Fill in the blank with the correct imperfect conjugation of the verb in parentheses. Ella ____ a asistir a la clase pero no fue.
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Dilation involves changing the size of a line segment
The scale factor is 2
From the question (see attachment), we have the following side lengths
So, the scale factor (k) from AB to A'B' is calculated using the following scale factor formula
This gives
Divide 2.5 by 1.25
Hence, the scale factor is 2
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The coefficients for the binomial expansion of (a + b)³ are 1, 3, 3, 1.
We have,
The binomial expansion (a + b)³,
So,
Now,
We know that,
Formula for binomial expansion,
i.e.
(u + v)ⁿ = ⁿC₀ · uⁿ · v⁰ + ⁿC₁ · uⁿ⁻¹ · v¹ + ⁿC₂ · uⁿ⁻² · v² + ⁿC₃ · uⁿ⁻³ · v³
Now,
According to the question,
Here,
u = a,
v = b,
And, n =3
Now,
Putting values,
i.e.
(a + b)³ = ³C₀ · a³ · b⁰ + ³C₁ · a³⁻¹ · b¹ + ³C₂ · a³⁻² · b² + ³C₃ · a³⁻³ · b³
We get,
(a + b)³ = ³C₀ · a³ · b⁰ + ³C₁ · a² · b¹ + ³C₂ · a¹ · b² + ³C₃ · a⁰ · b³
Now,
Using combination formula,
On solving we get,
(a + b)³ = a³ + 3 a² b + 3 a b² + b³
So,
Now,
The coefficients of :
a³ = 1,
3a²b = 3,
3ab² = 3,
b³ = 1,
So,
The coefficients of the given binomial expansion are 1, 3, 3, 1.
Hence we can say that the coefficients for the binomial expansion of (a + b)³ are 1, 3, 3, 1.
Learn more about binomial expansion here
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