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]
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
sin^6x + cos^6x = 1/4
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].
Graph the relation shown in the table. Is the relation a function? Why or why not?
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.
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?
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.
find H.C.F OF 4x²y and xy²
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
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.
Find x.
A. 6√6
B. 18
C. 9√2
D. 24√3
Answer:
C
Step-by-step explanation:
In the following diagram, ABCD is a parallelogram. Is AC the bisector of angle BAD? Show calculations and explain
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
Please help explanation if possible
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
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
Find the approximate side length of a square game board with an area of 145 in 2 Plz help!
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
Answer:
C
Step-by-step explanation:
you find the variable
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.
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.
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.
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
( 2 + 3 ) ^-1 x ( 2 ^-1 + 2^-1 )
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]
Given the functions below, find f(x) + g(x)
f(x) = 3x - 1
g(x) = x2 + 4
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]
Answer:
17Step-by-step explanation:
The number of terms:
2020 - 2004 = 16Each term is greater than 1, so the expression is greater than 16:
2150/2005 = 1 + 145/20052150/2006 = 1 + 144/2006...2150/2020 = 1 + 130/2020It'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 = 17So the largest integer not greater than S is 17.
Can someone help me on this
Answer:
The choose (C)
F(x)=x/ (x+1)(x-2)
Find the following ratios. PLEASE HELP QUICK!!
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
please helpp!!!!!!!!
Step-by-step explanation:
the answer is in picture
HELP ASAP
The graph of f(x)= |x| is chosen below. Write the equation for the stretched graph, g(x).
Answer:
y = |3x|
Step-by-step explanation:
what is the solution to the equation below? sqrt x-7 = 5
A. 144
B. 12
C. 2
D. 4
Answer:
I think the answer is B.12
If this not correct, Sorry.
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.
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)
Find the Value of y. 70 60 65 40
Answer:
125
Step-by-step explanation:
360-70-60-65-40
= 125
Answered by GAUTHMATH
Simplify the following without a calculator: (5)(6+4)
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
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
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
Find: 499 decreased by 100%
Answer:
0,
If you want, I can explain more into it.
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.
Answer:
1 1/3 hours
Step-by-step explanation:
I took the same test
i am having troubles solving this 4(x+3)=x+42 can i get some help please.
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!If 2 < 20x - 13 < 3. what is one possible value for x?
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)
Classify the polynomial 5x3 + 4x - 2 by degree.
Answer:
3
Step-by-step explanation:
3 would be the degree of the polynomial since it has the highest degree.
