Answer:
+ 1) is an even number.
Take any n ∈ N, then n is either even or odd.
• Suppose n is even ⇒ n = 2m for some m ⇒ n(n + 1) = 2m(n + 1) ⇒ n(n + 1) is even.
• Suppose n is odd ⇒ n+ 1 is even ⇒ n+ 1 = 2m for some m ⇒ n(n+ 1) = 2nm ⇒ n(n+ 1)
is even. QED
2. The sum of the first n natural num
Step-by-step explanation:
a>50A is greater than 50
a<50a<50
a≥50A is greater than or equal to 50
a≤50
Answer:
55 degrees
Step-by-step explanation:
All angles in a triangle must equal 180 degrees when added together
They provide you with 2 angles 35 degrees and 90 degrees
So, you add 35 + 90 = 125
So you know that the 2 angles they give you equal 125 degrees
Now, you subtract 180 - 125 = 55
So the missing angle is 55 degrees
Given the function h(x)=x^2+14x+41, to solve by completing square we procced as follows;
x^2+14x+41=0
x^2+14x=-41
but;
c=(b/2)^2
and b=14
hence;
c=(14/2)^2=49
substituting the value of c in the expression we get:
x^2+14x+49=-41+49
x^2+14x+49=8
(x+7)^2=8
this can be written in vertex form;
h(x)=a(x-h)^2+k
where:
(h,k) is the vertex;
thus
(x+7)^2=8
h(x)=(x+7)^2-8
hence the vertex will be at the point:
(-7,-8)
Hello!
To solve this problem, we will use a system of equations. We will have one number be x and the other y. We will use substitutions to solve for each variable.
x+y=9
x=2y-9
To solve for the two numbers, we need to solve the top equation. The second equation shows that x=2y-9. In the first equation, we can replace 2y-9 for x and solve.
2y-9+y=9
3y-9=9
3y=18
y=6
We now know the value of y. Now we need to find x. We can plug in 6 for y in the second equation to find x.
x=2·6-9
x=12-9
x=3
Just to check, we will plug these two numbers into the first equation.
3+6=9
9=9
Our two numbers are three and six.
I hope this helps!
