What is the binomial expansion of (x + 2)4? x4 + 4x3 + 6x2 + 4x + 1 8x3 + 24x2 + 32x x4 + 8x3 + 24x2 + 32x + 16 2x4 + 8x3 + 12x2 + 8x + 2
Answers
Answer-
[tex]\boxed{\boxed{(x+2)^4=x^4+8x^3+24x^2+32x+16}}[/tex]
Solution-
Given expression is [tex](x+2)^4[/tex]
Applying Binomial Theorem
[tex]\left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i[/tex]
Here,
a = x, b = 2 and n = 4
So,
[tex]\left(x+2\right)^4=\sum _{i=0}^4\binom{4}{i}x^{\left(4-i\right)}\cdot \:2^i[/tex]
Expanding the summation
[tex]=\dfrac{4!}{0!\left(4-0\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(4-1\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(4-2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(4-3\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(4-4\right)!}x^0\cdot \:2^4[/tex]
[tex]=\dfrac{4!}{0!\left(4\right)!}x^4\cdot \:2^0+\dfrac{4!}{1!\left(3\right)!}x^3\cdot \:2^1+\dfrac{4!}{2!\left(2\right)!}x^2\cdot \:2^2+\dfrac{4!}{3!\left(1\right)!}x^1\cdot \:2^3+\dfrac{4!}{4!\left(0\right)!}x^0\cdot \:2^4[/tex]
[tex]=1\cdot x^4\cdot \:1+4\cdot x^3\cdot \:2+6x^2\cdot \:4+4\cdot x\cdot \:8+1\cdot 1\cdot \:16[/tex]
[tex]=x^4+8x^3+24x^2+32x+16[/tex]
Answer:
The answer to this question can be viewed in the images attached.
Hope it helps. Thanks
Related Questions
Which equation best represents the line graphed above?
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I brought 1 1/4 lbs of grapes. 2 1/2 lbs of cherries and 2lbs of bananas. How much total pounds of fruit did i buy?
Answers
1 + 2 + 2 = 5
Now, add the fractions together:
1/4 = 2/8
1/2 = 4/8
2/8 + 4/8 = 6/8 or 3/4
Add your two amounts together to get:
5 3/4 lbs of fruit
Hope this helps!! :)
1/4 + 1/2
1/4 + 2/4 = 3/4
The answer will be 5 3/4
Hope I helped
identify the like terms 3x,4y,4z,5x
Answers
A rabbit lure on a greyhound racetrack is set to travel once around the track at 50 feet per second, and then its speed is increased to 65 feet per second for the second loop around the track. If the total time it takes for the lure to go around the track twice is 184 seconds, what is the distance once around the track?
Answers
184 = 65 Circumference/3250 + 50 Circumference/3250
184 = 115 Circumflex/3250
598000 = 115 Circumflex
Circumflex = 5200 ft
the answer would be 5200ft
What is the slope of a line that is perpendicular to the line that goes through (5,4) and (-2,-3)?
Answers
First, let us solve for the slope of the line which it intersects with:
m’ = (y2 – y1) / (x2 – x1)
m’ = (-3 – 4) / (-2 – 5)
m’ = 1
The slope of the perpendicular line is the negative reciprocal, therefore:
m = - 1 / m’
m = - 1 / 1
m = -1
So the slope of the line is -1.
Can someone please help me with math
Answers
at 2 seconds.....231 * 2 = 462 ft
If the decay of 742 mg of an isotope is described by the function A(t)= 742e-0.03t, where t is time in years. Find the amount left after 84 years. Round your answer to the nearest mg.
Answers
Answer:
The amount left after 84 years is 59.70 mg.
Step-by-step explanation:
Given : If the decay of 742 mg of an isotope is described by the function [tex]A(t)= 742e^{-0.03t}[/tex], where t is time in years.
To find : The amount left after 84 years?
Solution :
The function of decay of 742 mg of an isotope is given by,
[tex]A(t)= 742e^{-0.03t}[/tex]
We have to find the amount left after 84 years.
i.e. put t=84 in the given function,
[tex]A(84)= 742e^{-0.03\times 84}[/tex]
[tex]A(84)= 742e^{-2.52}[/tex]
[tex]A(84)= 59.701[/tex]
Therefore, The amount left after 84 years is 59.70 mg.
What is the expanded equivalent of cos(a – b)?
Answers
That should be your answer Hope this helps
The expanded equivalent of cos(a – b) is cos(a)cos(b)+sin(a)sin(b).
Given that,
The equation is cos(a - b).We need to find the expanded equivalent of the above equation.Based on the above information, the calculation is as follows:
= cos (a - b)
= cos(a)cos(b)+sin(a)sin(b)
Therefore we can conclude that the expanded equivalent of cos(a – b) is cos(a)cos(b)+sin(a)sin(b).
Learn more: brainly.com/question/12736770
¿A Sandra qué le gusta hacer los viernes?
A A Sandra le gusta comer papas fritas los viernes.
B A Sandra le gusta comer agua los viernes.
C A Sandra le gusta beber pizza los viernes.
D A Sandra le gusta beber galletas los viernes.
Answers
A states that "Sandra likes to eat fries on fridays."
B states that Sandra likes to eat water on fridays? (makes no sense)
C states that Sandra likes to drink pizza on fridays? (again makes no sense)
D states that Sandra likes to drink cookies on fridays? (NO SENSE)
Best answer choice is A.
Triangle A′B′C′ is the image of triangle ABC after a dilation. What is the scale factor of the dilation?
Answers
6 / 3 = 2
BC is 3, and B'C' is 1.
3 / 3 = 1
Therefore the dilation factor would be 1/3.
Hope this helps! :)
To which graph does the point (8, −2) belong?
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Does believing in god increases the probability that god does exist
Answers
If he exists then he does. More or less people "believing" doesn't change a fact.
It's like how we can't see all colors and other creatures can see "more" colors than us; and then having us claim they don't exist. Whether we decide to believe there's more colors we can't see or not will not change the fact of whether there IS or ISNT.
KInda if you love him then he loves personally i dont believe in him but thats everyone decision
What is the numerator of the fraction equivalent to 25/135 that has a denominator of27
Answers
Let n be a nonzero integer. find a domain on which f (x) = (1 − xn)1/n coincides with its inverse. hint: the answer depends on whether n is even or odd.
Answers
I believe that the correct equation given is:
f(x) = (1-x^n)^(1/n)
From this, we can say that:
When n is an
odd number then f(x) is cubic root function. The domain is (-infinite,
+finite)
When n is an even number then f(x) is sqrt root
function. The domain is (0, +finite)
Terry bought 2 1/2 dozen chocolate chip cookies. She paid $15 for her purchase. If there were 12 cookies in each dozen, what was the cost per cookie?
$0.17
$0.83
$1.25
$0.50
Answers
find f(-5) if f(x) = ???????
Answers
f(x) = Ιx+1Ι
x = -5
Ι-5Ι = 5
so equation is 5+1
answer is 6
in a survey respondents were asked which type of movie they watched most often. the bar graph shows how many males and how many females said they watched each type of movie most often.
how many more males said they watched action movies than drama movies
2
4
5
8
Answers
males that watched drama movies : 5
so there are (13 - 5) = 8 more that watched action then drama
Answer:
Option D) 8
Step-by-step explanation:
We are given the following information in the question:
A bar graph is given that shows how many males and how many females said they watched each type of movie most often.
To find:
We have to find that how many males said that they watched action movies than drama movies .
In the bar graph:
Number of action movies watched by males = 13
Number of drama movies watched by males = 5
Number of males males said that they watched action movies than drama movies = 13 - 5 = 8
Males watched 8 action movies more than the drama movies.
Hence, the correct option is D.
Antonio purchased adult and child tickets for the fair. Tickets cost $29.35 for each adult and $17.45 for each child. Let x represent the number of adult tickets purchased and y represent the number of child tickets purchased. Write an expression to represent the total cost of the tickets Antonio purchased.
$29.35y + $17.45x
$29.35x + $17.45y
($29.35 + $17.45)(x + y)
($29.35 - $17.45)(x + y)
Answers
Solve for x.
7(x - 3) = 4(x + 5)
Answers
7(x-3) = 4(x+5)
distribute:
7x-21 = 4x+20
add 21 to both sides
7x = 4x +41
subtract 4x from both sides
3x = 41
divide both sides by 3
x = 41 /3 = 13.67 ( repeating 6's) so it can be 13 2/3 as a fraction
the answer is 13 2/3
If you know that two triangles are congruent, you know that any unmarked corresponding parts are also congruent by
Answers
What is the smallest number greater than 100 that is :
a)divisible by two ?
b)divisible by ten?
c)divisible by four ?
Answers
102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130
104, 108, 112, 116, 120, 124, 128, 132, 136
110, 120, 130, 140
Now it's just a matter of finding the number that is the same for all three of them, which is 120.
The smallest number greater than 100 divisible by 2 is 102, divisible by ten is 110, divisible by four is 104.
What is Divisibility Test?It is an easy method of determining the divisibility of a number by a particular divisor, by just observing the number and not actually dividing it.
The number is 100
A smallest number greater than 100 has to be found which is divisible by 2.
All even numbers are divisible by 2, a number which has 0, 2, 4, 6, 8 at its ones position are divisible by 2.
The smallest number from 100 which is divisible by 2 is 102.
A smallest number greater than 100 has to be found which is divisible by 10.
A number is divisible by 10, if it has 0 at its ones position.
The number after 100 which has 0 at its ones position is 110.
A smallest number greater than 100 has to be found which is divisible by 4.
If last two digit of a number forms 00 or are divisible by 4, then the number is divisible by 4.
The smallest number from 100 which is divisible by 4 is 104.
To know more about Divisibility Rule
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what is the value for x (5x+15) (3x-3)
Answers
The value of x in the expression (5x+15) (3x-3) is 15x^2 + 30x - 45.
Explanation:The expression (5x+15) (3x-3) represents the multiplication of two binomials. To find the value of x, we can use the distributive property to simplify the expression:
Multiply the terms within the first set of parentheses: 5x * 3x = 15x^2.Multiply the terms within the second set of parentheses: 5x * -3 = -15x.Multiply the terms between the parentheses: 15 * 3x = 45x.Multiply the constant terms within the parentheses: 15 * -3 = -45.Putting it all together, we have 15x^2 - 15x + 45x - 45. Combining like terms, the expression simplifies to 15x^2 + 30x - 45.
So, the value for x in the given expression is 15x^2 + 30x - 45.
What's 4.50+4.50+2.39+2.39+1.99? What's the answer minus 25?? pls halp meh '-'
Answers
+
2.39+2.39=4.78
+
1.99
=
15.77
15.77-25=-9.23
Jeffrey is planning to tile his bathroom. He is taking measurements before he goes to the hardware store to buy the tile. What is the best unit of measure for Jeffrey to use?
Answers
Answer:
i think the answer would be square feet
Step-by-step explanation:
A sealed rectangular box measuring 8 x 6 x 18 contains 864 sugar cubes, each measuring 1 x 1 x 1. How many sugar cubes are touching the box?
Answers
Final answer:
A total of 456 sugar cubes touching the box.
Explanation:
To calculate the number of sugar cubes touching the box, we must consider the cubes that lie along each face of the box without double-counting the cubes that touch corners and edges.
The box dimensions are 8 x 6 x 18 inches, and each sugar cube is 1 x 1 x 1 inch.
For the top and bottom faces (6 x 18), we have
6*18 = 108 sugar cubes touching the box on each face, totaling 216 for both the top and bottom.
For the front and back faces (8 x 18), since we must exclude the top and bottom rows, we have
(8-2) x (18-2) = 6 x 16 = 96 sugar cubes for one face and 192 for both.
For the sides (8 x 6), excluding the top and bottom rows again, we have
(8-2) x (6-2) = 6 x 4 = 24 sugar cubes on one side and 48 in total for the two sides.
Adding all these together, we get 216 (top and bottom) + 192 (front and back) + 48 (sides) = 456 sugar cubes touching the box.
Remember, this method assumes a single layer of sugar cubes is in direct contact with the inside surface of the box.
Carly is 3 times her brother's age. The sun of their age is no more than 24 years.
Answers
brothers age = x
carly's age = 3x
3x +x <=24
4x<=24
x<=24/4 = 6
brothers age is x<=6
Solve x + 9 = 18 - 2x
Answers
3x+9=18
Subtract 9 from both sides. 3x=9
Divide both sides by 3.
x=3
The solution to the equation x + 9 = 18 - 2x is x = 3.
What is the solution to the equation?Given the equation in the question:
x + 9 = 18 - 2x
To solve the equation x + 9 = 18 - 2x, first, collect and combine the x terms on one side of the equation and the constant terms on the other side:
x + 9 = 18 - 2x
Add 2x to both sides of the equation:
x + 2x + 9 = 18 - 2x + 2x
x + 2x + 9 = 18
3x + 9 = 18
Subtract 9 from both sides of the equation:
3x + 9 - 9 = 18 - 9
3x = 18 - 9
3x = 9
Isolate x by dividing both sides by 3:
x = 9/3
x = 3
Therefore, the value of x is 3.
Learn more about equations here: brainly.com/question/14686792
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The equations y = -0.38x + 56.6 and y = 0.38x + 43.4 represent the percent of men and women, respectively, receiving bachelor's degrees, where x is the number of years since 1968. in approximately what year did the same percent of men and women receive bachelor's degrees?
Answers
y=-0.38x+56.6
y=0.38x+43.4
-0.38x+56.6=0.38x+43.4
-0.38x-0.38x=-56.6+43.4
-0.76x=-13.3
x=-13.3/-0.76
x=17.5
y=0.38(17.5)+56.6
y=63.25
Knowing that the initial year was 1968, add 17.5 years to find to find out when the same percent of men and women received a bachelor's degree.
1968+17.5= 1985.5
So, in the year 1985 and half, both men and women got the same number of bachelor's degrees.
Hope I helped :)
Please help!
This graph shows the amount of rain that falls in a given amount of time.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement
The slope of the line is ___
This means that ___ mm of rain falls every ___
Answers
To find the slope, we use the formula for slope,
[tex]m=\frac{y_{2}-y_{2}} {x_{2}-x_{1}}[/tex]
Letting the point (2,5) be [tex](x_{1},y_{1})[/tex] and the point (4,10) be [tex](x_{2},y_{2})[/tex].
Now plugging in these values in the formula for slope, we get,
[tex]m=\frac{10-5}{4-2} =\frac{5}{2}[/tex]. The slope is [tex]\frac{5}{2}[/tex].
This basically means 5 mm of rain falls in every 2 hours, or 2.5 mm of rain falls every hour ([tex]\frac{5}{2} =2.5[/tex])
ANSWER: Slope is [tex]\frac{5}{2}[/tex] and 5 mm of rain falls every 2 hours.
2x7+2 ?
What does x =