Answer:
16
um belo dia abençoado
Use the Binomial Theorem/Pascal's Triangle to expand (2a + 2b)^5
Answer:
32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5
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Explanation:
Let's use Pascal's Triangle
In the row that starts with 1,5,... we have the values 1,5,10,10,5,1
These will be the coefficients of the terms.
Let x = 2a and y = 2b
We want to expand out (x+y)^5
Using pascals triangle, we get the following expansion
(x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5
The numbers in bold are the coefficients 1,5,10,10,5,1 found earlier.
Note how the exponents for x start at 5 and count down to 0; while the y exponents start at 0 and count up to 5. For any term, the x and y exponents always add to 5 for the expansion of (x+y)^5. In general, the exponents of any term will add to n for (x+y)^n.
At this point, we plug in x = 2a and y = 2b
Since this will clutter things a bit, I'll do it term by term
1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^55x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^210x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^35x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^41x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5So in the end, the expression (2a+2b)^5 expands out to
32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5
The binomial theorem uses the same basic idea, but instead of using Pascal's Triangle to get the coefficients, you'll use the nCr combination formula.
Answer: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex].
Using Pascal's triangle we get:
[tex](x+y)^5 = 1x^5y^0+5x^4y^1+10x^3y^2+10x^2y^3+5x^1y^4+1x^0y^5[/tex]
Here, x = 2a and y = 2b
So the terms become:
[tex]1x^5y^0 = 1(2a)^5(2b)^0 = 1(32a^5)(1) = 32a^5\\5x^4y^1 = 5(2a)^4(2b)^1 = 5(16a^4)(2b) = 160a^4b\\10x^3y^2 = 10(2a)^3(2b)^2 = 10(8a^3)(4b^2) = 320a^3b^2\\10x^2y^3 = 10(2a)^2(2b)^3 = 10(4a^2)(8b^3) = 320a^2b^3\\5x^1y^4 = 5(2a)^1(2b)^4 = 5(2a)(16b^4) = 160ab^4\\1x^0y^5 = 1(2a)^0(2b)^5 = 1(1)(32b^5) = 32b^5\\[/tex]
Hence: [tex](2a+2b)^5 =32a^5+160a^4b+320a^3b^2+320a^2b^3+160ab^4+32b^5[/tex]
Learn more: https://brainly.com/question/13769924
Day 2 question: Get it right and I'll give you brainliest(or if I just like your answer). Who is my favorite American rapper?
A. Kevin Gates
B. Megan Thee Stallion
C. Moneybagg yo
D.Cardi B
Extra Question: If you could be one celebrity for the day then who?
Answer to the last question(which I think was deleted but i'll put it anyway)
My favorite kpop groups order is: B(P1Harmony, Seventeen, Ateez, Stray Kids)
Answer:
Cardi B
Step-by-step explanation:
and my kpop stan is SEVENTEEN and im a carat, my bias is woozi
Answer I think its money bagg yo and i would want to be Ariana Grande
Step-by-step explanation:
The larger of two numbers is sixteen less than twice the smaller number. If the sum of the numbers is 44, find the two numbers. Write your answer as two numbers separated by a coma.
Answer:
20, 24
Step-by-step explanation:
smaller: x
larger: 2x - 16
x + 2x - 16 = 44
3x -16 = 44
3x = 60
x = 20
smaller: x = 20
larger: 2x - 16 = 2(20) - 16 = 24
Somebody help me plzzZZZZ
Answer:
Step-by-step explanation:
9.
a1=-35
d=a2-a1=-28-(-35)=7
a35=a1+(35-1)7
=-35+34×7
=-35+238
=203
Which of the following is equivalent to the addition problem below?
27.93 +61.63
If a toy rocket is launched vertically upward from the ground level with an initial velocity of 128 feet per second, then its height h after t seconds is given by the equation:
h(t) = -16t^2 + 128t
What is the maximum height the rocket reaches?
Answer:
The maximum height of the rocket is 256 feet
Step-by-step explanation:
The vertex form of the quadratic function f(x) = ax² + bx + c is
f(x) = a(x - h)² + k, where
(h, k) is the vertex pointh = [tex]\frac{-b}{2a}[/tex] and k = f(h)(h, k) is a minimum point if a > 0 and a maximum point if a < 0Let us use these rules to solve the question
∵ h(t) = -16t² + 128t
→ Compare it by the form of the quadratic function above
∴ a = -16 and b = 128
∵ a < 0
∴ The vertex (h, k) is a maximum point
∴ The maximum height of the rocket is the value of k
→ Use the rule of h above to find it
∵ h = [tex]\frac{-128}{2(-16)}[/tex] = [tex]\frac{-128}{-32}[/tex]
∴ h = 4
→ Substitute x in the equation by the value of h to find k
∵ k = h(h)
∴ k = -16(4)² + 128(4)
∴ k = -256 + 512
∴ K = 256
∴ The maximum height of the rocket is 256 feet
find the LCM and HCF of 110 and 220 by prime factorization, what do u observe
Answer:
GCF= 2 x 5 x 11 = 110
LCM= 2 x 2 x 5 x 11 = 220
Step-by-step explanation:
Need Help ASAP I’m having trouble
Answer:
ok
Step-by-step explanation:
nerd nerd nerd nerd lolololollool
2 points
2) Mark bought a new suit for $139. The sales tax was 8.5%. What is the
total cost of the suit?*
Each letter of the word "supercalifragilisticexpialidocious" is placed into a bag and drawn at 3 times, replacing the letter after each draw. Find the probability that the letter "i" is drawn at least once.
Answer:
P(X ≥ 1) = 0.50
Step-by-step explanation:
Given that:
The word "supercalifragilisticexpialidocious" has 34 letters in which 'i' appears 7 times in the word.
Then; the probability of success = 7/34 = 0.20588
Using Binomial distribution to determine the probability; we have:
[tex]P(X = x) = ^nC_x \ \beta^x \ (1 - \beta)^{n-x}[/tex]
where;
x = 0,1,2,...n and 0 < β < 1
and x represents the number of successes.
However; since the letter is drawn thrice; the probability that the letter "i" is drawn at least once can be computed as:
P(X ≥ 1) = 1 - P(X< 1)
P(X ≥ 1) = 1 - P(X =0)
[tex]P(X \ge 1) = 1 - \bigg [ {^3C__0} (0.21)^0 (1-0.21)^{3-0} \bigg][/tex]
[tex]P(X \ge 1) = 1 - \bigg [ 1 \times 1 (0.79)^{3} \bigg][/tex]
P(X ≥ 1) = 1 - 0.50
P(X ≥ 1) = 0.50
Just answer correctly to get brainleist and 10 pts! :)
Answer:
B
Step-by-step explanation:
x is repeated
please help im so confused at math pls help
Answer:
where is the question ??
the perimeter of an isosceles triangle in which the equal sides measures 12cm each and third side is 8cm_____. please show the working too ^^
Use the formula P = 2a+ b.
Let a = 12
Let b = 8
P = 2(12) + 8
P = 24 + 8
P = 32
Plz answer these two and I will give you brainliest
Answer:
1. -9. 2.i cant see what all the options are but the slope is y= 1/2x -3
Step-by-step explanation:
Hope this helps :)
Determine the value of x.
Name the point of concurrency shown. Please please don’t answer if you don’t know it!!!
Answer:
Circumcenter
Step-by-step explanation:
give an example of a rational number
3
..
4) through: (-2,5), slope
2.
Answer:
y - 5 = 2(x + 2)
General Formulas and Concepts:
Point-Slope Form: y - y₁ = m(x - x₁)
x₁ - x coordinate
y₁ - y coordinate
m - slope
Step-by-step explanation:
Step 1: Define
Slope m = 2
Point (-2, 5)
Step 2: Create equation
y - 5 = 2(x + 2)
simplify each expression
(e^2)(g)(g^4)(e^3)
(e)(e^2)(e)
9514 1404 393
Answer:
e^5g^5e^4Step-by-step explanation:
The applicable rule of exponents is ...
(a^b)(a^c) = a^(b+c)
__
[tex](e^2)(g)(g^4)(e^3)=e^{(2+3)}g^{(1+4)}=\boxed{e^5g^5}\\\\(e)(e^2)(e)=e^{(1+2+1)}=\boxed{e^4}[/tex]
Jeff has two sticker-printing machines. Each machine can print 42 stickers per minute. On day 1, only the first machine was used, and it printed 89 stickers. On the following day, the first machine printed for x minutes and the second machine printed for y minutes. Which expression shows the total number of stickers printed by both machines during these two days? (1 point) a 131x + 42y b 42 + 89x + y c 89 + 42x + 42y d 89x + 84y
Answer:
c 89+42x+42y
Step-by-step explanation:
On day 1 :
First Machine= 89 stickers
Second Machine= none
On day 2 :
First Machine= ? stickers ( if in 1min = 42stickers
x min=?
( x min/1 min × 42stickers)
=42x stickers.
Second Machine=?stickers ( if in 1min = 42stickers
y min=?
( y min/1 min × 42stickers)
=42y stickers.
Total = 89 + 42x + 42y
Jonathan’s class has 30 boys. Of the students in his class, 60% are girls.How many girls are in Jonathan’s class?
Answer:
45=60%
15=20%
30=40%
60=80%
75=100%
Step-by-step explanation:
Answer: Approximately due to my calculations there are about 60 girls
Step-by-step explanation:60% as a decimal is 0.6
7. Find the slope of the line.
Answer:
5
Step-by-step explanation:
take 2 points on the graph, for example (4,20) and (2,10) use y2-y1/x2-x1 to solve ,plug in the values 20-10/4-2= 10/2 = 5
I need help please!!
Answer:
1
Step-by-step explanation:
The line goes through the point 1, so that will be the slope.
If a ∥ b and e ∥ f, what is the value of y?
87
88
91
92
Answer:
88 i believe
Step-by-step explanation:
Answer:
92
Step-by-step explanation:
Angle (x+1) is equal to 92 degrees, and x equals 91. If x equals 91, then (x+1) equals 92. (x+1) and angle y are equal angles, so therefore, you can determine that angle y is equal to 92 degrees.
-I got the question right on the test
Hope this helps!
I need help on this question!
Answer:
110 cookies in 180 minutes
Step-by-step explanation:
The number one selling item at Sam’s Swim Shop is a beach towel. It is priced at $7.50 , How much will Mrs. Wilson spend if she purchases 4 beach towels and pays 6% sales tax ?
Answer:
$31.80
Step-by-step explanation:
What is the distance between (4,-1) and (0,1)
Answer:
answer is in the image below
Step-by-step explanation:
Use the distance formula to determine the distance between two points.
Write the equation for a parabola with the focus at
(-1, 4) and the equation of the directrix x = 5.
(x + 1)2 = 3(y-4)
(y-4)2 = 12(x + 1)
(y-2)2 = -3(x – 4)
(y-4)2 = –12(x - 2)
Write the slope intercept form of the equation of the line through the given point with the given slope through (-2,5),slope-3/2
Answer:
Slope Intercept Form: y= -3/2× + 2
Need help ASAP please give answer in cm squared
Answer:
17×15=255
Step-by-step explanation:
you do base times height