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Answer:
k = 2
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - 3x + 5 ← is in slope- intercept form
with slope m = - 3
Parallel lines have equal slopes, thus the 2 points have a slope of - 3
calculate the slope using the slope formula and equate to - 3
m =
with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (k, 5)
m = =
= - 3 ( multiply both sides by (k - 4) )
- 3(k - 4) = 6 ( divide both sides by - 3 )
k - 4 = - 2 ( add 4 to both sides )
k = 2
A)
![\bf 1990-1910=80\leftarrow t \\\\\\ P(t)=8000(2)^{-\frac{t}{29}}\implies P(80)=8000(2)^{-\frac{80}{29}} \\\\\\ P(80)=8000\cdot \cfrac{1}{2^{\frac{80}{29}}}\implies P(80)=\cfrac{8000}{\sqrt[29]{2^{80}}}](https://tex.z-dn.net/?f=%5Cbf%201990-1910%3D80%5Cleftarrow%20t%0A%5C%5C%5C%5C%5C%5C%0AP%28t%29%3D8000%282%29%5E%7B-%5Cfrac%7Bt%7D%7B29%7D%7D%5Cimplies%20P%2880%29%3D8000%282%29%5E%7B-%5Cfrac%7B80%7D%7B29%7D%7D%0A%5C%5C%5C%5C%5C%5C%0AP%2880%29%3D8000%5Ccdot%20%5Ccfrac%7B1%7D%7B2%5E%7B%5Cfrac%7B80%7D%7B29%7D%7D%7D%5Cimplies%20P%2880%29%3D%5Ccfrac%7B8000%7D%7B%5Csqrt%5B29%5D%7B2%5E%7B80%7D%7D%7D)
and surely you know how much that is.
b)
since in 1910 t = 0, 174 years later from 1910, is 2084, so in 2084 they'll be 125 exactly, so the next year, 2085, will then be the first year they'd fall under that.
and surely you know how much that is.
b)
since in 1910 t = 0, 174 years later from 1910, is 2084, so in 2084 they'll be 125 exactly, so the next year, 2085, will then be the first year they'd fall under that.