The equation of a line that passes through (x1,y1) and has a slope of m is
y-y1=m(x-x1)
given
y-(-4)=-5(x-3)
the point is (3,-4)
A+5 is the same as 3+5 since A=3.
You would take five and count up by three, 6,7,8.
<u>Your answer would be 8.</u>
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
To find the mode, or modal value, it is best to put the numbers in order. Then count how many of each number. A number that appears most often is the mode.The Range is the difference between the lowest and highest values. Example: In {4, 6, 9, 3, 7} the lowest value is 3, and the highest is 9. So the range is 9 − 3 = 6 .
Answer:
d = 2.2
Step-by-step explanation:
Using the distance formula, you would plug in the numbers into the equation. d = √(5 - 3)^2 + ( -3 + 2)^2. So (5 - 3) is 2, and (-3 + 2) is -1. Then square both of the answers, and the equation becomes, d = √4 + 1. And that equals 5, so then you would find the square root, which would be approximately 2.2
