Answer:
x = 9
Step-by-step explanation:
take -6 to the other side so you add it to 30 = 36
equation is now 4x = 36
divide 4/4 and 36/4
x = 9
Answer:
Step-by-step explanation:
Hello,
<u>The mean of five numbers is 8</u> so we can write
<u>When another number is added the mean is 7</u>, let s note x the another number we can write
From the first equation we can say
So the second equation becomes
The solution is then 2
Hope this helps
Answer:
x= 10 In (17)
Step-by-step explanation:
Answer: The circumference would be 13.502
Step-by-step explanation: I totally forgot how to do the rest I am sorry
Answer:
Constructive Proof
Step-by-step explanation:
Let x be a positive integer
x must be equal to sum of all positive integers exceeding it
i.e.
x = x + (x - 1) + ( x - 2) + ......... + 2 + 1
Equivalently,
x = ∑i (where i = 1 to x)
The property finite sum;
∑i (i = 1 to x) = x(x + 1)/2
So,
x = x(x + 1)/2 ------- Multiply both sides by 2
2 * x = 2 * x(x + 1)/2
2x = x(x + 1)
2x = x² + x ------- subtract 2x from both sides
2x - 2x = x² + x - 2x
0 = x² + x - 2x ----- Rearrange
x² + x - 2x = 0
x² - x = 0 ------ Factorise
x(x - 1) = 0
So,
x = 0 or x - 1 = 0
x = 0 or x = 1 + 0
x = 0 or x = 1
But x ≠ 0
So, x = 1
The statement is only true for x = 1
This makes sense because 1 is the only positive integer not exceeding 1
1 = 1
It is a Constructive Proof
A proof is constructive when we find an element for which the statement is true.
