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2 years ago

PLEASE HURRY!!!!!! 10 points !!!!!!!!!!! What is the value of x??

Mathematics

1 answer:

horsena [70]2 years ago

3 0

Answer:

x = 98°

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

x is an exterior angle and 53° and 45° are the opposite interior angles, hence

x = 53° + 45° = 98°

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Find the 2th term of the expansion of (a-b)^4.

vladimir1956 [14]

The second term of the expansion is $-4a^3b$ .

Solution:

Given expression:

$(a-b)^4$

To find the second term of the expansion.

$(a-b)^4$

Using Binomial theorem,

$(a+b)^{n}=\sum_{i=0}^{n}\left(\begin{array}{l}n \\i\end{array}\right) a^{(n-i)} b^{i}$

Here, a = a and b = –b

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

Substitute i = 0, we get

$$\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}=1 \cdot \frac{4 !}{0 !(4-0) !} a^{4}=a^4$

Substitute i = 1, we get

$$\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}=\frac{4 !}{3!} a^{3}(-b)=-4 a^{3} b$

Substitute i = 2, we get

$$\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}=\frac{12}{2 !} a^{2}(-b)^{2}=6 a^{2} b^{2}$

Substitute i = 3, we get

$$\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}=\frac{4}{1 !} a(-b)^{3}=-4 a b^{3}$

Substitute i = 4, we get

$$\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}=1 \cdot \frac{(-b)^{4}}{(4-4) !}=b^{4}$

Therefore,

$$(a-b)^4=\sum_{i=0}^{4}\left(\begin{array}{l}4 \\i\end{array}\right) a^{(4-i)}(-b)^{i}$

$=\frac{4 !}{0 !(4-0) !} a^{4}(-b)^{0}+\frac{4 !}{1 !(4-1) !} a^{3}(-b)^{1}+\frac{4 !}{2 !(4-2) !} a^{2}(-b)^{2}+\frac{4 !}{3 !(4-3) !} a^{1}(-b)^{3}+\frac{4 !}{4 !(4-4) !} a^{0}(-b)^{4}$ $=a^{4}-4 a^{3} b+6 a^{2} b^{2}-4 a b^{3}+b^{4}$

Hence the second term of the expansion is $-4a^3b$ .

3 0

2 years ago

Quick help.<br> Will Mark as Brainliest if my laptop stops acting up.

Dimas [21]

Vertex is now at (-1,5)

for
y=a(x-h)^2+k
vertex is (h,k)
so veertex is (-1,5)

y=a(x-(-1))^2+5
y=a(x+1)^2+5
a is a constant, we will asssume that it is 1 because all the choices have 1

y=1(x+1)^2+5
y=(x+1)^2+5

2nd option

8 0

3 years ago

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Alex17521 [72]

Answer:

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2 years ago

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Georgia [21]

Answer:

answer=cos2 I ---------1

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2 years ago

Is this Network a HAMILTONIAN Circuit? If so write the path.

Anton [14]

The path of the given Hamiltonian diagram is A, E, B, C, D, F. See explanation below.

<h3>What is a Hamiltonian Path?</h3>

A Hamiltonian path, also known as a traceable path, is one that visits each vertex of the graph precisely once.

A traceable graph is one that contains a Hamiltonian path.

Hence, the path is given as;
A, E, B, C, D, F

Learn more about Hamiltonian Paths at;
brainly.com/question/15521630
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1 year ago