The missing parts of the proof are: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
<h3>What is a Square?</h3>
A square is a special type of rectangle whose consecutive sides are congruent. All four sides of a square are congruent.
In the proof given, the distance formula
was used to find ST = a units in step 2.
By the definition of congruence, RS = ST in step 4.
Finally, RSTU is stated to be a square because if two consecutive sides of a rectangle are congruent, then it is a square.
The option that completes the proof in the right order is: A. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it is a square.
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Answer:
Step-by-step explanation:
a
Okay, here we have this:
Considering the provided information, we are going to calculate the requested value, so we obtain the following:
Then we will substitute in the following formula:
Students who play soccer=Number of students*(Probability that they play soccer)
Replacing:
Students who play soccer=300*(12/25)
Students who play soccer=3600/25
Students who play soccer=144
Finally we obtain that 144 students would we expect to play soccer, based on Sean's experiment.
Answer:
4
Step-by-step explanation:
8-4=4
Answer:
Difference between the approximation and the actual value of f′(0.5) is 0.4330
Step-by-step explanation:
As complete question is not give, so considering the most relevant question to given statement in Fig below.
from table
x 0 1
f(x) 1 2
f'(0.5)=?
from numerical differentiation
![f'(0.5)=\frac{(2-1)}{(1-0)}\\\\f'(0.5)=1---(2)](https://tex.z-dn.net/?f=f%27%280.5%29%3D%5Cfrac%7B%282-1%29%7D%7B%281-0%29%7D%5C%5C%5C%5Cf%27%280.5%29%3D1---%282%29)
Given function is
![f(x)=2^{x^{3}}](https://tex.z-dn.net/?f=f%28x%29%3D2%5E%7Bx%5E%7B3%7D%7D)
Differentiating w.r.to x
![f'(x)=ln(2)2^{x^{3}}\frac{d}{dx}(x^{3})\\\\f'(x)=ln(2)2^{x^{3}}(3x^{2})\\\\f'(x)=3x^{2}2^{x^{3}}ln(2)\\at \quad x=0.5\\\\f'(0.5)=0.5669---(2)](https://tex.z-dn.net/?f=f%27%28x%29%3Dln%282%292%5E%7Bx%5E%7B3%7D%7D%5Cfrac%7Bd%7D%7Bdx%7D%28x%5E%7B3%7D%29%5C%5C%5C%5Cf%27%28x%29%3Dln%282%292%5E%7Bx%5E%7B3%7D%7D%283x%5E%7B2%7D%29%5C%5C%5C%5Cf%27%28x%29%3D3x%5E%7B2%7D2%5E%7Bx%5E%7B3%7D%7Dln%282%29%5C%5Cat%20%5Cquad%20x%3D0.5%5C%5C%5C%5Cf%27%280.5%29%3D0.5669---%282%29)
Difference between the approximation and the actual value of f′(0.5) is 0.4330