Answer:

To simplify first factorize both the numerator and the denominator
For the numerator
5x² + 20xy + 20y²
Factor 5 out
5 ( x² + 4xy + 4y²)
Using a² + 2ab + b² = ( a + b)²
The numerator is
5( x + 2y)²
For the denominator
x² - xy - 6y²
Rewrite -xy as a difference
x² + 2xy - 3xy - 6y²
Factorize
We have the denominator as
( x + 2y)( x - 3y)
So we now have
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Simplify
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We have the final answer as
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Hope this helps you
Answer:
Maria's string is 45 cm long and Katy's string is 39 cm long
Step-by-step explanation:
Let's call the size of Maria's string X, and the size of Katy's string Y.
So, using the information from the problem, we can formulate a system of equations:
If Maria's string is 6 cm longer than Katy's, so:
X = Y + 6
If the strings together have 84 cm, so:
X + Y = 84
The first equation can be rewritten as X - Y = 6
Summing up both equation, we have that:
2X = 90
X = 45
Using X value in the first equation, we have that:
45 = Y + 6
Y = 39
So, Maria's string is 45 cm long and Katy's string is 39 cm long
Short Answers:
Answer for part A: Given
Answer for part B: Angle A = Angle D (not sure why this isn't in word bank?)
Answer for part C: ASA
Answer for part D: BC = EF
Answer for part E: CPCTC
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Explanations:
Part A:
AB = DE is given at the very top of the problem. So we simply say "given". We always repeat what we are given at the very start of the proof. You can see this for lines 1 through 3, which are repeating the three givens.
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Part B:
The three givens are:
AB = DE
angle A = angle D
angle B = angle E
the first and last of this trio is used (for statements 1 and 3 respectively). So the only thing left is "angle A = angle D"
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Part C:
We're using ASA (angle side angle) because we're given two pairs of congruent angles. The side for each triangle is between the two angles. See the attached diagram for more info.
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Part D:
For any proof, you will ALWAYS have the last statement be the thing you want to prove. In this case, we want to prove BC = EF.
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Part E:
CPCTC stands for "Corresponding Parts of Congruent Triangles are Congruent"
If the two whole triangles are congruent, then the smaller corresponding parts that make up the triangles must be congruent as well.
Answer:
15.6
Step-by-step explanation: