Proof: Let m any odd integer.
The definition of even integer gives,
m=2p
Here, p is also integer.
According to the question,
3m + 5=3(2p) + 5
=6p + 5
=2(3p) + 2(2) + 1
=2(3p + 4) + 1
Let, (3p + 4)=a
Here, a is integer.
The above relation implies that,
3m + 5=2a + 1
The above relation 3m + 5=2a + 1 implies the definition of odd integer.
Therefore, for all integers m, if m is even then 3m + 5 is odd.

step-by-step explanation:

cats

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

true

step-by-step explanation:

intersecting chords are just lines that intersect. so a line is equal to 180 degrees, so when it is intersected by another chord, then it create supplementary angles, and because the lines cross, vertical angels are also formed.