The given points are the vertices of the quadrilateral
By Green's theorem, the line integral is
We know that the angles of a triangle sum to 180°. For ΔABC, this means we have:
(4x-10)+(5x+10)+(7x+20)=180
Combining like terms,
16x+20=180
Subtracting 20 from both sides:
16x=160
Dividing both sides by 16:
x=10
This means ∠A=4*10-10=40-10=30°; ∠B=5*10+10=50+10=60°; and ∠C=7*10+20=70+20=90.
For ΔA'B'C', we have
(2x+10)+(8x-20)+(10x-10)=180
Combining like terms,
20x-20=180
Adding 20 to both sides:
20x=200
Dividing both sides by 20:
x=10
This gives us ∠A'=2*10+10=20+10=30°; ∠B'=8*10-20=80-20=60°; and ∠C'=10*10-10=100-10=90°.
Since the angle are all congruent, ΔABC~ΔA'B'C' by AAA.
Answer:
It is a perfect square trinomial.
Step-by-step explanation:
The square of a binomial can be solved like this:
We have the expression:
Then, we consider a and b as:
The solution would be:
Answer:
By the parallelogram angle theorem, opposite angles of a parallelogram are congruent. Therefore, angle T must be congruent to angle G, and angle G must be congruent to angle L. By the transitive property of congruence, angle T is congruent to angle L.
Step-by-step explanation:
Answer:
The concentration of salt in the tank approaches 
Step-by-step explanation:
Data provide in the question:
Water contained in the tank = 8000 L
Salt per litre contained in Brine = 35 g/L
Rate of pumping water into the tank = 25 L/min
Concentration of salt 
Now,
Dividing both numerator and denominator by 
, we have
Here,
The concentration of salt in the tank approaches
