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Ksenya-84 [330]
3 years ago
13

Expand the binomial (4x + 3y)3. The coefficient of the second term in the expansion of the binomial (4x + 3y)3

Mathematics
2 answers:
Anettt [7]3 years ago
4 0
The answer is, 12x +9y
jonny [76]3 years ago
3 0

Answer:

The coefficient is 144.

Step-by-step explanation:

We have the binomial: (4x+3y)^3

The general formula for cubic binomials is:

(a+b)^3=a^3+3a^2b+3ab^2+b^3\\\\(a-b)^3=a^3-3a^2b+3ab^2-b^3

<em>Observation: (a+b)^3=(a+b)(a+b)(a+b) if you solve that the result is the general formula. The same for  (a-b)^3=(a-b)(a-b)(a-b) </em>

Then we have:

(4x+3y)^3=(4x)^3+3(4x)^2.(3y)+3(4x).(3y)^2+(3y)^3\\\\=64x^3+3.16x^2.3y+3.4x.9y^2+27y^3\\\\=64x^3+144x^2y+108xy^2+27y^3

The coefficient is the number before the variable, then the coefficient of the second term in the expansion of the binomial (4x+3y)^3 is 144.

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Use addition or substitution to find the value of y for this set of equations. 4x + 13y = 40 4x + 3y = -40
Aliun [14]
4x + 13y = 40
4x + 3y = -40

multiply second equation by -1

4x + 13y = 40
-4x - 3y = 40

add equations together

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y = 8

put y in either original equation

4x + 3(8) = -40
4x + 24 = -40

subtract 24 from both sides

4x = 64

x=16
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Which equation would you want to represent your bank account? <br> y=7x-4 <br><br> 7y+2x=6
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Answer:

y=7x-4

Step-by-step explanation:

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What are the values of the trigonometric ratios for this triangle?
nika2105 [10]

Answer:

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Two diameters of circle P are AB and CD. Find the measure of arc ACD and arc AC when arc AD has a measure of 20 degrees
steposvetlana [31]

Answer:

Hence measure of arc ACD and arc AC are 340 degrees and 160 degrees respectively.

Step-by-step explanation:

Given:

A Circle with p as center and AB and CD as 2 diameters for a circle.

To Find:

Measure of ACD, and arc AC when arc AD is 20 degrees.

Solution:

<em>As we know that , Diameter is biggest chord which passes through center of circle,</em>

<em>Hence it divides the circle into two equal parts and making center as midpoint of it</em> .

(Refer the attachment)

angle APD=20 degree or arc AD=20 degree.

So AB as diameter ,so  arc DB=160 degree  or BPD=160 degree as A-B-P are

and angle APD and BPC are vertical opposite angles so they are congruent BPC=20 degree

Now,

points A,C,B,D,A makes circle which measures 360 degrees.

to find ACD

measure of ACD=360-(meaure of arc AD or angle APD)

=360-20

=340 degree.

Now arc AC,

as AB is diameter with p as midpoint ,A-P-B

arc APB=180 and arc BC=20 or angle BPC=20 degrees.

For measure of arc AC= measure of arc APB- arc BC

arc AC=180-20 degrees.

arc AC=160 degrees.

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