By the binomial theorem,
[tex]\displaystyle \left(x^2-\frac1x\right)^6 = \sum_{k=0}^6 \binom 6k (x^2)^{6-k} \left(-\frac1x\right)^k = \sum_{k=0}^6 \binom 6k (-1)^k x^{12-3k}[/tex]
I assume you meant to say "independent", not "indecent", meaning we're looking for the constant term in the expansion. This happens for k such that
12 - 3k = 0 ===> 3k = 12 ===> k = 4
which corresponds to the constant coefficient
[tex]\dbinom 64 (-1)^4 = \dfrac{6!}{4!(6-4)!} = \boxed{15}[/tex]
How many 4th cups of flour are in 3 3/4 cups
Answer: 12 cups
Step-by-step explanation:
The points (4, 10) and (1,4) fall on a particular line. What is its equation in
slope-intercept form?
Answer:
Slope of the line (m): 2.0
Y-intercept of the line (b): 2.0
Slope Intercept Form (y = mx + b): y = 2x + 2
Step-by-step explanation:
Slope intercept calculator lol
#26: Angles
A triangle has angle measures of 42.5° and 86.7º. What is the measure of the third
angle in the triangle?
Answer:
50.8 degrees is the third angle
Determine if triangles with the following side lengths are possible.
A: 5 8 4
B: 3, 6, ,2
C: 7, 5, 4,
Answer:
a is possible
b is not possible
c is possible
A planet has a circular orbit around a star. It is a distance of 65,000,000 km from the centre of the star. It orbits at an average speed of 65,000 km/h. How many Earth days does it take the planet to orbit the star? Give your answer to 2 sf.
Answer:
Step-by-step explanation:
Orbit = 2*pi * r
r = 65000000 km
Orbit = 65000000 * 2 * 3.14
Orbit = 406 200 000 km
d = 406 200 000
s = speed = 65000 km / hr
t = time = d / s
t = 406,000,000 / 65000
t = 6280 hours.
1 day = 24 hours.
t = 6280 / 24 = 261.67 days
Find the area of a regular hexagon with side length of 2 m. Round your answer to the nearest tenth.
Answer:
12
Step-by-step explanation:
A regular hexagon has 6 equal sides
2 times 6 = 12
Answer:
10.4m²
Step-by-step explanation:
A≈10.39m²
A=33
2a2=3·3
2·22≈10.3923m²
= 10.4m²
can some pls help me ☹?
Answer:
????????????????
Step-by-step explanation:
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90 is 150 of what number HELP
Please quickly answer number 6 will give brainliest
Math help please
Thanks
A lot
Answer:
2 hours: 3968 [I don't understand the $ sign in the answer box]
At midnight: 12137
Step-by-step explanation:
The bacteria are increasing by 15% every hour. So for every hour we will have what we started with, plus 15% more.
The "15% more" can be represented mathematically with (1 + 0.15) or 1.15. Let's call this the "growth factor" and assign it the variable b. b is (1 + percent increase).
Since this per hour, in 1 hour we'll have (3000)*(1.15) = 3450
At the end of the second hour we're increased by 15% again:
(3450)*(1.15) = 3968.
Each additional hour add another (1.15) factor, If we assign a to be the starting population, this can be represented by:
P = a(1.15)^t for this sample that increase 15% per hour. t is time, in hours.
If a represents the growth factor, and P is the total population, the general expression is
P = ab^t
Using this for a = 3000 and b = 1.15, we can find the total population at midnight after starting at 2PM. That is a 10 hour period, so t = 10
P = (3000)*(1.15)^10
P = 12137
I need help with my math homework from The Hung Vuong Learning Centre Incorporated, like immediately please!!! Here is an image for you to answer the questions will receive the Brainliest award if you answer the questions completely! Well anyways, good luck on answering the questions and I will check the answers are appropriate! :)
Answer:
Give me some hint please
Answer:
2. d) L = 10, W = 20
3. c) P = 100
Step-by-step explanation:
2. 2L + W = 40
W = 40 - 2L
A = L x W
= L (40 - 2L)
= 2L^2 + 40L
=-2 (L^2 - 20L)
= -2 (L^2 - 20^2 + 100 - 100)
= -2 (L^2 - 20L + 100) +200
= -2 (L - 10)^2 +200
L = 10
W = 40 - 2(10
=20
3. c. P = 2(L + W)
= 2(49 + 1)
= 100
a. P = 53
b. P = 32.5
d. P = 28
How here we get 2 x 22 x 10
And how we multiply the formula of pi with any number
Answer:
The formula of pi is approximately 3.14 2×3.14
Kasey had to make a down payment of 17% of the selling price of her house. She was approved for a $255,000 mortgage. What range of costs might she expect to pay at the closing?
Answer:
aq lang to Yung d na binalikan Yung iniwan na parang basura
When Zainab started work, her original hourly wage was ‘y’ dollars. Her wage was then doubled, and then increased by $4. If Zainab now gets paid $17 an hour, what was her original hourly wage?
Answer:
$6.5 dollars
Step-by-step explanation:
We can make an equation to find out the original total.
2y+4=17
(subtract 4 from both sides)
2y=13
(divide by 2)
y=6.5
Hope this helped :D
tASAP HELP + 50 POINTS
Find the value of x. Show all the work
Answer:
7
Step-by-step explanation:
im pretty sure at least. since x is on a midpoint, it'd half of 14.
See those similar lines
The line.of length x passes through midpoint of the traingles on opposite sides
At this case according to BPT theorem
2x=14x=14/2x=7The graph of the function, fx) = -2x + 6x-3, opens blank
and has a blank
value.
The graph of function [tex]f(x) = -2x^2 +6x - 3[/tex] opens down and has a maximum vertex.
The function is given as:
[tex]f(x) = -2x^2 +6x - 3[/tex]
See attachment for the graph of function f(x).
From the attachment, we can see that the graph opens down, and it crosses the x-axis at two distinct points.
Hence, the graph of function [tex]f(x) = -2x^2 +6x - 3[/tex] opens down and has a maximum vertex.
Read more about quadratic functions at:
https://brainly.com/question/11631534
please help anybody hm
Answer:
The answer is 1
Step-by-step explanation:
38 degrees 2x degrees +6 degrees
Find the slope of the line below. Enter your answer as a fraction or decimal.
Use a slash mark (/) as the fraction bar if necessary.
5
|(2, -1) 5
(-2,-3)
2
Answer:
The slope is 2/4 or 1/2
Step-by-step explanation:
Andrew spent $80 on travel last month.
Work out the amount Andrew spent on household bills last month.
Will give brainliest
If all three angles of a triangle are congruent, what is each angle measure?
Answer:
60°
Step-by-step explanation:
180° in a triangle.
180° ÷ 3 = 60°
The measure of each of the given angles of a triangle is 60°.
What are congruent triangles?If two triangles have the same size and shape they are called congruent triangles. If we flip, turn or rotate one of two congruent triangles they are still congruent. If the sides of two triangles are the same then the triangles must have the same angles and therefore must be congruent.Given is that all three angles of a triangle are congruent.
Consider a triangle ΔABC. Since the angles of the triangle are congruent, we can say that -
∠A = ∠B = ∠C = X°
and also we can write -
X° + X° + X° = 180°
3X° = 180°
X° = 60°
Therefore, the measure of each of the given angles of a triangle is 60°.
To solve more questions on congruent triangles, visit the link below -
https://brainly.com/question/22062407
#SPJ2
8. Jordan has $11.40 to spend at the used book store. Each book costs $280. How many books can Jordan buy?
Answer:
0
Step-by-step explanation:
Jordan hasn't got enough money to buy any books, as $11.40<$280.
Let g(x) = root of 4x and f(x) = 3x^3 + 8x^2 , what is the expression of the compound h(x) = g(f(x)) ?
h(x) = g(f(x))
Take f(x) and plug it into g(x).
g(f(x)) = sqrt{4x}
g(f(x)) = sqrt{4(3x^3 + 8x^2)}
g(f(x)) = sqrt{12x^3 + 32x^2}
We are done.
Answer:
h(x) = sqrt{12x^3 + 32x^2}
The composite function as shown is [tex]g(f(x)) =\sqrt{12x^3+32x^2}[/tex]
Composite functions
Given the following fnctions
[tex]f(x) = 3x^3 + 8x^2\\g(x) = \sqrt{4x}[/tex]
The composite function g(f(x)) is expressed as:
[tex]g(f(x)) =g(3x^3 + 8x^2)\\g(f(x) )=\sqrt{4(3x^3 + 8x^2)} \\g(f(x)) =\sqrt{12x^3+32x^2}[/tex]
Hence the composite function as shown is [tex]g(f(x)) =\sqrt{12x^3+32x^2}[/tex]
Learn more on composite function here: https://brainly.com/question/10687170
Write an equation of the line that passes through (7,10) and is perpendicular to the line y=1/2x−9.
y = -2x + 24
hope this is helpful!
Answer:
y+2x=24
Step-by-step explanation:
the equation of the line: y=1/2x -9
Get the slope by using derivative:
dy/dx= 1/2
dy/dx= slope of the normal line
Since we are looking for slope of the tangent line:
Use Mn=-1/Mt
The slope of the tangent line is -2
Using point slope form:
(y-y1)=m(x-x1) ; where x1=7, y1=10, and m=-2
y-10=-2(x-7)
y-10=-2x+14
ANSWER: y+2x=24
What is the domain of the function?
Enter your answer in the box.
demos.
Answer: the x or the input of a function
Step-by-step explanation:
Compare: The graphs below show the number of points you earn in each level of a game. Which games, if any, have a proportional relationship between the number of points you earn and the level of 7the game? In which game can you earn the most points in level 2? Explain your answer.
Answer:
Ok A and C are both proportional because it goes through the origin.
Step-by-step explanation:
If the line doesn't start or go through the origin will not be proportional. So If the line went through or started from the origin will be proportional. Which leaves B as Non-proportional graph.
: Use ratio language to describe the relationship of any two things you can think of. Example: For every 5 minutes of jogging, I ran 500 yards. Be creative and come up with your own idea.
For every 5 minutes of jogging, I ran 500 yards
To Find : Use ratio language to describe the relationship of any two things
Determine the unit rate
Solution:
every 5 minutes of jogging, I ran 500 yards
=> 500/5 = 100 yards/ minute
For every 20 minutes , I can type 1000 words in
unit rate = 1000/20 = 50 words per minute
For every 1 hr (60 minutes) I can solve 10 Questions
unit rate = 10/60 = 1/6 Question per minute
For every 10 minutes , i can read 5 pages
unit rate = 5/10 = 1/2 pages per minute
Learn More:
Selma uses a jogging trail that runs through a park near her home ...
brainly.in/question/21297587
Keith is saving money for a car. He has saved the same amount ...
brainly.in/question/14056417
15×15×2+10-1=?
HELP!!! answering is worth 69 (hehe nice) points, will mark brainiest if you can make me laugh in the while of answering the question :)
Answer:
459
Step-by-step explanation:
15×15×2+10-1
15×15= 225 × 2 +10 - 1
225 × 2= 450 + 10 -1
450 + 10 = 460 - 1
460 - 1 = 459
A little true story:
A five your old boy (little boy blue( was out with is siblings when he fell over a bridge and passed away. Now at the very same river he passed all you have to do is go up there turn off your lights and put baby powder all over you car and sit and wait. Soon enough you will see a little blue light and than little hand prints on your car.
Evaluate the expression when a=-2 and x=7.
-2a+x
Step-by-step explanation:
-2a + x
Putting values of a = - 2 and x = 7
-2(-2) + 7
4 + 7
= 11
could some one answer this
Answer:
12
Step-by-step explanation:
So she went there 4 times. Each time, she pays for the salad itself (we don't know how much) and she also leaves a 1,50 dollar tip. All together, she paid 54 dollars.
-> TIPS: 4x 1,50= 6 (dollars)
-> SALADS: 54 (total amount she paid) - 6 (tips) = 48 (all the 4 salads she bourght)
-> 1 SALAD: 48/4=12
-----------linear equation:-------------
54 = 4 x 1,5 + 4 x c
54 = 6 + 4c
48 = 4c
12 = c