Two line segments, AB and CD, bisect one another at point 0. Prove that the lines AC and BD are parallel.
I suggest you start with the diagram.
Consider triangles OAC and OBD
OA=OB Since 0 bisects AB
OC=OD since o bisects CD
angleBOD=angleAOC Vertically opposite angles
triangle OAC is congruent to triangle OBD Two sides and included angle test.
angle OAC = angle OBC corresponding angles in congruent triangles
Now consider AB as the transversal that cuts the lines AC and BD
angle OAC angle OBC are alternate angles and since they are equal AC must be parallel to BD
If a line meets two parallel lines and is perpendicular to one of them, prove that it is perpendicular to the other.
If two parallel lines are cut by a transversal then the cointerior angles are supplementary.
(If one is x the other is 180-x)
If one is 90 then thte other is 180-90=90.
So if the transversal is perpendicular to one of the lines it must be perpendicular to the other as well.
I have never seen notation like this.
f[-4(x=1)] looks super odd.
Maybe another mathematician has seen something like this before?
By the way, your heading does not inspire me to answer at all. I am just interested in the question.
I like the 'please' but the word 'fast' inspires me to answer more slowly.
I am just telling you this because you said 'please' and I am giving you the opportunity to ask differently next time.
1) The angle sum of a quadriateral is 360 degrees
2) the angle at a point is 360 degrees
3) When subtended from the same arc, the angle at the centre is twice the angle at the circumference.
In this case the angles are subtended from arc BC
Use facts 3 and 2 to get all the angles of the quadrilateral in terms of x and then use fact 1 to solve for x
Yes it is (-2z)^1 Because the terms are 4x+y+(-2z)
I am very pleased that you are so interested in mathematics and that you learned from this challenge.
It would be very nice if you worked on your presention.
Yours all runs together so it is very difficult to make sense of. Plus you do not use brackets when they are needed.
For most people maths is really hard. When they see a big block of letters and numbers and symbols they just turn off.
That is not what you want.
It is great to see that my post sparked some interest. :)
The first one is great.
You did make one small error though. (It is a very common error all through mathematics)
Can you find it?
The second one is also good. I haver not checked it I am just impressed that you did it. I assume it is correct since you did it with a program.
However I do not understand your formula. How can 6+3- a positive number =28
Oh maybe my detective work has worked.... do you mean ???
where n=6+3-1 [Exponent of polynomial + number of terms - 1]
and r = 6 [exponent of polynomial]
So that is 8C6 = 28 Bingo
So for a nomal cubic binomial (a+b)^3 There would be (3+2-1)C3 = 4C3 = 4 terms.
Das ist Ausgezeichnet!
1. A ball is thrown upward from the roof of a building 60 m tall. The ball reaches a height of 80 m above the ground after 2s and hits the ground 6 s after being thrown. Determine an equation of the function.
When t=0 h=60 (0,60)
when t=2 h=80 (2,80)
when t=6 h=0 (6,0)
The equation is h=ax^2+bx+c
Use these points (substitution and simultaneous equations) to determine the values of a b and c.