Answer:
y = - 3x + 11
Step-by-step explanation:
the altitude is a line from the vertex A drawn perpendicular to the opposite side BC
calculate the slope of BC using the slope formula
m = 
with (x₁, y₁ ) = B (- 7, 3 ) and (x₂, y₂ ) = C (- 1, 5 )
=
=
=
= 
given a line with slope m then the slope of a line perpendicular to it is
= -
= -
= - 3
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept ) , then
y = - 3x + c ← is the partial equation
to find c substitute A (4, - 1 ) into the partial equation
- 1 = - 12 + c ⇒ c = - 1 + 12 = 11
y = - 3x + 11 ← equation of altitude from A
Answer:
48 sq. units
Step-by-step explanation:
The area of a trapezoid is given by half sum of the bases multiplied by the height

where a and b are the two parallel sides of the trapezoid and h is the height or amplitude of the trapezoid
But you are aware that, the median of a trapezoid is equal to half the sum of the bases, thus the first part of the formulae is covered by the median

Hence area, A, of a trapezoid is simplified to product of median and amplitude

Don't know whether or not you've encountered differential equations yet, but will try that approach here.
The growth rate is dy/dt = ky (which states that the rate is proportional to the size of the population, y, and k is a constant.
Grouping like terms,
dy
--- = kt, so y = Ne^kt
y
We are told that at t=0, there are 880 bacteria. Thus, 880=N. Therefore,
y = 880e^(kt). After 5 hours the pop will be 4400; using this info, find k:
4400=880e^(5k), or 5 = e^(5k). So, our y = 880e^(kt) becomes
y = 880e^(5t).
What will be the pop after 2 hours? y(2)=880e^(10) = 880(22026) =
approx. 19,383,290 bacteria
Time to reach a pop of 2550? 2550 = 880e^(5t). Find t.
ln 2550 = ln 880 + 5t, so ln 2550 - ln 880 = 5t. Divide both sides by 5 to obtain this time, t.