By definition, congruent triangles should have all the corresponding sides and all the corresponding angles equal or congruent to each other. Thus, in the given question, all corresponding sides and angles of ΔEFG and ΔE'F'G' should be congruent. But, as we can see clearly it is given that, EF = 10 and E'F'= 12, thus, the corresponding sides EF and E'F' are not equal. Thus, we can never prove that:

Thus, 
the diagonal of a rectangle is square root of (w^2 +l^2)
so square root of (14^2 +10^2) = 17.2 inches
since 20" is longer than 17.2 it can't be a rectangle
3(2x+1)=2(x+1)+1
6x+3=2x+2+1
6x+3=2x+3
minus 2x
4x+3=3
minus 3
4x=0
divide by 4
x=0
her work is correct
her conclusion is wrong; there is one solution which is x=0
Answer:
1.26 feets
Step-by-step explanation:
Given the following :
Vertex (0, 0)
Focus of reflector = 6 feets
Extension = 5.5 feets
Equation to obtain conic section of a parabola:
(x - h)² = 4p(y - k)
Vertex (0, 0)
h =0 ; k = 0, p = 6, x = 5.5
(5.5 - 0)² = 4*6(y - 0)
30.25 - 0 = 24(y - 0)
30.25 = 24y
y = 30.25 / 24
y = 1.26
Hence, depth of reflector = 1.26 feets
Answer:
Thus, the coffee shop is willing to supply 6 pounds per week at a price of $4 per pound.
Step-by-step explanation:
We are given the following information in the question:
The marginal price per pound (in dollars) is given by:

where x is the supply in pounds.

The coffee shop is willing to supply 9 pounds per week at a price of $7 per pound.
Thus, we are given that
P(9) = 7
Putting the values, we get,


Now, we have to find how many pounds it would be willing to supply at a price of $4 per pound.
P(x) = 4

Thus, the coffee shop is willing to supply 6 pounds per week at a price of $4 per pound.