our answer is m = -20
Please see attached image for the graph.
a.
Yes, it is mathematically possible because the
degree of vertices for P=3, T=3, M=2, C=4, and R=2 and in Euler’s theorem, the
graph has to be connected, which in this case it is and the number of vertices
in the graph whose vertices is odd, is 0 or 2. And in this case, we have 2 that
have a degree of vertices that are odd, therefore mathematically this is
possible for the driver. The route would be P > R > C > M > T > C
> P > T.
b.
<span>It is mathematically possible. The router would be P
> C > R > T > M > C > T. Essentially, you travel each road
once.
</span>
c.
The driver would use a Hamiltonian circuit. The route
would be J > R > A > C > V > M > T > P > J.
Answer:
The information we need is that the angle between the sides (that is, angle TVU for triangle TVU and angle WVX for triangle WVX) need to be equal.
These angles are vertically opposite angles, because they are formed by two lines crossing, so these angles are equal.
Step-by-step explanation:
The SAS Congruence Theorem says that if two triangles have 2 equal sides and the angle between these sides are also equal, the triangles are congruent.
In this question, we know that the sides UV and VW are congruent, as V is the midpoint of UW. We also know that TV = VX, so now we have two equal sides for each triangle.
The information we need is that the angle between the sides (that is, angle TVU for triangle TVU and angle WVX for triangle WVX) need to be equal.
These angles are vertically opposite angles, because they are formed by two lines crossing, so these angles are equal.
Now we can conclude that the triangles are congruent.
Hello!
As the figure is a rectangle, AE ≅ EC.
AE = x + 11
EC = 6x + 1
Set the two equal to each other:
x + 11 = 6x + 1
Subtract x from both sides:
11 = 5x + 1
Subtract 1 from both sides:
10 = 5x
Divide both sides by 5:
10/5 = 5x/5
x = 2.
Since there are 2 semesters per year we have:
(1/2)(24,870 - 7,560) = $8,655
David would have to contribute $8,655 per semester.
