Hi guys actually I have forgotten the steps do it yesterday my online school opened so I don't how to solve it can you help me please
Answers
Answer:
(i) (x +4)^3 = x^3 +12x^2 +48x +64
(ii) (2m +1)^3 = 8m^3 +12m^2 +6m +1
(iii) (a -2b)^3 = a^3 -6a^2b +12ab^2 -8b^3
Step-by-step explanation:
Powers of a binomial have a pattern. The coefficients of the terms of the expanded product are the numbers in the corresponding row of Pascal's Triangle. Here, you want the 3rd power, so the coefficients of interest are ...
1, 3, 3, 1
The pattern is ...
(a +b)^2 = a^2 +2ab +b^2
(a +b)^3 = a^3 +3a^2b +3ab^2 +b^3
The total of powers of the variable is equal to the exponent of the binomial. The powers of the first variable decrease to 0 while the powers of the second variable increase from zero.
When 'a' or 'b' is something with a coefficient, that whole term is raised to the appropriate power.
__
i) (x+4)^3 = x^3 +3·4x^2 +3·4^2x +4^3
(x +4)^3 = x^3 +12x^2 +48x +64
__
ii) (2m +1)^3 = (2m)^3 +3·1·(2m)^2 +3·1^2·(2m) +1^3
(2m +1)^3 = 8m^3 +12m^2 +6m +1
__
iii) (a -2b)^3 = a^3 +3·a^2·(-2b) +3·a·(-2b)^2 +(-2b)^3
(a -2b)^3 = a^3 -6a^2b +12ab^2 -8b^3
_____
Additional comment on Pascal's triangle
The numbers in each row are the sums of the two numbers immediately above. For binomial expansion, you're only interested in the contents of a row. The "patterns" shown in the attachment are an extra added attraction, not particularly relevant to binomial expansion.
Related Questions
First answer gets brainliest!
Answers
Answer:
the answer is 6561m^4
Step-by-step explanation:
9^4 = 9^4m^4
9^4=6561
6561m^4
Answer:
♫ :::::::::::::::::::::::::::::: // Hello There ! // :::::::::::::::::::::::::::::: ♫
➷ The correct answer would be option D.
❄️
➶ Hope This Helps You!
➶ Good Luck (:
➶ Have A Great Day ^-^
Step-by-step explanation:
ok i saw this felt like posting it :P
answer: 6561m^4
9 is multiplied by the cube of a number
Answers
Some friends went to lunch and split the bill equally. If each person paid $6.75, how many people went to lunch thinking. Use a diagram or equation to explain your thinking. The total is 27$. 27 divided by 6.75 is 4. Suppose
$7.00 was added to the bill for a dessert tha everyone shared. How much more would each person have to pay?
Answers
Answer:
Step-by-step explanation:
We’ve all been there. You know how it goes… you’re out with your friends, you order an inexpensive item on the menu to be your frugal/responsible self, and then the bill comes and someone says, “Let’s just split it equally! That’ll make it easy!” Then, out come the wallets, credit cards, and cash. It’s awkward to pipe up and say, “Uh, but, uh, I only had the $7 thing not the $35 thing, and no wine or dessert or appetizers!”
No one what’s to be the cheap/poor/miser in the group. I’ve been there. Trust me. It’s not a fun place to be. So, how do you deal?
Lucky for us, a reader wrote in with that very question:
“This weekend I went out to a friend’s birthday dinner which was out at a restaurant. We’d recently gone out to eat for this friends’ sisters birthday and everyone in the group paid for themselves. Additionally, during all the other previous times we went out, that I can remember, we all pay for ourselves.
Well this weekend, when the bill came, one of the guests at the table suggested that we all split the bill 6 ways to make things simpler and so that the birthday girl wouldn’t have to pay. This was devastating to me and my wallet! I’d looked at the menu before getting to the restaurant and chose one of the cheapest entrees, which was $15.75. With tax and tip I figured my bill would be no more than about $20. I even brought about that amount of cash. The final bill was $300. Split six ways and its $50!!! I sucked it up and paid $50 because I was too embarrassed to say anything, particularly since I only really knew the birthday girl, her husband and her sister. Any advice on what to do in those situations or what to do before the bill comes to avoid those types of situations?”
Erm. Completely awkward, right.
$1.75 more each person would have to pay if the $7.00 was added to the bill for a dessert that everyone shared.
What is a fraction?Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.
It is given that:
If each person paid $6.75.
The total is 27$. 27 divided by 6.75 is 4. Suppose
$7.00 was added to the bill for a dessert that everyone shared.
Let x be the amount that each friend needs to share.
Addtional amount = $7.00
Number of people 4
Each people need to pay = 7/4 = $1.75
Thus, $1.75 more each person would have to pay if the $7.00 was added to the bill for a dessert that everyone shared.
Learn more about the fraction here:
brainly.com/question/1301963
#SPJ2
Solve the following equation for x: 2x – 3y = 6.
x= 3/2y+3
x=3/2y-3
x=-3/2y-3
x=-3/2y+3
Answers
Answer:
x=3/2y+3
Step-by-step explanation:
Let's solve for x.
2x−3y=6
Step 1: Add 3y to both sides.
2x−3y+3y=6+3y
2x=3y+6
Step 2: Divide both sides by 2.
2x2=3y+62
x=32y+3
Try to solve this (-98)+(-24)
Answers
Answer:
(-98)+(-24) = -122
-5y + 8 = -7 Solve for Y HELP PLEASE!?
Answers
Answer:
y = 3
Step-by-step explanation:
First, subtract 8 on both sides (because we have to get the variable alone):
-5y = -15
Then, divide -5 on both sides (simplify):
y = 3
Hope this helps ^^
Answer: 3
Step-by-step explanation: :)
Mean for 16, 12, 13, 22
Answers
Answer:
mean = sum of the terms/total no. of terms
mean = (16+12+13+22)/4
mean = 63/4 or 15.75
Answer:15.75
Step-by-step explanation:
16+13+12+22=63
Then divide by 4 because that is how many numbers they.
Jonathan's family took a road trip to the Grand Canyon. Jonathan fell asleep after they had travelled 260 miles. If the total length of the trip was 400 miles, what percentage of the total trip had they travelled when Jonathan fell asleep?
Answers
James cut a rope that is 2 2/5 inches long. What is the length in inches of 9 of these ropes? *
Answers
Answer:
21.6 inches = 21 3/5
Step-by-step explanation:
A jacket is on sale for $15 off. As part of a one-day sale, a 20% discount is applied to all purchases. If x represents
the original price of the jacket, which expression represents the final price of the jacket during this sale?
O 0.2x - 3
0.8x - 12
0.8x - 15
0.2x - 15
Answers
Answer:
.2x - 3
Step-by-step explanation:
15 x .20 = 3
15 - 3 = 12
put the following decimals in order of size, starting with the one of least value 0.125 0.4 0.62 1.05 0.05
Answers
Answer:
0.05, 0.125, 0.4, 0.62, 1.05
Step-by-step explanation:
A dog runs 200 meters in 20 seconds. The speed of the dog is
Answers
Answer:
200 × 20 = 4000
speed of the dog is 4000 m/s
True or False: -4.7 is a rational but not an integer
Answers
Answer:
True
Step-by-step explanation:
Any decimal number with a finite number of digits, whether positive or negative, is a rational number. If the decimal fraction part is zero, then it is also an integer.
-4.7 is rational, but not an integer
A carpenter has a board that is 2/3 yard wide. He cuts the board into 5 pieces. If all the pieces are the same width, how wide is each piece?
Answers
Answer:
[tex]\huge\boxed{\frac{2}{15} \text{ yards}}[/tex]
Step-by-step explanation:
We have a board that is [tex]\frac{2}{3}[/tex] yards long. If we want to cut the board into 5 equal pieces, we must divide [tex]\frac{2}{3}[/tex] by 5.
[tex]\frac{2}{3} \div 5[/tex]
5 is the same thing as [tex]\frac{5}{1}[/tex], so:
[tex]\frac{2}{3} \div \frac{5}{1}[/tex]
To divide a fraction by a fraction, we multiply by the reciprocal. This means we take the reciprocal of [tex]\frac{5}{1}[/tex] and multiply the two fractions.
The reciprocal of [tex]\frac{5}{1}[/tex] is [tex]\frac{1}{5}[/tex] - we swap the numerator and denominator.
[tex]\frac{2}{3} \cdot \frac{1}{5}[/tex]
Multiply the numerator and denominators to get our final fraction:
[tex]2\cdot 1 = 2\\3 \cdot 5 = 15\\\\\frac{2}{15}[/tex]
Hope this helped!
two consecutive integers have a sum of 83. Find the largest integer.
Answers
Answer:
Let the first integer be x. Then first number is 41,and second number is 42. 41+42=83 ... therefore these are the required integers.
Step-by-step explanation:
Answer:
41,42
Step-by-step explanation:
Let the first integer be x. Then first number is 41,and second number is 42. 41+42=83 ... therefore these are the required integers.
What is the slope of the line?
Answers
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
Pretty sure this is it.
I haven't done this in a long time.
Find the slope of the line passes through the points
(4, -18) and (13, 6)
Answers
can some one help find x
5/6 x +10=30
Answers
the answer for this question is x= 24
Find the coordinates of Dif M (3, -1) is the midpoint of CD and Chas the coordinates (-1,2).
Answers
Answer:
don't know sorry
Step-by-step explanation:
helppppppppppppppppppppppppp
Write an equation on the line with a slope of 2/3 and y intercept of -8
Answers
Answer:
y = 2/3x-8
Step-by-step explanation:
in the equation y = mx+b, m = slope and b = y-intercept. all you have to do is plug the numbers in!!
I need help with slope if u guys can please help me
Answers
Answer:
B
Step-by-step explanation:
Rise/Run - Y/X
x is going up 5
y is going up 1
so the slope is 1/5
Answer:
b
Step-by-step explanation:
cuz
What is the domain of the function
Answers
Answer:
A domain is the possible x-values in a ordered pair or an input value in a table
Step-by-step explanation:
I learned this by reading a lesson about it.
Also, here are some additional tips given from me to any of you when writing a domain or range!
When you write a domain or range:
1. List the numbers separated by commas instead of braces (if it is listed in braces and not in a table or ordered pair)
2. List the value(s) from least to greatest
Note: Duplicate numbers listed in an table or braces should only be listed once.
Hope this helps!
Paul needs to purchase a new flat screen TV for the entertainment center in his game room. Future Electronics is selling a 50-inch television. This distance is the diagonal distance across the screen. If the television has a height of 30 inches, what is the area of the 50-inch TV?
Answers
Answer:80 inches
Step-by-step explanation:
What does the point (0, 35) represent?
Answers
Answer:
I am sorry but i do not fully understand your question but i am going to try and help. in simplest terms the answer is 0
Answer:
its d
Step-by-step explanation:
Find the difference 12 - 16
Answers
Answer:
-4
Step-by-step explanation:
Ray UW is the angle bisector of Angle VUT. If the measure of Angle VUW = (4x + 6)° and the measure of Angle WUT = (6x – 10)°, what is the measure of Angle WUT?
Answers
Hello! :)
Answer:
[tex]\huge\boxed{38^{\circ}}[/tex]
--------------------------------------------------------------------------
An angle bisector divides an angle in half, therefore:
m∠VUW ≅ m∠WUT
Set the expressions equal to each other:
4x + 6 = 6x - 10
Subtract 4x from both sides:
6 = 2x - 10
Add 10 to both sides:
16 = 2x
Divide 2 from both sides:
x = 8.
Substitute in the value of "x" into the equation for ∠WUT:
6(8) - 10 = 48 - 10 = 38°.
HELP ME!! ASAP!!!! IT'S A SLOPE EQUATION!!!!
Answers
Q 10. Numbers 1 to 10 are written on
ten separate slips (one number on one
slip), kept in a box and mixed well.
One slip is chosen from the box
without looking into it. What is the
probability of getting a 1-digit
number? / ਦਸ ਵੱਖਰੀਆਂ ਵੱਖਰੀਆਂ ਸਲਿੱਪਾਂ ਤੇ ਸੰਖਿਆ
AANAAALA
Answers
Answer:
90% or 9/10
Step-by-step explanation:
There are ten numbers and nine of them are 1-digit numbers
solve this equation
m- -7 = -24
Answers
Answer:
m=-31
Step-by-step explanation:
[tex]m--7=-24\\\\m+7=-24\\\\m+7-7=-24-7\\\\m=-31[/tex]
Answer:
m = -31
Step-by-step explanation:
Are there any parenthesis?
If I'm understanding the question right, you're solving for m, and the equation is this.
m - (-7) = -24
You can subtract 7 from both sides.
m = -31
Solve -3 = t + 4s for s.
Answers
Answer:
[tex]s = \frac{-3}{4} - \frac{t}{4}[/tex]
Step-by-step explanation:
-3 = t + 4s
-3 - t = 4s
-3/4 - t/4 = s
