Answer:
Yes.
Step-by-step explanation:
If the slope between successive points have the same slope then they will form a straight line.
Slope = ( 3.5- -1) / (-2 - -8) = 4.5/6 = 3/4
Slope = (12.5 - 3.5) / (10 - -2) = 9 / 12 = 3/4
Slope = (20-12.5)/(20-10) - 7.5/10 = 3/4 .
So the answer is yes.
The point-slope form of a line:
We have the points (-9, -5) and (2, -4). Substitute:
The standard form of a line:
<em>multiply both sides by 11</em>
<em>subtract 9 from both sides</em>
<em>subtract 11y from both sides</em>
Step-by-step explanation:
(a²-b²)(c²-d²) = a²c² - a²d² - b²c² + b²d²
(b²-d²)(c²-a²) = b²c² - a²b² - c²d² + a²d²
the sum of both is
a²c² + b²d² - a²b² - c²d² = a²(c²-b²) + d²(b²-c²) =
= a²(c²-b²) - d²(c²-b²) = (c²-b²)(a²-d²) = 2021
after a little check we find 2021 is only divisible by 43 and 47 (or 1 and 2021).
so, it is clear that our expression resembles
43×47 = 2021
that means that e.g. c²-b² = 43, and a²-d² = 47
or the other way around, it does not matter.
what squared integer numbers give a difference of 43 ? and 47 ?
squared numbers
1 4 9 16 25 36 49 64 81 100 121 144 169 196 225 256
289 324 361 400 441 484 529 576
aha ! 484 - 441 = 43
and 576 - 529 = 47
so, we get
a = sqrt(576) = 24
b = sqrt(441) = 21
c = sqrt(484) = 22
d = sqrt(529) = 23
one could also use the formula for consecutive squared numbers
(n+1)² = n² + 2n + 1
under the assumption that the 2 numbers are convective (which it turns out they are in this example) we get
(n+1)² - n² = 2n + 1 = 43
2n = 42
n = 21
n+1 = 22
and for 47
2n + 1 = 47
2n = 46
n = 23
n+1 = 24
