The unknown vertex is on the perpendicular bisector of the opposite side. So the x coordinate is the same as that of the midpoint, x=(18+52)/2=35.
2/10 because there are 10 cards and there are 5 circles and 3 triangles
Answer:
y = 6x - 13
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 )
Calculate m using the slope formula
m = (y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (1, - 7)
m = 
= 
= 6, thus
y = 6x + c ← is the partial equation
To find c substitute either of the 2 points into the partial equation
Using (1, - 7), then
- 7 = 6 + c ⇒ c = - 7 - 6 = - 13
y = 6x - 13 ← equation of line
Answer:
A(t) = 300 -260e^(-t/50)
Step-by-step explanation:
The rate of change of A(t) is ...
A'(t) = 6 -6/300·A(t)
Rewriting, we have ...
A'(t) +(1/50)A(t) = 6
This has solution ...
A(t) = p + qe^-(t/50)
We need to find the values of p and q. Using the differential equation, we ahve ...
A'(t) = -q/50e^-(t/50) = 6 - (p +qe^-(t/50))/50
0 = 6 -p/50
p = 300
From the initial condition, ...
A(0) = 300 +q = 40
q = -260
So, the complete solution is ...
A(t) = 300 -260e^(-t/50)
___
The salt in the tank increases in exponentially decaying fashion from 40 grams to 300 grams with a time constant of 50 minutes.
