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fgiga [73]
2 years ago
9

Find the tenth term of the expansion (x+ y)¹³

Mathematics
1 answer:
Anon25 [30]2 years ago
3 0

Answer:

715x^4y^9

Step-by-step explanation:

Given

(x + y)^{13

Required

Determine the 10th term

Using binomial expansion, we have:

(a + b)^n = ^nC_0a^nb^0 + ^nC_1a^{n-1}b^1 + ^nC_2a^{n-2}b^2 +.....+^nC_na^{0}b^n

For, the 10th term. n = 9

So, we have:

(a + b)^n = ^nC_{9}a^{n-9}b^{9

(x + y)^{13} = ^{13}C_{9}x^{13-9}y^9

(x + y)^{13} = ^{13}C_{9}x^4y^9

Apply combination formula

(x + y)^{13} = \frac{13!}{(13-9)!9!}x^4y^9

(x + y)^{13} = \frac{13!}{4!9!}x^4y^9

(x + y)^{13} = \frac{13*12*11*10*9!}{4!9!}x^4y^9

(x + y)^{13} = \frac{13*12*11*10}{4!}x^4y^9

(x + y)^{13} = \frac{13*12*11*10}{4*3*2*1}x^4y^9

(x + y)^{13} = \frac{17160}{24}x^4y^9

(x + y)^{13} = 715x^4y^9

Hence, the 10th term is 715x^4y^9

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Answer:

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Name the relationship between the angles below. What is the sum of the angles? Explain how you would find the missing angle. Explain each step. (replace with 120 & x)

Step-by-step explanation:

Name the relationship between the angles below. What is the sum of the angles? Explain how you would find the missing angle. Explain each step. (replace with 120 & x)

8 0
2 years ago
Find the total surface area of this triangular prism.<br> 17 cm<br> 8 cm<br> 2 cm<br> 15 cm
kumpel [21]

Answer:

<em> 200cm²</em>

Step-by-step explanation:

Total surface area of the prism = bh + L(s1+s2+s3)

b is the base of the triangle = 15cm

h is the height of the triangle = 8cm

Perimeter of the triangular base = s1 + s2 + s3 = 8+17+15

Perimeter of the triangular base = 40cm

L is the lateral height = 2cm

Substitute the given values into the formula;

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Total surface area of the prism  = 200cm²

<em>Hence the total surface area of the prism is 200cm²</em>

8 0
2 years ago
Plz help asap......................................
ziro4ka [17]

Option B:

Law of cosine, two sides and the included angle are known.

Solution:

Let us first know the law of cosines and law of sines.

Law of cosine:

If we know the sides a, b and the included angle θ, then we can find the third side c. This is known as the law of cosine.

c^2=a^2+b^2-2abcos\theta

Law of sine:

The sides of a triangle are to one another  in the same ratio as the sines of their opposite angles.

$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}

Given ∠P and the sides r, q are known.

<u>To find the value of p:</u>

Option A: Law of cosines, all sides are known.

It is false by the above definition of law of cosine.

Option B: Law of cosine, two sides and the included angle are known.

It is true by the above definition of law of cosine.

Option C: Law of sines, all sides are known.

It is false, because one angle is given in question.

Option D: Law of sines, two angles and the included side are known.

It is false, because two angles are not given.

Option B is the correct answer.

Hence the answer is "Law of cosine, two sides and the included angle are known".

7 0
3 years ago
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yKpoI14uk [10]

Answer:

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Step-by-step explanation:

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New price = $60 - $18

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The new price for the jeans is $42

3 0
3 years ago
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Answer:

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Solve for x

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4 0
3 years ago
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