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3 years ago

Write the first three terms in the binomial expansion, expressing the result in simplifies form.

Mathematics

1 answer:

Pani-rosa [81]3 years ago

8 0

You need to foil it out. That's how you get the answer.

(x+4)^20
=
(x+4) x (x+4)^19
=
(x+4)^2 x (x+4)^18
etc.

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(Brainliest) PLEASE HELPP MEEE

zloy xaker [14]

Answer:

1. According to the angle bisector theorem, DAC = BAC

2. Same kind of goes for BC

3. X must be equal in both equations. x= 3

9(3) -7 = 20

4(3) +8 = 20

Hope this helped!

8 0

2 years ago

Integrate Sec (4x - 1) Tan (4x - 1) Dx

Delicious77 [7]

$\bf \displaystyle\int~sec(4x-1)tan(4x-1)dx \\\\[-0.35em] ~\dotfill\\\\ sec(4x-1)tan(4x-1)\implies \cfrac{1}{cos(4x-1)}\cdot \cfrac{sin(4x-1)}{cos(4x-1)}\implies \cfrac{sin(4x-1)}{cos^2(4x-1)} \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~\cfrac{sin(4x-1)}{cos^2(4x-1)}dx \\\\[-0.35em] ~\dotfill\\\\ u=cos(4x-1)\implies \cfrac{du}{dx}=-sin(4x-1)\cdot 4\implies \cfrac{du}{-4sin(4x-1)}=dx \\\\[-0.35em] ~\dotfill$

$\bf \displaystyle\int~\cfrac{~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{u^2}\cdot \cfrac{du}{-4~~\begin{matrix} sin(4x-1) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies -\cfrac{1}{4}\int\cfrac{1}{u^2}du\implies -\cfrac{1}{4}\int u^{-2}du \\\\\\ -\cfrac{1}{4}\cdot \cfrac{u^{-2+1}}{-1}\implies \cfrac{1}{4}\cdot u^{-1}\implies \cfrac{1}{4u}\implies \cfrac{1}{4cos(4x+1)}+C$

5 0

3 years ago

The amount of money in a saving account increase from $250 to $270 what is the precent increase of the money in the savings acco

saveliy_v [14]

Answer:

Step-by-step explanation:

percent increase = [ (difference between initial value and final value) ÷ initial value] x 100

⇒ percent increase = [ (270 - 250) ÷ 250] x 100 = 8%

7 0

2 years ago

Read 2 more answers

Verify the identity. 4 csc 2x = 2 csc2x tan x

vlada-n [284]

Step-by-step explanation:

$4csc(2x) = 2csc^2(x) tan(x)$

We start with Left hand side

We know that csc(x) = 1/ sin(x)

So csc(2x) is replaced by 1/sin(2x)

$4 \frac{1}{sin(2x)}$

Also we use identity

sin(2x) = 2 sin(x) cos(x)

$4 \frac{1}{2sin(x)cos(x)}$

4 divide by 2 is 2

Now we multiply top and bottom by sin(x) because we need tan(x) in our answer

$2\frac{1*sin(x)}{sin(x)cos(x)*sin(x)}$

$2\frac{sin(x)}{sin^2(x)cos(x)}$

$2\frac{1}{sin^2(x)} \frac{sin(x)}{cos(x)}$

We know that sinx/ cosx = tan(x)

Also 1/ sin(x)= csc(x)

so it becomes 2csc^2(x) tan(x) , Right hand side

Hence verified

6 0

3 years ago

huong and kathyrn each day impeoved their yards by planting rose bushes and ornamental grass. they bought their supplies from th

marta [7]

Answer:

One rose bush = $3

One bunch of ornamental grass = $4

Step-by-step explanation:

We can set up a system of equations to solve for this. Let cost of 1 rose bush be r and cost of 1 ornamental grass be g. Thus we can form 2 equations:

$14r+7g=70\\5r+14g=71$

We can multiply the first equation by -2 so that we can eliminate g. Thus, we have:

$(*-2)14r+7g=70\\5r+14g=71\\-------\\-28r-14g=-140\\5r+14g=71\\--------\\-23r=-69\\r=\frac{-69}{-23}=3$

Thus, 1 rose bush is $3. Now plugging in r = 3 into the first original equation, we can solve for g:

$14r+7g=70\\14(3)+7g=70\\42+7g=70\\7g=70-42\\7g=28\\g=\frac{28}{7}=4$

Thus, 1 bunch of ornamental grass is $4.

5 0

3 years ago