Recall the binomial theorem:
[tex]\displaystyle (a + b)^n = \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]
where [tex]\binom nk = \frac{n!}{k!(n-k)!}[/tex] is the binomial coefficient.
Take a = x/3, b = -3, and n = 7. Then we get the x⁵ and x⁴ terms when 7 - k = 5 and 7 - k = 4, respectively; or when k = 2 and k = 3.
[tex]k=2 \implies \dbinom 72 \left(\dfrac x3\right)^{7-2} (-3)^2 = 21 \cdot \dfrac{x^5}{243} \cdot 9 = \dfrac79 x^5[/tex]
[tex]k=3 \implies \dbinom 73 \left(\dfrac x3\right)^{7-3} (-3)^3 = 35 \cdot \dfrac{x^4}{81} \cdot (-27) = -\dfrac{35}3 x^4[/tex]
Then when multiplying this expansion by x - 6, we get an x⁵ terms from the products
[tex]\dfrac79 x^5 \cdot (-6)[/tex]
and
[tex]-\dfrac{35}3 x^4 \cdot x[/tex]
so that the x⁵ term in the overall expansion of (x/3 - 3)⁷ (x - 6) has a coefficient of
[tex]\dfrac79\cdot(-6) + \left(-\dfrac{35}3\right) \cdot 1 = \boxed{-\dfrac{49}3}[/tex]
Thomas finished the 200-meter race in 25.7 seconds while Mikah finished in 28.1 seconds. How much faster did Thomas run the race than Mikah?
Answer:
2.4 seconds
Step-by-step explanation:
We can use subtraction to solve this problem.
28.1 - 25.7 = 2.4 seconds
[] Fun Fact: For men, the world record in the 200-meter dash is by Usain Bolt with a time of 19.30 seconds
Have a nice day!
I hope this is what you are looking for, but if not - comment! I will edit and update my answer accordingly. (ノ^∇^)
- Heather
I need help with this plz
Answer:Mmm
Step-by-step explanation:
I am doing the work I will thell you the answer
How do you multiply fractions? Please explain step by step to get marked
Answer: 10/3
Step-by-step explanation
2/3x5
2/3x5/1
Now goahead and multiply the top and bottom numbers
For every 2 books that Tom buys, he can buy 3 magazines. If he pays $60 fo 4 books and 4 magazines, how much does he have to pay for each book?
Answer:
Price of book is [tex]9\$[/tex]
Step-by-step explanation:
Let the price of book be [tex]x[/tex] and price of magazine be [tex]y[/tex]
We have
[tex]2x=3y[/tex]
We also have
[tex]4x+4y=60[/tex]
[tex]2\times 2x+4y=60\\\\2\times3y+4y=60\\\\10y=60\\\\y=6\\\\2x=3\times6\\\\x=9\$[/tex]
Price of book is [tex]9\$[/tex]
A furniture maker used 2/3 of a can of paint to paint some chairs. He used 1/6 of a can of paint for each chair. How many chairs did he paint?
Answer:
4 chairs
Step-by-step explanation:
Start with 2/3 can of paint: (2/3)
He used 1/6 of the can to paint each chair: (divided by 1/6)
Now use the 'keep, change, flip' method to get the expression: (2/3x6/1)
Then simplify your answer: (12/3)
Lastly simplify again: (4)
Thus, he painted 4 chairs.
PLEASE HELP!!!!!!!!!
Which of the following are properties of parallelograms? Select all that apply!
Consecutive angles are congruent.
One pair of parallel sides.
Consecutive angles are supplementary.
Both pairs of opposite sides are congruent.
Both pairs of opposite of angles are congruent.
Answer:
If I have to guess, I’ll say
Consecutive angles are congruent.
One pair of parallel sides.
Consecutive angles are supplementary.
Step-by-step explanation:
if I’m wrong, I’m sorry. If I’m right, mark me brainlest!
Answer:
Consecutive angles are supplementary.
Both pairs of opposite of angles are congruent.
Both pairs of opposite sides are congruent.
Step-by-step explanation:
I took the quiz and this was the correct answer.
I will mark brainly, help me with this question please.
Step-by-step explanation:
Since [tex]x[/tex] varies directly as [tex]\sqrt{y}[/tex] we can write the relation as
[tex]x = k\sqrt{y}[/tex]
where k is the constant of proportionality.
a) To solve for the k, we substitute the given values:
[tex]5 = k\sqrt{13} = k(13)[/tex]
[tex]\Rightarrow k = \dfrac{5}{13}[/tex]
b) The equation relation x and y can be written as
[tex]x = \dfrac{5}{13}\sqrt{y}[/tex]
c) When y = 9,
[tex]x = \dfrac{5}{13}\sqrt{9} = \dfrac{5}{13}(3) = \dfrac{15}{13}[/tex]
PLS HELP PLEASSSS ILL MARK U AS BRAIN KING THINGY WTV U CALL IT
Answer: infinitley many solutions
Step-by-step explanation:
A Biology test has 20 questions and is worth a total of 100 points. The test
consists of True/False questions worth 2 points each and multiple choice questions
worth 7 points each. How many of the test questions are multiple choice and how
many of the test questions are True/ False?.
# of true/false questions =
# of multiple choice questions
PLEASE HELP ME I WILL GIVE BRAINLY
Answer:
12 multiple choice and 8 True/False
Step-by-step explanation:
To do this we set up a system of equations. Let x represent the True/Fale questions and y represent the multiple-choice questions. Here is a system we can use:
x + y = 20
2x + 7y = 100
We can solve this by using elimination. To do this we multiply one equation by a number, and add them together. If we multiply the first equation by -2, the "x"s will, when added together, cancel out so we can solve for y.
-2(x + y = 20)
-2x - 2y = -40
Now add them together
5y = 60
Solve for y.
y = 12
This means there are 12 multiple choice questions. 20 - 12 is 8 True/False questions.
Hope this helps and have a great day! :D
Answer:
8 True/False and 12 Multiple Choice
Step-by-step explanation:
x+y=20 ...1
2x+7y=100 ...2
Now you can multiply 2 on 1
2x+2y=40
2x+7y=100
Subtract:
-5y=-60
Divide -5 on both sides:
y=12
Substitute y with 12
x+12=20
Subtract 12 on both sides:
x=8
So there are 8 True/False and 12 Multiple Choice
Hope this Helps!
Answer helped by: azailiaskoglund
Which characteristics did early Japanese, Chinese, and Korean civilizations share?
They were friendly nations that shared culture and customs.
They were nations at war that shared a common religion.
They were neighboring countries that shared a common history.
They were countries with dissimilar culture and customs.
Answer:They were nations at war that shared a common religion.
Step-by-step explanation:
edge
Answer:
B. They were nations at war that shared a common religion.
Explanation: I got it right.
A line with a slope of -8/3
passes through the point (0, 10). What is its equation in
slope-intercept form?
Write your answer using integers, proper fractions, and improper fractions in simplest form
Answer:
y = - [tex]\frac{8}{3}[/tex] x + 10
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mc + c ( m is the slope and c the y- intercept )
Here m = - [tex]\frac{8}{3}[/tex] and crosses the y- axis at (0, 10 ) ⇒ c = 10
y = - [tex]\frac{8}{3}[/tex] x + 10 ← equation of line
Help help math math math please
Answer:
-2) -14
0) -8
2) -2
4) 4
Step-by-step explanation:
Plug in each input for x, and solve for y
Answer: 2) -140) -82) -24) 4
Step-by-step explanation:
The length of a photograph is 6 inches less than little twice the width. The photograph is mounted in a frame that is 3 inches wide on all sides. If the area of the framed picture is 270 square inches, find the dimensions of the unframed photograph.
Answer:
syuare root 270 to get 16.4 then subtract 6 to get 10.4
A shipment contains 25 defective items and 100 nondefective items. Two items are randomly chosen in succession without replacement. Find the probability that both items are defective. 25) ______ A) B) C) D) E) none of these
Answer:
non of these because you are a good friend and look at the house to you nanu you nanu to get the house ☺️ to get well and
The cost of 5 story books is Rs 800. How many books can be bought for Rs 1,440?
Answer:
cost of 5 story book=800
cost of 1 story book=800/5
=160
how many. book can be bought on rs.1400
=1400/160
=8.75
Step-by-step explanation:
=
what is the domain and range of : {(2,4) (3'6) (4,8) (5,10) (6,12)}
Answer:
2,3,4,5,6 is the domain
4,6,8,10,12 is the range
Step-by-step explanation:
Answer:
The domain is {2,3,4,5,6} and the range is {4,6,8,10,12}.
Step-by-step explanation:
A sweatshirt was on sale for 32% off and cost $40.80 without tax. What was the original price of the sweatshirt?
Answer:
The original price of the sweatshirt was $127.50
Step-by-step explanation:
$40.80 / .32(32%) = $127.50
What is the value of a in this linear system?
a + b + c = 62
a - b = 12
2a + b + c = 92
O A.
14
OB.
30
OC.
18
o
c
D.
26
Answer:
Step-by-step explanation:
C
x^2+2x+8=0, Find x?aaaaaaa
1. Bianca can walk 5/6 of a mile in 1/3 of an hour. What is her walking speed, in miles per hour?
2. How long, in minutes, does it take Bianca to walk 1 mile?
Answer:
1. 2.5 miles/hour
2. 24 minutes
Step-by-step explanation:
1. 5/6 of mile in 1/3 of an hour. In 1 hour, Bianca can walk 5/6 x 3 = 15/6 miles or 2.5 miles/hour
2. 5/6 of mile in 1/3 of an hour, hour in 1 mile = (1 x 1/3)/(5/6) = 2/5 = 0.4 hour = 24 minutes
14. What's the least common denominator of 3/4, 4/5, and 2/3?
A. 60
B. 20
C. 15
D. 12
What is the range of y = sin x?
A. In
72 T
o
B. -1Sys1
c. -1SIS 1
o
D. All real numbers
Answer:
See below
Step-by-step explanation:
The function [tex]f(x)=sin(x)[/tex] oscillates between -1 and 1, so the range is [tex]-1\leq x\leq 1[/tex].
help me please!! <33
13/20 - 1/2
===================================================
Explanation:
Ignore the big X and the shading for now. This figure has 4 rows by 5 columns of rectangles. So there are 4*5 = 20 little rectangles total. Each little rectangle represents 1 brownie.
Then let's say the shaded region represents the amount of brownies Mary receives. We have 13 rectangles shaded in out of the 20 total. This means 13/20 is the fractional amount Mary gets.
She then eats 10 of the 20 total, so she eats 10/20 = 1/2 of the brownies.
Therefore, we end up with the expression 13/20 - 1/2 to represent the fractional amount that Mary still has that she hasn't eaten yet (which is 3/20).
We can say: 13/20 - 1/2 = 13/20 - 10/20 = 3/20
Can someone help me answer please
Answer:
i dont know sry
Step-by-step explanation:
What is 1,000 x 10,090g
Answer:
10,090,000 grams
Step-by-step explanation:
Just add three zeros to 10090g.
Please hurry!! This assignment is almost due!!
Answer: x = 17
Step-by-step explanation:
Hi there!
First, since we know that these two lines are parallel, 3x+14 is going to be congruent to the supplementary side of 7x-4. Given this, we are able to solve for x as we know that the sum of supplementary angles is 180. All you have to do is set up 3x+14+7x-4=180
Now, just use simple order of operations and combining like terms to isolate x. you will end with 17! :)
Hope this helps!
question in file .
give me brainlg anserf
Explanation
Formula to be used,
1st equation of motion, v = u + at • 3rd equation of motion,v² - u² = 2 asSolution,
Putting all the values, we get
v=u + at
⇒0 = u + (-0.5) × 20
⇒-u=-0.5 × 20
⇒u = 10 m/s
Hence, the initial velòcity of the car is 10
city of the car is 10m/s.
Now, the distance covered,
v²-u² = = 2as
⇒ (0)²-(10)² = 2 × (-0.5) × s
⇒-100 = - 1s
⇒ s = 100 m
Hence, the distance covered is 100 m.
Need help asap please !!!
Please help, very urgent!!!! 50 points!!
Answer:
f = 14
Step-by-step explanation:
it is because skephalo and hot and poggers science and dnf
Given f(1) = 8 and
f(n) = 3 f(n-1) - 2 then f (4) =
Answer:
190
Step-by-step explanation:
f(1)=8
f(2)=3f((2-1))-2, f(2)=22
f(3)=3f((3-1))-2, f(3)=64
f(4)=3f((4-1))-2, f(4)=190