We have to present the number 41 as the sum of two squares of consecutive positive integers.
1² = 1
2² = 4
3² = 9
4² = 16
5² = 25
16 + 25 = 41
<h3>Answer: 4 and 5</h3>
Other method:
n, n + 1 - two consecutive positive integers
The equation:
n² + (n + 1)² = 41 <em>use (a + b)² = a² + 2ab + b²</em>
n² + n² + 2(n)(1) + 1² = 41
2n² + 2n + 1 = 41 <em>subtract 41 from both sides</em>
2n² + 2n - 40 = 0 <em>divide both sides by 2</em>
n² + n - 20 = 0
n² + 5n - 4n - 20= 0
n(n + 5) - 4(n + 5) = 0
(n + 5)(n - 4) = 0 ↔ n + 5 = 0 ∨ n - 4 =0
n = -5 < 0 ∨ n = 4 >0
n = 4
n + 1 = 4 + 1 = 5
<h3>Answer: 4 and 5.</h3>
Answer:
A (1,-2) B(10,1) C(6,2)
Step-by-step explanation:
You add 4 to the x value and subtract 3 from the y value to get the answer.
<h3>hello!</h3>
Let's write this verbal phrase as an inequality.
First of all, let the number be n.
"three times n" can be written like so:-
Now, 18 is greater than 3n:-
Which means 3n is less than 18:-
<h3>note:-</h3>
Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I'll comment and/or edit my answer :)
Answer:
If you are looking for what w equals, the w would equal 3
Step-by-step explanation:
You would take the absolute value which is how far away a value is from zero.
So you would get 4w+2=14
Then you would bring the positive 2 to the other side making it negative
now we have 4w=14-2 which is the same as 4w=12
and then, you would divide 12 by 4 and then you would get 3
so
w=3
