Formula for midpoint between two points is M(x,y)
x=(x1+x2)/2 and y=(y1+y2)/2
In our case (x1,y1)=(m,b) and (x2,y2)=(0,0)
x=(m+0)/2=m/2 and y=(b+0)/2=b/2 M(m/2,b/2)
Good luck!!!
<span><span>1. m2</span><span>(36<span>m4</span>+12<span>m2</span>+1)</span></span>2. Rewrite <span><span>m4</span><span>m4</span></span> as <span><span><span>(<span>m2</span>)</span>2</span><span><span>(<span>m2</span>)</span>2</span></span>.<span><span>3. m2</span><span>(36<span><span>(<span>m2</span>)</span>2</span>+12<span>m2</span>+1)</span></span>4. Let <span><span>u=<span>m2</span></span><span>u=<span>m2</span></span></span>. Substitute <span>uu</span> for all occurrences of <span><span>m2</span><span>m2</span></span>. =m2(36u2+12u+1)
5. Rewrite <span><span>36<span>u2</span></span><span>36<span>u2</span></span></span> as <span><span><span>(6u)</span>2</span><span><span>(6u)</span>2</span></span>.<span><span>5. m2</span><span>(<span><span>(6u)</span>2</span>+12u+1)</span></span>6. Rewrite <span>11</span> as <span>12</span><span><span>7. m2</span><span>(<span><span>(6u)</span>2</span>+12u+<span>12</span>)</span></span>8. Check the middle term by multiplying <span>2ab</span> and compare this result with the middle term in the original expression.<span><span>9. 2ab=2⋅<span>(6u)</span>⋅1</span><span>2ab=2⋅<span>(6u)</span>⋅1</span></span>10. Simplify. 2ab=12u
11. Factor using the perfect square trinomial rule <span><span><span>a2</span>+2ab+<span>b2</span>=<span><span>(a+b)</span>2</span></span><span><span>a2</span>+2ab+<span>b2</span>=<span><span>(a+b)</span>2</span></span></span>, where <span><span>a=6u</span><span>a=6u</span></span> and <span><span>b=1</span><span>b=1</span></span>.<span><span><span>12. m2</span><span><span>(6u+1)</span>2</span></span><span><span>m2</span><span><span>(6u+1)</span>2</span></span></span>13. Replace all occurrences of <span>uu</span> with <span><span>m2</span><span>m2</span></span>. m^2(6m^2+1)^2
Answer:
Step-by-step explanation:
Remark
The diagonal is found by using the Pythagorean Theorem: a^2 + b^2 = c^2. This only works for certain figures. The rectangle is one of them.
Givens
a = 10
b = 8
c = ? This is the length of the diagonal.
Solution
a^2 + b^2 = c^2
10^2 + 8^ = c^2
100 + 64 = c^2
c^2 = 164
√c^2 = √164
c = 12.806
The required proof of parallelogram is given below,
What is parallelogram?
A parallelogram is a straightforward quadrilateral with two sets of parallel sides in Euclidean geometry. The opposing or confronting sides and the opposing angles in a parallelogram are of equal length.
For a parallelogram, opposite sides are always equal and parallel.
So for the given parallelogram, we get AD = BC and AD and BC are parallel.
AD and BC is parallel and DC is common side, therefore, ......(1)
Given .......(2)
Therefore, from condition (1) and (2), we get
If then DC bisects the angle . [Proved]
To learn more about parallelogram from the given link
brainly.com/question/970600
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Answer: 999 games
Step-by-step explanation:
There are many ways to illustrate the rooted tree model to calculate the number of games that must be played until only one player is left who has not lost.
We could go about this manually. Though this would be somewhat tedious, I have done it and attached it to this answer. Note that when the number of players is odd, an extra game has to be played to ensure that all entrants at that round of the tournament have played at least one game at that round. Note that there is no limit on the number of games a player can play; the only condition is that a player is eliminated once the player loses.
The sum of the figures in the third column is 999.
We could also use the formula for rooted trees to calculate the number of games that would be played.
where i is the number of "internal nodes," which represents the number of games played for an "<em>m</em>-ary" tree, which is the number of players involved in each game and l is known as "the number of leaves," in this case, the number of players.
The number of players is 1000 and each game involves 2 players. Therefore, the number of games played, i, is given by