According to Khayyam-Pascal triangle ,
the value of n is 8.
[tex] look \: \\ \\ {(x + 1)}^{8} = {x}^{8} + 8 {x}^{7} + 28 {x}^{6} + 56 {x}^{5} + 70 {x}^{4} + 56 {x}^{3} + 28 {x}^{2} + 8x + 1 \\ \frac{56}{28} = 2 [/tex]
Recall the binomial theorem:
[tex](a+b)^n=\displaystyle\sum_{k=0}^n\binom nk a^k b^{n-k}[/tex]
where
[tex]\dbinom nk=\dfrac{n!}{k!(n-k)!}[/tex]
is the binomial coefficient. So
[tex](x+1)^n=\displaystyle\sum_{k=0}^n\binom nk x^k[/tex]
The x² term occurs for k = 2, which has coefficient
[tex]\dbinom n2=\dfrac{n!}{2!(n-2)!}=\dfrac{n(n-1)}2[/tex]
The x³ occurs for k = 3, with coefficient
[tex]\dbinom n3=\dfrac{n!}{3!(n-3)!}=\dfrac{n(n-1)(n-2)}6[/tex]
The latter coefficient is twice the other one, so that
[tex]\dfrac{n(n-1)(n-2)}6=2\cdot\dfrac{n(n-1)}2[/tex]
Solve for n :
[tex]\dfrac{n(n-1)(n-2)}6=n(n-1)[/tex]
[tex]n(n-1)(n-2)=6n(n-1)[/tex]
[tex]n-2=6[/tex]
[tex]\boxed{n=8}[/tex]
if you ride your bike around the block, returning to the exact point where you started, your displacement is _____m?
help please <3
Answer:
tbh idek
Step-by-step explanation:
sorryyyyyyyyyy
Need help pls I dot understand
pic below...............................
. 。 • ﾟ 。 .
. . 。 。 .
. 。 ඞ 。 . • •
ﾟ Red was not An Impostor. 。 .
' 1 Impostor remains 。
ﾟ . . , . .
can red have brainliest?
Choose the correct equation to solve the problem: Five friends equally split a restaurant bill that comes to $32.50. How much does each person pay?
x/5 = 32.50
5x = 32.50
x + 5 = 32.50
x - 5 = 32.50
{(2,-1),(-2,4),(2,5),(3,6)}
What’s the domain and range?
Answer:
Domain(x): -2,2,3
Range(y): -1,4,5,6
(I put them in order numerically)
Step-by-step explanation:
The Domain is all the x values of the points given. It's always the first number of a point.
The range is the y values, it's always the second number given in a ordered pair!
Hope this helps! :)
Rearrange w = 3(2a + b) – 4 to make a the subject.
Sonya works on a cruise ship and sleeps in a cabin that is 6 feet below sea level. The main deck is 35 feet above Sonya's cabin. How far above sea level is the main deck? add unit of measure!*
Answer: 29 ft above sea level
Step-by-step explanation:
if she is 6 feet under that could be considered -6, the main deck is above sea level so +35, so it would be 35-6=29 ft
Solve by using the elimination method.
Sally spent $14.85 to buy 13 flowers. She bought lilies, which cost $1.25 each, and tulips, which cost $0.90 each. How many of each flower did Sally buy?
CAN SOMEONE HELP ME WITH THIS ONE PLEASE!!!!!!!
a = lilies
13 - a = tulips
We have: 1.25a + 0.90(13 - a) = 14.85
=> 1.25a + 11.7 -0.90a = 14.85
=> 0.35a = 14.85 - 11.7 = 3.15
=> a = 3.15 ÷ 0.35 = 9
=> She bought 9 lilies and 4 tulips
60 people attend a game night. Everyone chooses to play chess, a two-player game, or cribbage, a four-player game. All 60 people are playing either chess or cribbage.
There are 3 more games of cribbage being played than games of chess being played. How many of each game are being played
Answer: 8 chess matches and 11 cribbage matches.
Step-by-step explanation:
60 people, 4 people play a match of cribbage, so if theres 3 more matched than chess we can subtract that from the total 60 to get the answer. 3x4=12 60-12=48, 2 people per chess game and 4 people per cribbage game add them 6, 48 divided by 6 since its an even amount now, 48/6=8 add 8 matched to the remaining 3 for the cribbage.
8 chess games are being played while 11 cribbage games are being played.
Let x represent the number of chess games and y represent the number of cribbage games.
Since there are 60 people, chess is a two-player game and cribbage is a four-player game, hence:
2x + 4y = 60 (1)
There are 3 more games of cribbage than games of chess, hence:
y = x + 3
-x + y = 3 (2)
Solving equations 1 and 2 simultaneously gives:
x = 8, y = 11
Therefore 8 chess games are being played while 11 cribbage games are being played.
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Written as a simplified polynomial in standard form, what is the result when
(3x – 2)2 is subtracted from 4x?
Answer:
Yes, will be
[tex](3x - 2)2 = 6x - 2 = 4x[/tex]
Because the 4x it doesn't t affect the 6x and the 6x is
[tex]6 \times x[/tex]
So the result will be 4x
Answer:
-9x^2 + 16x - 4
Step-by-step explanation:
In the figure, PQ is parallel to RS. The length of RP is 5 cm; the length of PT is 30 cm; the length of QT is 60 cm. what is the length of SQ?
A. 10 cm
B. 2 cm
C. 6 cm
D. 20 cm
thank you!
Answer:
10 cm
Step-by-step explanation:
because RT = 35 and RS = 75 so ST = 70
The length of SQ is 10 cm.
Option A is the correct answer.
We have,
Two similar triangles.
ΔTPQ and ΔTRS
So,
TR/TP = TS/TQ
TR = (TP +PR)
TS = (TQ + QS)
Substituting.
TR/TP = TS/TQ
(TP + PR)/TP = (TQ + QS)/TQ
(30 + 5) / 30 = (60 + QS) / 60
35/30 = (60 + QS) / 60
7/6 = (60 + QS) / 60
7 = (60 + QS) / 10
70 = 60 + QS
QS = 70 - 60
QS = 10
Thus,
The length of SQ is 10.
Learn more about triangles here:
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what is the awnser i need to know and brainleist
Answer:
The answer would be D
Step-by-step explanation:
2.10 would be a little after 2.
Hoped this helped :)
Answer:
the answer is
Step-by-step explanation:
D
1
What is the measure of angle x?
64°
X
45
109
64
180
71
Answer:
A
Step-by-step explanation:
The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.
x is an exterior angle of the triangle, thus
x = 64° + 45° = 109° → A
Answer:
A
Step-by-step explanation:
64+45=109
180-109=71
180-71=109 *
*This step is only if you want to check your work!
Triangle FGH is graphed on the coordinate plane below.
On a coordinate plane, triangle F G H has points (negative 6, negative 8), (negative 2, negative 3), (negative 4, negative 2).
The figure is rotated 180° using the origin as the center of rotation. How do the coordinates of the vertices of the preimage compare to the coordinates of the vertices of the image?
(x, y) right-arrow (y, x)
(x, y) right-arrow (negative y, negative x)
(x, y) right-arrow (negative x, negative y)
(x, y) right-arrow (x, negative y)
Answer:
(x, y) right-arrow (negative x, negative y) ⇒ (x, y) → (-x, -y)
Step-by-step explanation:
Let us revise the rotation about the origin
If point (x, y) rotated about the origin by angle 90° counterclockwise (or 270° clockwise), then its image is (-y, x) . The rule is (x, y) → (-y, x)If point (x, y) rotated about the origin by angle 180° counterclockwise ( or 180° clockwise), then its image is (-x, -y) . The rule is (x, y) → (-x, -y)If point (x, y) rotated about the origin by angle 270° counterclockwise (90° clockwise), then its image is (y, -x) . The rule is (x, y) → (y, -x)Let us solve the question
∵ The vertices of triangle FGH are (-6, -8), (-2, -3), (-4, -2)
∵ The figure is rotated 180° using the origin as the center of rotation
→ By using the 2nd rule above
∴ The vertices of its image are (6, 8), (2, 3), (4, 2)
∴ The rule is (x, y) → (-x, -y)
The coordinates of the vertices of the preimage compare to the coordinates of the vertices of the image do (x, y) right-arrow (negative x, negative y) ⇒ (x, y) → (-x, -y)
Answer:
B. they over explaining
Step-by-step explanation:
Use the graph of the lines to determine if the two lines
are parallel.
units and right
Line MN was translated down
units to create line M'N'.
The slope of MN
The slope of M'N'
Answer:
(in order): 4, 8, -2, -2
Step-by-step explanation:
The slope of MN = -1.
The slope of M.N. = -1.
What is a slope?The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
Given information:
The two lines MN and M'N' are parallel.
Transformation rule:
Line MN was translated down to 4 units and right to 6 units to create line M'N'.
And line MN passes through two points (-2, 0) and (-6, 8).
Therefore, the slope of line MN,
= (8- 0)/(-6-2)
= -1
Since lines MN and M'N' are parallel, they have the same slope.
Therefore, the slope of M'N' is also -1.
To learn more about the slope;
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Can someone pleasee help I’ll mark brainlist!!!
Answer:4/C
Step-by-step explanation:
Answer:
2.4
It is the 1st one
Step-by-step explanation:
There are 60 min in 1 hour so divide 60/20min = 3
Then multiply 4/5*3 = 2.4
HOpe this helps
6(p+6)- (p-6) I need help anyone pls
Answer:
5p + 42
Step-by-step explanation:
Step 1: Write expression
6(p + 6) - (p - 6)
Step 2: Distribute
6p + 36 - p + 6
Step 3: Combine like terms
5p + 42
solve for x. 3x+2=38
The value of x by solving for x from 3x +2 = 38 is; 12.
According to the question;
We are required to solve for x from 3x+2=383x+2 = 383x = 38 - 23x = 36x = 12The value of x from the equation is; x = 12
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if the area of the rectangle is given by the polynomial 2x-7-15 what is the dimension of the rectangle in terms of x
Answer:
2-7x
Step-by-step explanation:
hope i helped gl <3Is Mabel correct?
A. Mabel is correct.
B. No, she made a mistake in step 2
C. No, she made a mistake in step 3
D. No, she made a mistake in step 4
Answer:
D. No, she made a mistake in step 4
Step-by-step explanation:
What is the value of -2/5 divided by 6/8 PLEASE HELPPP
Answer:
The steps to do :
[tex] - \frac{2}{5} \div \frac{6}{8} [/tex]
[tex] = - \frac{2}{5} \times \frac{8}{6} [/tex]
[tex] = - \frac{1}{5} \times \frac{8}{3} [/tex]
[tex] = - \frac{1 \times 8}{5 \times 3} [/tex]
[tex] = - \frac{8}{15} [/tex]
Express the fraction 11/30 in decmail form
Answer:
.36666667
Step-by-step explanation:
Are tools ‘required’ to make accurate and precise measurements?
What is 24.9% to a fraction in simplest form?
Answer:
The answer is 249/1000
Step-by-step explanation:
Need help ASAP, Tysm to anyone who responds!
Answer:
320
Step-by-step explanation:
2(-7)²-8(-7)(4)-√4=
98-(-224)-2=
98+224-2=
322-2=
320
Describe the transformation for the equaton below:
f(x) = 12 – 4 + 3
Answer:
f(x)=11
Step-by-step explanation:
f(x)=12-4+3
f(x)=8+3
f(x)=11
máximo comun divisor de 20 12 36
Answer:
El procedimiento para hallar el MCD de 12, 20, 36:Descomponer los números en su factores primos
12 2 6 2 3 3 1
20 2 10 2 5 5 1
36 2 18 2 9 3 3 31
Factores primos de 12 = 22 . 3
Factores primos de 20 = 22 . 5
Factores primos de 36 = 22.32
MCD = 21 = 2
Step-by-step explanation:
What is the measure of C?
Answer:C
Step-by-step explanation:
The angles must equal 180 degrees.
Answer:
I think the answer is b it looks like a equilateral triangle which means all sides are equal.
HELP IMMEDIATELY PLEASE, WILL GIVE BRAINLIEST!!!
Answer:
The slope is -1/3 I think.
Answer:
slope = 1/3
Step-by-step explanation:
We can look at the points where the graph exactly intersects a point. Those points are: (10, 50), (40, 60), and (70, 70). The slope is the difference of y divided by the difference of x. You can subtract any two points. Your final answer would be (70-60)/(70-40) = 10/30 = 1/3
Karen cut away 49 centimeters of rope. Before that, she had 807.49 centimeters of rope. How much rope does Karen have left?
Answer:
758.49 cm
Step-by-step explanation:
1. Subtract
8 0 7 . 4 9
4 9 . 0 0
7 5 8 . 4 9