The complete proof for the given parallelogram is given in the image attached below.
<h3>What is a Parallelogram?</h3>
A parallelogram is a quadrilateral whose opposite sides are parallel and also congruent to each other.
The complete proof would be as shown below:
1. ABCD is a parallelogram [given]
2. AB║CD [Definition of parallelogram]
3. ∠1 ≅ ∠2, ∠3 ≅ ∠4 [alternate interior angles theorem]
4. AB ≅ CD [Definition of parallelogram]
5. ΔABE ≅ ΔCDE [ASA]
6. AE ≅ CE, BE ≅ DE [CPCTC]
7. AC and BD bisects each other at E [definition of segment bisector]
Learn more about parallelogram on:
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*Given
Money of Phoebe - 3 times as much as Andy
Money of Andy - 2 times as much as Polly
Total money of Phoebe, - £270
Andy and Polly
*Solution
Let
B - Phoebe's money
A - Andy's money
L - Polly's money
1. The money of the Phoebe, Andy, and Polly, when added together would total £270. Thus,
B + A + L = £270 (EQUATION 1)
2. Phoebe has three times as much money as Andy and this is expressed as
B = 3A
3. Andy has twice as much money as Polly and this is expressed as
A = 2L (EQUATION 2)
4. This means that Phoebe has ____ as much money as Polly,
B = 3A
B = 3 x (2L)
B = 6L (EQUATION 3)
This step allows us to eliminate the variables B and A in EQUATION 1 by expressing the equation in terms of Polly's money only.
5. Substituting B with 6L, and A with 2L, EQUATION 1 becomes,
6L + 2L + L = £270
9L = £270
L = £30
So, Polly has £30.
6. Substituting L into EQUATIONS 2 and 3 would give us the values for Andy's money and Phoebe's money, respectively.
A = 2L
A = 2(£30)
A = £60
Andy has £60
B = 6L
B = 6(£30)
B = £180
Phoebe has £180
Therefore, Polly's money is £30, Andy's is £60, and Phoebe's is £180.
Answer:
The answer is 3,019.92 cubic millimeter
Step-by-step explanation:
take 375 plus 375 to get 750
then 3769.91 - 750 to get the 3,019.92
Answer:
The correct option is D) 
Step-by-step explanation:
Consider the provided information.
People are entering a building at a rate modeled by f (t) people per hour and exiting the building at a rate modeled by g (t) people per hour,
The change of number of people in building is:
Where f(t) is people entering in building and g(t) is exiting from the building.
It is given that "The functions f and g are non negative and differentiable for all times t."
We need to find the the rate of change of the number of people in the building.
Differentiate the above function with respect to time:
![h'(x)=\frac{d}{dt}[f(t)-g(t)]](https://tex.z-dn.net/?f=h%27%28x%29%3D%5Cfrac%7Bd%7D%7Bdt%7D%5Bf%28t%29-g%28t%29%5D)
It is given that the rate of change of the number of people in the building is increasing at time t.
That means 
Therefore, 
Hence, the correct option is D)
