Answer:
1/3(n+1)³
Step-by-step explanation:
1x2+2x3+3x4+4x5+...= 1²+1+2²+2+3²+3+...+n²+n+1=
=(1²+2²+3²+...+n²)+(1+2+3+...+n+1)=
=1/6n(n+1)(2n+1)+1/2(n+1)(1+n+1)=
=1/6(n+1)(n(2n+1)+3(n+2))=
=1/6(n+1)(2n²+4n+2)=
=1/6(n+1)*2(n+1)²=
=1/3(n+1)³
Slope is found by the formula (y2 -y1) divided by (x2 - x1). We plug in the numbers, and get ((-2) - 2) divided by (6 - (-3)). So the slope will be -0.44
The midpoints are (8,3) and (6.5,6).
<u>Step-by-step explanation</u>:
Midpoint formula = ((x1+x2)/2 , (y1+y2)/2)
(x1,y1) = (5,2)
(x2,y2) = (11,4)
Midpoint = ((5+11)/2 , (2+4)/2)
⇒ ((16/2) , (6/2))
⇒ (8,3)
(x1,y1) = (3,8)
(x2,y2) = (10,4)
Midpoint = ((3+10)/2 , (8+4)/2)
⇒ ((13/2) , (12/2))
⇒ (6.5,6)
Answer:
These lines are perpendicular.
Step-by-step explanation:
Put both equations in the slope intercept form of a line.
y = -6x - 8 This is already in the slope intercept form for a line
-x + 6y = 12 Add x to both sides of the equation
6y = x + 12 Divide through the whole equation by 6
y = 1/6x +2
Now we compare the two slopes of -6 and 1/6. They are negative reciprocals of each other. That means that the line are perpendicular.
The -2 at the end means that while the x remains constant, the y will be smaller - it shifts it 2 units down
the other change is that it's x+4 now, not x, and this shifts the graph left. (the value of function is now the same as previously when x was smaller)
the answer is B!
