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Mathematics

1 answer:

ExtremeBDS [4]3 years ago

3 0

Answer:

TRUE

Step-by-step explanation:

We are given 2 triangles, ∆ABC and ∆DEF.

For the two trinagles to be considered similar, both must have their set of corresponding angles congruent to each other. That is, their corresponding angles are equal.

From the information given, the following are the set of corresponding angles:

<B = <E = 31°

<B = <D = 90°

<C = <F = 59° [180 - (90+31)]

The corresponding angles of both triangles are congruent. Therefore, it is guaranteed that ∆ABC is similar to ∆DEF (∆ABC ~ DEF).

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What is the fourth term in the binomial expansion (a+b)^6)

Dafna11 [192]

Answer:

$20a^3b^3$

Step-by-step explanation:

<u>Binomial Series</u>

$(a+b)^n=a^n+\dfrac{n!}{1!(n-1)!}a^{n-1}b+\dfrac{n!}{2!(n-2)!}a^{n-2}b^2+...+\dfrac{n!}{r!(n-r)!}a^{n-r}b^r+...+b^n$

<u>Factorial</u> is denoted by an exclamation mark "!" placed after the number. It means to multiply all whole numbers from the given number down to 1.

Example: 4! = 4 × 3 × 2 × 1

Therefore, the fourth term in the binomial expansion (a + b)⁶ is:

$\implies \dfrac{n!}{3!(n-3)!}a^{n-3}b^3$

$\implies \dfrac{6!}{3!(6-3)!}a^{6-3}b^3$

$\implies \dfrac{6!}{3!3!}a^{3}b^3$

$\implies \left(\dfrac{6 \times 5 \times 4 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}{3 \times 2 \times 1 \times \diagup\!\!\!\!3 \times \diagup\!\!\!\!2 \times \diagup\!\!\!\!1}\right)a^{3}b^3$