Find the third term of (x^2 + 2)^4.

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]in~the~expansion~of~(x+a)^n\\T_{r+1}=ncr x^{n-r}a^r\\r+1=3\\r=3-1=2\\n=4\\4c2=\frac{4 \times 3}{2 \times 1} =6\\T_{2}=4(x^2)^{4-2}(2)^2\\=16(x^2)^2\\=16x^4[/tex]

Answer 2

the third term is: 24*x^4

We want to find the third term of the equation:

(x^2 + 2)^4

So we need to expand that.

Remember the rule:

(a + b)^2 = a^2 + 2*a*b + b^2

(a + b + c)^2 = a^2 + b^2 + c^2 + 2*a*b + 2*b*c + 2*c*a

Then we can write:

(x^2 + 2)^4 = (x^2 + 2)^2*(x^2 + 2)^2

and we have:

(x^2 + 2)^2 = (x^4 + 2*2*x^2 + 2^2) = (x^4 + 4*x^2 + 4)

Then we have:

(x^2 + 2)^4 = (x^2 + 2)^2*(x^2 + 2)^2

(x^2 + 2)^4 = (x^4 + 4*x^2 + 4)^2

And we can expand this as:

(x^4)^2 + (4*x^2)^2 + 4^2 + 2*(x^4)*(4*x^2) + 2*(4*x^2)*(4) + 2*(x^4)*(4)

now we have this expanded, so we need to simplify this:

x^8 + 16*x^4 + 16 + 8*x^6 + 32*x^2 + 8*x^4

Putting the terms in order (larger degrees go in the left) we get:

x^8 + 8*x^6 + 16*x^4 + 8*x^4 + 32*x^2 + 16

x^8 + 8*x^6 + (16 + 8)*x^4 + 32*x^2 + 16

x^8 + 8*x^6 + 24*x^4 + 32*x^2 + 16

So the third term would be the third counting from the left, which is:

24*x^4

If you want to learn more, you can read:

https://brainly.com/question/12556222


Related Questions

In the following diagram, ABCD is a parallelogram. Is AC the bisector of angle BAD? Show calculations and explain

Answers

AC is not the bisector of angle BAD. AC made both sides a triangle and every triangles angles have to add to 180 degrees. So 115+30= 145 meaning angle DAC is 35 degrees. So AC cuts through BAD but one side is 30 degrees and the other is 35(DCB and DAB are the same angle…they both have to add up to 65 degrees)

Answer:

yes

Step-by-step explanation:

in parallelogram ,<A=<C

<C=<D

then <D=115=<C=115

X+115+30=180....TRIANGLE THEROME

X=35

so that,<A=65

<C=65

Find the following ratios. PLEASE HELP QUICK!!

Answers

Answer:

sin(A) = 5/13 ≈ 0.38

cos(B) = 5/13 ≈ 0.38

tan(A) = 5/12 ≈ 0.42

Step-by-step explanation:

If you need more explanations just say it :)

Answer:

I hope your dreams come true! Beileve in your self! and do ur best <3

find H.C.F OF 4x²y and xy²​

Answers

Answer:

xy

Step-by-step explanation:

The HCF is known as the highest common factor. To find the HCF of two values, we have to take the greatest number that fits into all of their factors.

To start, we can list each value's factors.

For 4x²y, this can also be written as 4*x²*y = 4*x*x*y. In multiplication, we can take the factors of each value that is multiplied. Therefore, we can start with the factors of 4 and then go to the factors of x² and so on. Our factor list is thus 1,2,4,x,x²,y

Similarly, for xy² = x*y*y, our factors are x, y, and y²

The common factors for each of these are x and y. Assuming all values are positive and greater than 1, the x*y will be greater than either x or y. Therefore, the highest common factor would be x*y = xy

Classify the polynomial 5x3 + 4x - 2 by degree.

Answers

Answer:

3

Step-by-step explanation:

3 would be the degree of the polynomial since it has the highest degree.

Find the approximate side length of a square game board with an area of 145 in 2 Plz help!

Answers

Answer:

Side length ≈ 12.04

Step-by-step explanation:

145 = x²

144 is the closest  square, with the root 12

The square root of 145 is approximately 12.04

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer:

The approximate side length is 12.0 in

Step-by-step explanation:

The area of a square is given by

A = s^2  where s is the side length

145 = s^2

Taking the square root of each side

sqrt(145) = sqrt(s^2)

12.04159458 = s

The approximate side length is 12.0 in

From the table below, determine whether the data shows an exponential function. Explain why or why not. x 3 1 -1 -3 y 1 2 3 4 a. No; the domain values are at regular intervals and the range values have a common sum 1. b. No; the domain values are not at regular intervals. c. Yes; the domain values are at regular intervals and the range values have a common factor 2. d. Yes; the domain values are at regular intervals and the range values have a common sum 1. Please select the best answer from the choices provided A B C D

Answers

A………………………………………………….

Answer:

C

Step-by-step explanation:

you find the variable

Find x.

A. 6√6
B. 18
C. 9√2
D. 24√3

Answers

Answer:

C  

Step-by-step explanation:

( 2 + 3 ) ^-1 x ( 2 ^-1 + 2^-1 )

Answers

Answer:

Step-by-step explanation:

[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boxed{ \boxed{\boldsymbol{Rule : a^{-1}=\frac{1}{a} }}} \\\\\\\\ (2+3)^{-1} \times (2^{-1}+2^{-1}) = \\\\1)\ (2+3)^{-1}=5^{-1}=\frac{1}{5} \\\\2)\ 2^{-1}+2^{-1}=\frac{1}{2} +\frac{1}{2} } =1 \\\\3)\ \frac{1}{5} \cdot 1=\boxed{\frac{1}{5} }[/tex]

what is the solution to the equation below? sqrt x-7 = 5
A. 144
B. 12
C. 2
D. 4

Answers

Answer:

I think the answer is B.12

If this not correct, Sorry.

Ian has 300 counters in a bag. Paul
takes 42 of them. Derek takes 65 of
them. Anne takes 33 of them. What
fraction does Ian have left? Give your
answer in its simplest form.

Answers

42 + 65 + 33 = 140, so Ian has 160 counters left. 160/300 in its simplest form is 8/15

Simplify the following without a calculator: (5)(6+4)

Answers

Answer:

your answer is 50 I hope it's helps you t

Answer:

50

Step-by-step explanation:

(5)(6+4)

5(6)+5(4)

30+20

50

THANK YOU

If 2 < 20x - 13 < 3. what is one possible value for x?

Answers

Answer:

one possible value for x is 31/40

Step-by-step explanation:

Let's isolate the 20x term.  Add 13 to all three terms:

2 + 13 < 20x - 13 + 13 < 3 + 13

and this simplifies to:

15 < 20x < 16

Dividing all three terms by 20, we get:

15/20 < x < 16/20

A fraction halfway between 15/20 and 16/20 is (31/20)/2, so

one possible value for x is 31/40.

Check by substituting this into the original equation and checking whether that equation is now true:

2 <20(31/40) - 13 < 3

or

2 < 31/2 < 16, or 2 < 15.5 < 16 (this is true, so 31/40 is a solution)

Please help explanation if possible

Answers

Answer:

17.6

Step-by-step explanation:

Answer:

80 pennies ; 160 nickels

Step-by-step explanation:

Given the 2 equations

0.01p + 0.05n = 8.80 → (1)

n = 2p → (2)

Substitute n = 2p into (1)

0.01p + 0.05(2p) = 8.80

0.01p + 0.1p = 8.80

0.11p = 8.80 ( divide both sides by 0.11 )

p = 80

Substitute p = 80 into (2)

n = 2 × 80 = 160

There are 80 pennies ; 160 nickels

Help!!!! Please!! Thanks

Answers

never saw an indian guy asking for help in so simple question

Step-by-step explanation:

ans of 3rd   given statement is true, conclusion, mb=nb

ans of 4th    given statement is true, conclusion alt int angles of paralel lines are equal

AB=BA
∠ABM=∠ABN
MB=NB
△AMB≌△ANB (SAS)

∠CBM=∠ADM
∠BCM=∠DAM
∠BMC=∠DMA
△BCM∽△DAM (AAA)

Hope my answer helped u :)

Graph the relation shown in the table. Is the relation a function? Why or why not?

Answers

Answer:

what can i help u with

Step-by-step explanation:

No; the relation passes the vertical-line test. Yes; only one range value exists for each domain value

Yes; two domain values exist for range

yes; only one range value exists for each domain.

Find the coordinates of the image of a triangle with vertices A(0, – 3), B(3, 0), and
C(-7, 4) under a rotation of 90° clockwise about the origin.

Answers

Answer:

A'(-3,0), B'(0,-3) and C'(4,7)

Step-by-step explanation:

We are given that the vertices of triangle are A(0,-3), B(3,0) and C(-7,4).

We have to find the coordinates of the image of triangle under a rotation of 90° clockwise about the origin.

90° clockwise about the origin

Rule:[tex](x,y)\rightarrow (y,-x)[/tex]

Using the rule

The coordinates of A'

[tex]A(0,-3)\rightarrow A'(-3,0)[/tex]

The coordinates of B'

[tex]B(3,0)\rightarrow B'(0,-3)[/tex]

The coordinates of C'

[tex]C(-7,4)\rightarrow C'(4,7)[/tex]

Hence, the vertices of image of triangle is given by

A'(-3,0), B'(0,-3) and C'(4,7)

Whats the chance of rolling the correct number 1-6500
When every time you guess a number the number changes
So if i guess 800 every time how many guesses to get the correct number

Answers

There is an 8.125 chance you can get the correct number , If you keep getting 800 every time due to the random probability , For when you divide it as 6500 ÷ 800 = 8.125

Thanks , Please mark me brainliest

From TyrantMC

HELP ASAP

The graph of f(x)= |x| is chosen below. Write the equation for the stretched graph, g(x).

Answers

Answer:

y = |3x|

Step-by-step explanation:

Can someone help me on this

Answers

Answer:

The choose (C)

F(x)=x/ (x+1)(x-2)

Given the functions below, find f(x) + g(x)
f(x) = 3x - 1
g(x) = x2 + 4

Answers

Answer:

x^2+3x+3

Step-by-step explanation:

f(x) = 3x - 1

g(x) = x^2 + 4

f(x) + g(x) = 3x-1+ x^2 +4

                 Combine like terms

                   = x^2+3x+3

Find the largest integer not greater than the following expression :
[tex]\displaystyle \large \boldsymbol{} \frac{2150}{2005} +\frac{2150}{2006} +\frac{2150}{2007 } + ...+\frac{2150}{2020}[/tex]

Answers

Answer:

17

Step-by-step explanation:

The number of terms:

2020 - 2004 = 16

Each term is greater than 1, so the expression is greater than 16:

2150/2005 = 1 + 145/20052150/2006 = 1 + 144/2006...2150/2020 = 1 + 130/2020

It's easy to note each of the numbers getting smaller like 145/2005 > 144/2006 etc. Taking the smallest fraction.

The sum is:

S > 16 + 16*130/2020 = 16 + 2080/2020 > 16 + 1 = 17

So the largest integer not greater than S is 17.

A shopkeeper sells house numbers. She has a large supply of the digits, 1, 2, 7, and 8, but no other digits. How many different three-digit house numbers could be made using only the digits in her supply?

Answers

Answer:

64.

Step-by-step explanation:

The digits used are 1 , 2, 7 and 8

To make a number of three digits, the digits are repeated.

To make the three digit number

The ones place is filled by 4 ways.

The tens place is filled by 4 ways.

The hundred place is filled by 4 ways.

So, the total number of ways to make a three digit number is 4 x 4 x 4 = 64.

please helpp!!!!!!!!​

Answers

Step-by-step explanation:

the answer is in picture

Hassan drove 78 miles in 1ị hours. If he drove at a constant rate, how far did he
travel in one hour? Enter your answer as a whole number, proper fraction, or mixed
number in simplest form.

Answers

Answer:

1 1/3 hours

Step-by-step explanation:

I took the same test

Find: 499 decreased by 100%

Answers

Answer:

0,

If you want, I can explain more into it.

Find the Value of y. 70 60 65 40

Answers

Answer:

125

Step-by-step explanation:

360-70-60-65-40

= 125

Answered by GAUTHMATH

Identify the vertex of this absolute value function: f(x) = -2|x + 1| + 2. Type the correct answer in each box. Use numerals instead of words.

Answers

Answer:

Step-by-step explanation:

x+1=0

then f(x)=2

x=-1

vertex is (-1,2)

Answer:

-1,2

Step-by-step explanation:

Plato

Determine which equations have the same solution set as 2/3 -x +1/6 = 6x by recognizing properties, rather than solving. Check all that apply.

Answers

Answer:

The answer is "0.1190".

Step-by-step explanation:

Given:

[tex]\to \frac{2}{3} -x +\frac{1}{6} = 6x\\\\\to \frac{2}{3} +\frac{1}{6} = 6x+x\\\\\to \frac{4+1}{6} = 7x\\\\\to \frac{5}{6} = 7x\\\\\to x=\frac{5}{6\times 7} \\\\\to x=\frac{5}{42}\\ \\\to x= 0.1190[/tex]

Answer:

A.) 4 - 6x + 1 = 36x

B.) 5/6 - x = 6x

F.) 5 = 42x

Step-by-step explanation:

edge.

i am having troubles solving this 4(x+3)=x+42 can i get some help please.

Answers

Answer:

x=10

Step-by-step explanation:

Step 1: Multiply 4 with X and 3. You'll get 4x+12=x+42

Step 2: Keep the variable on one side and the number on the other side. you would subtract X and subtract 12. You'll get 3x=30

Step 3: Divide by the 3 on both sides and you'll get x=10

Given:

[tex] \\ ⇢ \tt \: 4(x + 3) = x + 42 \\ [/tex]

Solution:

[tex] \\ ⇢ \tt \: 4(x + 3) = x + 42 \\ \\ \\ \tt⇢ 4x + 12 = x + 42 \: \: \\ \\ \\ \tt \: ⇢4x - x = 42 - 12 \: \\ \\ \\ \tt \: ⇢3x = 30 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: ⇢x = \frac{30}{3} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt \: \pink{ \pmb{ \mathfrak{⇢x = 10}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ [/tex]

Verification:

[tex] \\ ⇢ \tt \: 4(10+ 3) = 10+ 42 \\ \\ \\ \tt⇢ 40 + 12 = 10 + 42 \: \: \\ \\ \\ \tt \: ⇢52 = 52 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \: ⇢ \purple{ \pmb{ \bold{L.H.S = R.H.S}}}\\ \\ \\ [/tex]

Hence Verified!

sin^6x + cos^6x = 1/4

Answers

Answer:

[tex]\displaystyle x = \frac{\pi}{4} + k\, \pi[/tex] for integer [tex]k[/tex] (including negative numbers.)

Step-by-step explanation:

Pythagorean Identity: [tex]\sin^{2}(x) + \cos^{2}(x) = 1[/tex]. Equivalently, [tex]\cos^{2}(x) = 1 - \sin^{2}(x)[/tex].

Rewrite the original equation and apply this substitution to eliminate [tex]\cos(x)[/tex]:

[tex]\displaystyle \sin^{6}(x) + \cos^{6}(x) = \frac{1}{4}[/tex].

[tex]\displaystyle (\sin^{2}(x))^{3} + (\cos^{2}(x))^{3} = \frac{1}{4}[/tex].

[tex]\displaystyle (\sin^{2}(x))^{3} + (1 - \sin^{2}(x))^{3} = \frac{1}{4}[/tex].

Let [tex]y = \sin(x)[/tex] ([tex]-1 \le y \le 1[/tex].) The original equation is equivalent to the following equation about [tex]y[/tex]:

[tex]\displaystyle y^{6} + (1 - y^{2})^{3} = \frac{1}{4}[/tex].

Expand the cubic binomial in the equation:

[tex]\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, (y^{2})^{2} - (y^{2})^{3} = \frac{1}{4}[/tex].

[tex]\displaystyle y^{6} + 1 - 3\, y^{2} + 3\, y^{4} - y^{6} = \frac{1}{4}[/tex].

Simplify to obtain:

[tex]\displaystyle 1 - 3\, y^{2} + 3\, y^{4} = \frac{1}{4}[/tex].

Rearrange and simplify:

[tex]12\, y^{4} - 12\, y^{2} + 3 = 0[/tex].

[tex]3\, (2\, y^{2} - 1)^{2} = 0[/tex].

[tex]2\, y^{2} - 1 = 0[/tex].

[tex]\displaystyle y^{2} - \frac{1}{2} = 0[/tex].

Solve for [tex]y[/tex]:

Either [tex]\displaystyle y = \frac{1}{\sqrt{2}}[/tex] or [tex]\displaystyle y = -\frac{1}{\sqrt{2}}[/tex].

If [tex]\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}[/tex], then [tex]\displaystyle x = \frac{\pi}{4} + 2\, k\,\pi[/tex] for all [tex]k\in \mathbb{Z}[/tex].

On the other hand, if [tex]\displaystyle \sin(x) = y = \frac{1}{\sqrt{2}}[/tex], then [tex]\displaystyle x = \frac{3\, \pi}{4} + 2\, k\,\pi = \frac{\pi}{4} + (2\, k + 1) \, \pi[/tex] for all [tex]k\in \mathbb{Z}[/tex].

Combine both situations to obtain:

[tex]\displaystyle x = \frac{\pi}{4} + 2\, k\, \pi[/tex] for all [tex]k \in \mathbb{Z}[/tex].

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