35 = 1/2h (6+1)
35 = 1/2 h + 7
28 = 1/2h
14 = 1h
14 = h
Assume a is not divisible by 10. (otherwise the problem is trivial).
<span>Define R(m) to be the remainder of a^m when divided by 10. </span>
<span>R can take on one of 9 possible values, namely, 1,2,...,9. </span>
<span>Now, consider R(1),R(2),......R(10). At least 2 of them must have the sames value (by the Pigeonhole Principle), say R(i) = R(j) ( j>i ) </span>
<span>Then, a^j - a^i is divisible by 10.</span>
Given:
The figure of a rhombus QRST.
To find:
A. The value of x.
B. The measure of angle RQP.
Solution:
A. We need to find the value of x.
We know that the diagonals of a rhombus are perpendicular bisectors. It means the angles on the intersection of diagonals are right angles.
[Right angle]
Divide both sides by 5.
Therefore, the value of x is 15.
B. We need to find the measure of angle RQP.
From the given figure, it is clear that
Putting , we get
Therefore, the measure of angle RQP is 33 degrees.
Answer:
Step-by-step explanation:
The common difference (d) can be found using the first and 4th terms:
a1 = 3
a4 = a1 +d(4 -1)
-9 = 3 +3d . . . . . simplify
-3 = 1 + d . . . . . . divide by 3
-4 = d . . . . . . . . . subtract 1
Then ...
x = a1 + d = 3 -4 = -1
y = x + d = -1 -4 = -5
The values of x and y are -1 and -5, respectively.
