Answer:
[tex] (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656{x}^{} + 46656 [/tex]
Step-by-step explanation:
we want to solve the following binomial:
[tex](x + 6 {)}^{6} [/tex]
There is a handy way to expand powers of binomials which is known as binomial theorem . and it describes the algebraic expansion of powers of a binomial. binomial theorem is given by
[tex] \displaystyle (a + b {)}^{n} = \sum _{k = 0 }^{n} \binom{n}{k} {a}^{n - k} {b}^{k} [/tex]
comparing (x+6)⁶ to (a+b)ⁿ , we get
[tex]a \implies \: x[/tex][tex]b\implies \: 6[/tex][tex]n\implies \: 6[/tex]now substitute them on the formula which yields:
[tex] \displaystyle (x + 6 {)}^{6} = \sum _{k = 0 }^{n} \binom{6}{k} {x}^{6 - k} \cdot {6}^{k} [/tex]
converting the summation notation into sum yields:
[tex] \displaystyle (x + 6 {)}^{6} = \binom{6}{0} {x}^{6 - 0} \cdot {6}^{0} + \binom{6}{1} {x}^{6 - 1} \cdot {6}^{1} + \binom{6}{2} {x}^{6 - 2} \cdot {6}^{2} + \binom{6}{3} {x}^{6 - 3} \cdot {6}^{3} + \binom{6}{4} {x}^{6 - 4} \cdot {6}^{4} + \binom{6}{5} {x}^{6 - 5} \cdot {6}^{5} + \binom{6}{6} {x}^{6 - 6} \cdot {6}^{6} \\ \implies(x + 6 {)}^{6} = \binom{6}{0} {x}^{6 } \cdot 1 + \binom{6}{1} {x}^{5} \cdot {6} + \binom{6}{2} {x}^{4} \cdot 36+ \binom{6}{3} {x}^{3} \cdot 216 + \binom{6}{4} {x}^{2} \cdot 1296+ \binom{6}{5} {x}^{} \cdot 7776+ \binom{6}{6} {x}^{0} \cdot 46656 \\ \implies(x + 6 {)}^{6} = 1 \cdot {x}^{6 } \cdot 1 + 6 \cdot{x}^{5} \cdot {6} + 15 \cdot {x}^{4} \cdot 36+ 20 \cdot {x}^{3} \cdot 216 + 15 \cdot{x}^{2} \cdot 1296+ 6 \cdot {x}^{} \cdot 7776+ 1 \cdot {x}^{0} \cdot 46656 \\ \implies \boxed{ (x + 6 {)}^{6} = {x}^{6 } + 36{x}^{5} + 540{x}^{4} + 4320 {x}^{3} + 19440{x}^{2}+ 46656 {x}^{} + 46656 }[/tex]
and we're done!
HELPPPPPPP URGENT :L
Answer:
17.5
Step-by-step explanation:
The area for a triangle is (base*height)/2 this means
(5*7)/2 = 17.5 units^2
Answer:
Step-by-step explanation:
base = b = 5 units
height = h = 7 units
[tex]\bf \boxed{\text{Area of triangle = $\dfrac{1}{2}bh$}}[/tex]
[tex]=\dfrac{1}{2}*5*7\\\\\\=\dfrac{35}{2}\\\\\\= 17.5 \ square \ units[/tex]
Write the equation in spherical coordinates. (a) x2 y2 z2 = 64
The equation in spherical coordinates will be a constant, as we are describing a spherical shell.
r(φ, θ) = 8 units.
How to rewrite the equation in spherical coordinates?The equation:
x^2 + y^2 + z^2 = R^2
Defines a sphere of radius R.
Then the equation:
x^2 + y^2 + z^2 = 64
Defines a sphere of radius √64 = 8.
Then we will have that the radius is a constant for any given angle, then we can write r, the radius, as a constant function of θ and φ, the equation will be:
r(φ, θ) = 8 units.
If you want to learn more about spheres, you can read:
https://brainly.com/question/10171109
The equation in spherical coordinates is r(φ, θ) = 8 units.
What are the spherical coordinates?Spherical coordinates of the system denoted as (r, θ, Φ) is the coordinate system mainly used in three-dimensional systems.
The equation of the spherical coordinates is written as;
[tex]\rm x^2 + y^2 + z^2 = R^2[/tex]
Where R is the sphere of radius.
The given equation of the spherical coordinates is;
[tex]\rm x^2 + y^2 + z^2 = 64^2[/tex]
Here 8 is the sphere of radius.
Hence, the equation in spherical coordinates is r(φ, θ) = 8 units.
Learn more about spheres here;
brainly.com/question/10171109
#SPJ4
help! complete the table with the missing measurements. the perimeter is 40ft is that helps
therer sorry for the cropped pic btw lol
I have 936 pencil . A box holds a dozen pencil . How many boxes will I be able to fill
Answer:
you will fill 78 boxes
Step-by-step explanation:
dozen = 12
936 divided by 12=78
The two figures shown below are similar. What is the value of x?
12
24
19
30
Answer: 24
Step-by-step explanation:
Corresponding sides of similar figures are proportional.
What is the surface area of the figure made from this net?
Answer:
there is no net? Maybe you forgot to include your attatchement, and without it, I cannot answer your question. sorry...
Step-by-step explanation:
Having difficulty finding the correct explanation for the boxes.
Answer:
agree - the central angle is 360°/nagree - a hexagon has 6 degrees of rotational symmetryagree - the altitude is r×cos(180°/n)Step-by-step explanation:
a)Agree. All radii of a circle are the same length, so any triangle drawn from the center of a circle to points on the circle will be an isosceles triangle. By definition, all interior angles and all side lengths of a regular polygon are congruent. So, an n-sided regular polygon inscribed in a circle can be divided into n non-overlapping congruent isosceles triangles. That means the central angle is 360°/n, a value found based on the rotational symmetry of the figure.
__
b)Agree. See the explanation in part (a). A regular hexagon has six congruent sides. Each of those can form the base of an isosceles triangle. Hence, the hexagon can be decomposed into 6 congruent isosceles triangles.
__
c)Agree. The altitude divides each of the isosceles triangles of parts (a) and (b) into two congruent right triangles. The length of the altitude can be found as the product of the radius of the circle and the cosine of half the central angle of the isosceles triangle. That is, trigonometry can be used to find the altitude.
The altitude (apothem of the polygon) is ...
a = r·cos(180°/n)
_____
Additional comment
A "correct" explanation is one that makes sense to you and your grader. The explanation you read here may not be "correct" in that sense. YMMV
Evaluate the function for the given value of x.
Answer:
f(-6)= -41 923
Step-by-step explanation:
f(-6)= -( -6)⁶ +5(-6)⁴+8(-6)³+2(-6) -7 you substitute x with -6 the you use a calculator which will then give you - 41923
Select all the expressions that are equal to 12x + 36
12(x + 24)
x(12 + 36)
3(4x + 12)
4(3x + 9)
4(3x + 9x)
Answer:
The answer are
12(x + 24) ❌
x(12 + 36) ❌
3(4x + 12) ✅
4(3x + 9) ✅
4(3x + 9x) (Again?) ✅
Step-by-step explanation:
12x + 36 equals 12(x + 3) (Keep that in mind)
12(x + 24) is not correct because the result is 12x + 288. Therefore, the first option is incorrect. ❌
x(12 + 36) isn't correct either. This is because the result is 48x. Therefore, the second option is incorrect too. ❌
3(4x + 12) is correct because the result is 12x+36, but wait! Remember how I told you to keep 12(x + 3) in mind? Well, when you solve 12x+36, the result is 12(x + 3). Therefore, the third option is correct. ✅
4(3x + 9) is correct because the result is 12x+36 just like the third option, but wait! Since it is the same as the third option, that means that the result will be 12(x + 3). Therefore, the fourth option is correct too.✅
4(3x + 9) is correct because the result is 12x+36 just like the third option, but wait! Since it is the same as the third option, that means that the result will be 12(x + 3). Therefore, the fourth option is correct too. (Again?) ✅
Hope this helped! Keep strong and good luck! :)
Can you mark me brainliest? But wait! It's your choice. I don't have the right to brag. Have a nice day!! :D
Let me know if you want me to help you with anything else. I'll be happy enough to help you. :>
- ✨7272033Alt✨
Joel has 24 sports trophies. Of the trophies 1/8 are soccer trophies. How many soccer does Joel have ?
Answer:
We are given that Joel has 24 sports trophies, of the 24 trophies there are 1/8 soccer trophies.
1/8 of 24 is 3.
24 divided by 8 = 3 soccer trophies
There are 3 soccer trophies all the rest of the trophies, which is 21 trophies, will be other sports. 21 trophies + 3 soccer trophies = 24 trophies in total
Step-by-step explanation:
Have a great rest of your day
#TheWizzer
six hundred kilograms of tea were packed in 500 g packets. how many packets of tea were there?
Answer:
1200
Step-by-step explanation:
600 in grams = 600 x 1000
= 6 x 10^5
(6 x 10^5) / 500 = 1200.
Answer:
1200 packets
Step-by-step explanation:
1 kg = 1000 gram
600 kg = 1000 × 600 = 600,000
now,
packets of tea were ( 600000 ÷ 1000) = 1200 packets
A teacher assigns a score from 1 to 4 to each student project. the table below shows the probability distribution of the scores for a randomly selected student. which score is most likely? probability distribution score: x probability: p(x) 1 0.06 2 0.20 3 0.48 4 0.26 1 2 3 4
The generalization of the weighted average is the expected value of a distribution. The score that is most likely to occur is 3.
How to find the mean (expectation)?The generalization of the weighted average is the expected value of a Probability distribution. It is given by the formula,
[tex]Mean = E(X) = \sum_{\forall x_i} f(x_i)x_i[/tex]
As we need to calculate the score that is most likely to occur, therefore, we need to calculate the expected value of the given probability distribution, therefore, the expected value can be written as,
[tex]E(x) = \sum xP[/tex]
where x is the score and P is the probability of the score occurring.
[tex]E(x) = (1 \times 0.06)+(2 \times0.20)+(3 \times 0.48)+(4 \times 26)\\\\E(x) = 2.94[/tex]
Since 2.94 is the most expected value to occur which is close to 3, therefore, the score that is most likely to occur is 3.
Also, the probability of score 3 coming is maximum which is equal to 0.48.
Hence, the score that is most likely to occur is 3.
Learn more about Expectation:
https://brainly.com/question/4515179
Answer:c
Step-by-step explanation: just took the test
Convert 30% to a fraction in lowest terms
Answer:
3/10
Step-by-step explanation:
Hope this helped
9 and 12 are relatively prime.
True or false
Answer:
False.
Step-by-step explanation:
Because 12 and 9 are both multiples of 3.
Mark and Henry win some money and share it in the ratio 1:3. Mark gets £9. How much did Henry get?
Answer:
Hope this helps!!!!!!
Mark Brainlest!!!!!!!!!!
Step-by-step explanation:
Mark and Henry win some money and share it in the ratio 1:3. Mark gets £9. How much did Henry get?
Ratio = 1 : 3
Let Mark's share be 1x = x
and Henry's share be 3x
We know that Mark gets £9
So,
1x = x = £9
Then 3x = £(3 * 9) = £27
HENCE,
Mark's share = £9
Henry's share = £27
Total money = Mark's share + Henry's share = £9 + £27 = £36
Answer:
£27
Step-by-step explanation:
so it shows mark is 1 while Henry is 3
we know that Mark is 1/4 while Henry is 3/4
/4 because the total is 4 so whatever their ratio is over their total
so we do: 1 = 9
3 = ?
and then u cross multiply
3*9 = 27 ÷ 1 = 27
so Henry receives £27
3x - 12y = 6
x - 4y = 2
solve by elimination
3x-12y=6
x-4y=3--(1)x-4y=2--(2)Lets convert to slope intercept form
4y=x-34y=x-2Slopes are equal so lines are parallel
Hence no solutions
What are the linear equations for the lines passing through the following points (3,4) and (5,8)
Answer:
The equation of the line is y = 2x + 2
Step-by-step explanation:
Given:The two points are (3, 4) and (5, 8)To find:- Equation of a linear line Solution:-
Equation of a linear line can be placed in the format:
y = mx + cFormula for finding the slope(m):
[tex] \sf{}m = \frac{x- x_1}{y - y_1} = \frac{y_2 - y_1}{x_2 - x_1} \\ \\ \sf{}m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex] \sf{}m = \frac{8 - 4}{5 - 3} = \cancel \frac{4}{2} = 2[/tex]
Form the intermediate equation:
y = mx + c
[tex] \mathtt{y = 2x + c}[/tex]
Find the y-intercept:
Substitute (3,4) into the equation
[tex] : \longrightarrow \: \mathtt{y = 2x + c} \\ \\ : \longrightarrow \:\mathtt{4 = 2(3) + c} \\ \\ : \longrightarrow \: \mathtt{4 = 6 + c} \\ \\ : \longrightarrow \: \mathtt{c = 6 - 4} \\ \\ : \longrightarrow \: \mathtt{c = 2}[/tex]
Form the equation:
[tex]: \longrightarrow \: \mathtt{y = 2x + c} \: \\ \\ \mathtt{putting \: values \: of \: c} \\ \\ : \longrightarrow \: \mathtt{y = 2x + 2}[/tex]
The equation of the line is [tex]\underline\mathfrak\red{{{y = 2x + 2}}}[/tex]
Helpp me with my sister's math
Answer:
the 1/2w +22 one is a binomial
Step-by-step explanation:
a binomial is a equation with one two separate numbers AFTER simplifcation. so "1+1" is not a binomial because its equal to just 2, but "1 + x" is a binomial because its simplifed
Answer please!!!
Best answer gets brainliest!!!
Answer:
8
Step-by-step explanation:
hope this is right????
im not sure if i did it correctly but i tryed
Please help, I’ll mark your answer as brainliest.
Answer: the answer is
Step-by-step explanation:
-
Find the equation of the line that
is perpendicular to y = -2x - 9 and
contains the point (8, -4).
Answer:
[tex]y=\frac{1}{2} x-8[/tex]
Step-by-step explanation:
The final answer is in the slope-intercept form, which is y=mx +c, where m is the slope and c is the y-intercept.
The slope of a perpendicular line is the negative reciprocal of the slope of the given line (the line it is perpendicular to). Thus, let's find the slope of the given line first.
Given line: y= -2x -9
The above equation is already in the slope-intercept from and thus, the slope is the coefficient of x.
Slope of given line= -2
The coefficient is the number that comes before a variable and it includes the positive or negative sign, which explains why the slope of the given line is -2 instead of 2.
Slope of perpendicular line= [tex]\frac{1}{2}[/tex]
Substitute the value of the slope into the equation:
[tex]y=\frac{1}{2} x+c[/tex]
To find the value of c, substitute a pair of coordiantes the line passes through.
When x= 8, y= -4,
[tex]-4=\frac{1}{2}(8)+c[/tex]
-4= 4 +c
c= -4 -4
c= -8
Thus, the equation of the perpendicular line is [tex]\bf{y=\frac{1}{2} x-8}[/tex].
What is reciprocal?
The reciprocal of a number is 1 divided by that numberFor example, the reciprocal of 2 is [tex]\frac{1}{2}[/tex]In this question, we are interested in negative reciprocal. This means that if the slope of the given line is m, the slope of the perpendicular line is [tex]-\frac{1}{m}[/tex].a shopkeeper selling an article at discount of 20% looses rs 400 if he allow 10% discount he gains rs 200 find the marked price and the cost price of the article
Answer:700
Step-by-step explanation:
Let the M.P of the article be x .
A discount of 20% was given on the M.P .
So the selling price of the article ( S.P ) will be M.P - Discount .
Discount = 20 % of x
⇒ Discount = 20/100 of x
⇒ Discount = 1/5 × x
⇒ Discount = x/5
Now S.P = M.P - Discount .
⇒ S.P = x - x/5
⇒ S.P = ( 5 x - x ) / 5
⇒ S.P = 4 x / 5
The shopkeeper loses Rs 200 .
Loss = C.P - S.P
⇒ C.P = Loss + S.P
⇒ C.P = 200 + 4 x / 5
⇒ C.P = ( 1000 + 4 x )/5
Now if he allows 10 % discount then the gain is Rs 150 .
Gain = S.P - C.P
⇒ S.P = Gain + C.P
⇒ S.P = 150 + ( 1000 + 4 x )/5
⇒ S.P = ( 750 + 1000 + 4 x )/5
⇒ S.P = ( 1750 + 4 x )/5
Discount = 10 % of x .
⇒ Discount = 10/100 × x
⇒ Discount = x/10
S.P = M.P - Discount
⇒ ( 1750 + 4 x )/5 = x - x/10
⇒ ( 1750 + 4 x )/5 = 9 x / 10
⇒ 1750 + 4 x = 9 x / 2
⇒ 3500 + 4 x = 9 x
⇒ 9 x - 4 x = 3500
⇒ 5 x = 3500
⇒ x = 3500/5
⇒ x = 700
4 9/10 X 1/4. {State your answer as a mixed number in simplest form.} State your answer as a mixed number in simplest form
Answer:
1 9/40
Step by step explanation:
\frac{49}{40}=1\frac{9}{40}
How many solutions are there for the quadratic equation?
Y=x^2+12x+36
Show work
Answer:
1 solution
x = -6Explanation:
[tex]\rightarrow \sf y=x^2+12x+36[/tex]
[tex]\rightarrow \sf x^2+12x+36=0[/tex]
[tex]\rightarrow \sf x^2+6x+6x+36=0[/tex]
[tex]\rightarrow \sf x(x+6)+6(x+6)=0[/tex]
[tex]\rightarrow \sf (x+6)(x+6)=0[/tex]
[tex]\rightarrow \sf x=-6[/tex]
Hence there is only one solution for this quadratic equation and the value is -6
[tex]\\ \rm\rightarrowtail x^2+12x+36=0[/tex]
[tex]\\ \rm\rightarrowtail x^2+6x+6x+36=0[/tex]
[tex]\\ \rm\rightarrowtail (x+6)(x+6)=0[/tex]
Only one solution present
x=-6
3x+2x+6v-9g+hd+2v-1g
Answer:
5x+8x-10g+hd
Step-by-step explanation:
please mark me as brainlest
Hey there!
3x + 2x + 6v - 9g + hd + 2v - 1g
= 3x + 2x + 6v - 9g + 1hd + 2v - 1g
COMBINE the LIKE TERMS
= (3x + 2x) + (6v + 2v) - (9g - 1g) + (1hd)
= 3x + 2x + 6v + 2v - 9g - 1g + 1hd
= 5x + 7v - 10g + 1hd
= 5x + 7v - 10g + hd
= hd - 10g + 8v + 5x
Therefore, your answer is:
hd - 10g + 8v + 5x
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
ILL GIVE BRAINLIST THING IF YOU HELP PLEASE QUICK
Answer:
B and C are wrong
B: 7.89 x 10^-4
C: 3.15 x 10^2
Step-by-step explanation:
B is not written correctly. The purpose of scientific notation is to get rid of the decimal places with 0s. So instead of 0.789, it should be 7.89 x 10^-4
C is wrong, it should be 3.15 x 10^2
For the rotation 379°, find the coterminal angle from 0 <0 360°, the quadrant
and the reference angle,
To find the coterminal angle, it is similar to going around the entire circle once and then a bit more.
379 - 360 = 19
Coterminal Angle = 19 degrees
---All the way around and a bit more
Quadrant = 1
---Where the angle is
Reference Angle = 19 degrees
---Distance between the x-axis and the angle
Hope this helps!
can someone plssss help
manipulating algebraic fractions
Answer:
the answer is 5x divide by 12
The current temperature is 48°F. It is expected to drop 1.5°F each hour.
Which equation can be used to find in how many hours, h, the temperature will be 36°F?
A) 36 + 48h = 1.5
B) 48 – 1.5h = 36
C) 48 + 1.5h = 36
D) 36 - 1.5h = 48
Answer:
B
Step-by-step explanation:
1 doller bill and a 10 doller bill and for quarters makes what?
Answer:
12$
Step-by-step explanation:
1 plus 10 from the singular dollar bill and the 10 dollar bill now we have 11 then we add one because there are 4 quarters which are 1 dollar that is why we have 12 dollars