Answer:
<em>First.</em> Let us prove that the sum of three consecutive integers is divisible by 3.
Three consecutive integers can be written as k, k+1, k+2. Then, if we denote their sum as n:
n = k+(k+1)+(k+2) = 3k+3 = 3(k+1).
So, n can be written as 3 times another integer, thus n is divisible by 3.
<em>Second. </em>Let us prove that any number divisible by 3 can be written as the sum of three consecutive integers.
Assume that n is divisible by 3. The above proof suggest that we write it as
n=3(k+1)=3k+3=k + k + k +1+2 = k + (k+1) + (k+2).
As k, k+1, k+2 are three consecutive integers, we have completed our goal.
Step-by-step explanation:
They are based on SSS. They have the middle side which they share and is equal. And those other two lines also make those sides equal, so all sides are equal and they’re congruent
Hello!
So, 9 is a multiple of 36, we know that much.
36 is NOT a factor of four.
9 is a factor of 36.
So, check the first box and the third box.
Have a wonderful day! :)
-L
Answer:
-<u>One Equation</u>: is set equal to a variable
Example:
y = 2x + 1
x + 3y = -12
You already have y, plug it back into x + 3y = -12
x + 3(2x + 1) = -12
x + 6x + 3 = -12
7x + 3 = -12
(Subtract 3 from each side)
7x = -15
(Divide by 7)
x = - 2.14
-<u>No Equation</u>: is set equal to a variable
Example:
2x + y = 10
4× + 2y = -3
Subtract 2x from each side of 2x + y = 10, you should get y= -2x + 10. Now that you have found y, substitute y into 4x+ 2y = -3.
4x + 2(-2x + 10) = -3
4x + -4x + 20 = -3
(Subtract 20 from each side)
4x + -4x = -23
(Add 4x and -4x)
0 = -23
No Solution
<u>-Both</u><u> </u><u>Equations</u>: are set equal to a variable
Example:
y = x + 5
y = -x + 3
(you already have y so plug it into the other equation to solve for x)
-x + 3 = x + 5
(Add -x on both sides)
3 = 2x + 5
(subtract 5 from both sides)
-2 = 2x
(Divide by 2 on each side)
x = -1
I hope this helped!
I believe the answer is 62