Answer:
28
Step-by-step explanation:
Consider the expansion:
[tex]$(x+y)^2=\sum_{k=0}^{n} \binom{n}{k}y^{n-k}x^k$$[/tex]
[tex]$ \binom{n}{k}=\frac{n!}{(n-k)!k!}[/tex]
We have
[tex]$\left(x + y\right)^{8}=\sum_{k=0}^{8} \binom{8}{k} \left(y\right)^{8-k} \left(x\right)^k[/tex]
I'm sorry but I will not write and solve everything, typing LaTeX takes time. But that's the idea:
For [tex]k=0[/tex]
[tex]$\binom{8}{0} \left(y\right)^{8-0} \left(x\right)^{0}=\frac{8!}{(8-0)! 0!}\left(y\right)^{8} \left(x\right)^{0}=y^{8}[/tex]
For [tex]k=2[/tex]
[tex]$\binom{8}{2} \left(y\right)^{8-2} \left(x\right)^{2}=\frac{8!}{(8-2)! 2!}\left(y\right)^{6} \left(x\right)^{2}=28 x^{2} y^{6}[/tex]
[tex](x+y)^8={x}^{8} + 8{x}^{7}y + 28{x}^{6}{y}^{2} + 56{x}^{5}{y}^{3} + 70{x}^{4}{y}^{4} + 56{x}^{3}{y}^{5} + 28{x}^{2}{y}^{6} + 8x{y}^{7} + {y}^{8}[/tex]
Hi All,
I have some Maths Questions for you all to have a look at.
Please answer - I am giving 20 points!
I will mark Brainliest as well.
Take care,
Jake
Answer:
a) modal number of teachers in a car is 3
b) median number of teachers in a car is 3
c) mean number of teachers in a car is 2.5
Step-by-step explanation:
modal number is 3 because that is the highest frequency of numbers of carsmedian number is 3 because it is the middle number when you expand the frequency table.mean number is 2.5 because that is the approximate average of all the numbers.Can someone please answer b and c please thank you
Answer:
a: 1.8 b: 11.8 c: 23.6
Step-by-step explanation:
what is the volume of the cone below:
Answer:
D is the correct answer
Step-by-step explanation:
V=πr2h
3=π·52·12
3≈314.15927
Thank me later
Hope this helps!!!
On a coordinate plane, 2 triangles are shown. The first triangle has points A (negative 2, 1), C (negative 4, 1), and B (negative 3, 4). The second triangle has points A prime (1, negative 2), B prime (4, negative 3), and C prime (1, negative 4).
What is the rule for the reflection?
ry=x(x, y) → (–y, –x)
ry=–x(x, y) → (–y, –x)
ry=x(x, y) → (y, x)
ry=–x(x, y) → (y, x)
Answer:
R(y=x) = (x, y) → (y, x)
Step-by-step explanation:
The coordinates of A are (-2, 1).
The coordinates of A' are (1, -2).
Clearly, the values have been swapped in accordance with ...
(x, y) → (y, x)
This is the result of a reflection across the line y = x. Hence the rule and its name are ...
R(y=x) = (x, y) → (y, x)
Answer:
R(y=x) = (x, y) → (y, x)
Step-by-step explanation:
egd2020
What is the probability that this spinner lands on an even number? Select both the fraction and the percentage
1/2
30%
40%
3/10
50%
10%
4/10
1/10
Answer:
1/2 and 50%
Step-by-step explanation:
5/10 is equal to 1/2 and 50%
ANSWER QUICK PLEASE WILL MARK BRAINLIEST!!!!!!
Answer: A is correct
Step-by-step explanation:
They’re the only lines perfectly parallel, I got this correct
Answer:
A is the correct answer
Step-by-step explanation:
A spinner has four equal sections, with one letter from the word "MATH" in each section.
Type your response in each blank below.
1. You spin the spinner 20 times. About how many times do you expect it will land on A?
2. You spin the spinner 80 times. About how many times do you expect it will land on something other than A?
Explain your reasoning.
Answer:
1. 5 times
2. 60 times
Step-by-step explanation:
there is only one a so its 1/4 times 20 and 4 because that is the total
20/4= 5
there is 3 because there is letters that are not a
3/4 times 80
240/4
1. The number of times expected that should be landed on A should be 5 times.
2. The number of times expected should be 60 times.
Calculation of the number of times:1. Since A spinner has four equal sections, with one letter from the word "MATH" in each section.
So, here the number of times should be
= [tex]20\div 4[/tex]
= 5
2. The number of times should be
[tex]= 3/4 \times 80\\\\= 240\div 4[/tex]
= 60
Learn more about spinner here: https://brainly.com/question/9222927
f(0)=g(0)
f(-2)=g(-2)
f(0)=g(-2)
f(-2)=g(0)
Answer:
F(-2)=G(-2)
Step-by-step explanation:
Given: circle: k(O), m∠A = 101° m∠L = 79°, m LK = 122° Find: m AJ
Answer:
m arc AJ = 78°
Step-by-step explanation:
If angle A is 101° that means arc LKJ is 202° (the measure of an arc that an inscribed angle intercepts is twice the angle measure). If arc LKJ is 202° and arc LK is 122°, then arc KJ is 80° (m arc LK + m arc KJ = m arc LKJ).
If angle L is 79°, then the m arc AJK = 158° (the measure of an arc that an inscribed angle intercepts is twice the angle measure). If m arc AJK = 158° and m arc KJ is 80°, then the m arc AJ is 158 - 80 = 78º
edit: i think im right but im not completely sure
edit#2: i checked my answer portal after turning it in and yeah im right
What is the solution of 4−6x≥−8 A.) x≥2 B.) x≤23 C.) x≤2 D.) x≤−2
Answer: I cant tell which one is a or b or c or d but ill say its b
You have 180 feet of fence to make a rectangular pen. What are the
dimensions of the rectangle with the maximum area?(include explanation or step-by-step)
Answer:
45 x 45 = 2025
Step-by-step explanation:
What is the volume of the cup in gallons
which two functions are inverses of each other
Answer:
f(x) = 4x, g(x) = [tex]\frac{1}{4}x[/tex]
Step-by-step explanation:
Inverse function is when you switch the x and the y and solve for x
f(x) = 4x
y = 4x
x = 4y
Now solve for x
y = [tex]\frac{1}{4}x[/tex]
g(x) = [tex]\frac{1}{4}x[/tex]
If you try that with the other functions, none of them work.
Answer:
C. f(x)= 4x, g(x)= 1/4x
Step-by-step explanation:
inverse functions are flipping x and y corrdinates so let's plug in x=1 into f(x) and get y = 4
now plug in x = 4 into g(x) and check if the answer is 1 - yes ,it is!
Can someone please help me with this?
Answer:
The lenght is 8 cm
Step-by-step explanation:
Answer:
8 cm.
Step-by-step explanation:
The area of the square base = volume / height
= 960/15
= 64 cm^2.
So the length of each side of the square base = √64
= 8 cm.
Which of the following values of x is a solution to the equation 5(x-2)+7=37?
Answer:
x = 8
Step-by-step explanation:
5x - 10 + 7 = 37
5x - 3 = 37
5x = 40
x = 8
I dont know the question to this What is 6÷1/7
Answer:
42
Step-by-step explanation:
6÷(1/7) equals forty two.
Solution,
6/1/7
=6*7/1
=42
Hope it helps
Good luck on your assignment
If a boy 5 feet tall casts a shadow 14 feet long, what will be the length of the shadow of a tree that is 25 feet high?
Answer:
70 feet
Step-by-step explanation:
This problem can be answered by using proportions based on similar triangles.
Notice that a person and its shadow on the ground form a right angle (therefore they can be considered the two "legs" of a right angle triangle)
The same runs for the tree and its shadow.
Since the inclination of the rays of the sun are the same at the same time for both objects (the boy and the tree), their hypothenuses form the same angles with the ground and therefore belong to similar triangles.
We can create the following proportion to solve for the shadow of the tree (ST) using the information provided: the height of the boy (HB), the shadow of the boy (SB), and the height of the tree (HT)
[tex]\frac{SB}{HB} =\frac{ST}{HT}\\\frac{14}{5} =\frac{ST}{25}\\\frac{ST}{25}=\frac{14}{5} \\ST=\frac{14*25}{5}\\ST=70\,\,ft[/tex]
In the story “My Wonder Horse”, what key words and phrases does the author use to contrast the “legend” with the actual horse?
Answer:
what is the math?
Step-by-step explanation:
Segment AB falls on line 2x − 4y = 8. Segment CD falls on line 4x + 2y = 8. What is true about segments AB and CD?
They are perpendicular because they have the same slope of −2.
They are perpendicular because they have slopes that are opposite reciprocals of −2 and .
They are lines that lie exactly on top of one another because they have the same slope and the same y-intercept.
They are lines that lie exactly on top of one another because they have the same slope and a different y-intercept.
Answer:
They are perpendicular because they have slopes that are opposite reciprocals of −2 and .Step-by-step explanation:
The given lines are
[tex]2x-4y=8[/tex]
[tex]4x+2y=8[/tex]
Let's rewrite each equation in the form [tex]y=mx+b[/tex]
[tex]2x-4y=8\\2x-8=+4y\\y=\frac{2x-8}{4} \\y=\frac{x}{2}-2[/tex]
[tex]4x+2y=8\\2y=8-4x\\y=\frac{8-4x}{2}\\ y=4-2x[/tex]
Now, let's use the perpendicular rule
[tex]m_{1} \times m_{2} =-1\\\frac{1}{2} \times (-2)=-1 \implies -1=-1[/tex]
As you can observe, the slopes satisfy the perpendicular rule, that means the lines are perpendicular.
Therefore, the right answer is the second choice because it states the rule of perpendicularity between the given lines.
Answer:
They are perpendicular because they have slopes that are opposite reciprocals of −2 and .
Step-by-step explanation:
I took the test and the dot is 1/2
Help a homie w an extra chromi out
Answer:
(2a + 1)
----------------
(2 - a^2)
Step-by-step explanation:
(2 + 1/a)
----------------
(2/a - a)
Multiply by a/a
(2 + 1/a) *a
----------------
(2/a - a) *a
(2a + 1)
----------------
(2 - a^2)
PLS HURRY IM BEING TIMED!!! which graph shows a positive slope?
Answer:
The bottom left one
Step-by-step explanation:
it has a positive slope
Answer:
I’m pretty sure it’s the bottom left corner one
Step-by-step explanation:
The line increases from left to right, so it has a positive slope
(05.06)Which interval on the graph could be described as linear decreasing?
7.
6-
5-
D
B
4.
с
3
A
2.
13
А
ОА
Ов
Ос
OD
Oml fellow FLVS student here, it would be C.:)
Explanation: I got it right lol
In the given graph, interval C could be described as linear decreasing.
What is an interval?"An interval is a set of real numbers that contains all real numbers lying between any two numbers of the set."
In the given graph,
A is the interval(0, 2) where the graph is linear increasing.
B is the interval(2, 4) where the graph is constant.
C is the interval(4, 5) where the graph is linear decreasing.
D is the interval(5, 8) where the graph is linear increasing.
Therefore, the required interval is C.
Learn more about an interval here: https://brainly.com/question/1643786
#SPJ2
What is the volume of the following triangular prism?
5 cm
15 cm
4 cm
cubic centimeters. You must submit your neat and organized work once you have submitted the test.
Write only the number.
10 points need fast
Answer:
[tex]V=150cm^3[/tex]
Step-by-step explanation:
First we need to find area of the triangle with a base of 4 cm and a height of 5cm, and then multiply that by the length of the prism of 15cm.
The area of the triangle is given by the formula:
[tex]A_T=\frac{bh}{2}[/tex]
where b is the base: [tex]b=4cm[/tex] and h is the height: [tex]h=5cm[/tex]
thus, in this case we have:
[tex]A_T=\frac{(4cm)(5cm)}{2}\\ \\A_T=\frac{20cm^2}{2} \\\\A_T=10cm^2[/tex]
And now, the volume will be the area of the triangle multiplied by the length [tex]l=15cm[/tex] of the prism:
[tex]V=A_T*l[/tex]
Substituting the known values:
[tex]V=10cm^2*15cm\\V=150cm^3[/tex]
The volume in cubic centimeters is 150.
Please someone help me
Answer:
92.4 m^2
Step-by-step explanation:
Area of Trapezoid: h(b1+b2)/2
6.6 (14.2 + 7.6 + 6.2) / 2
= 6.6 (28) / 2
= 184.8/2
= 92.4 m^2
Write a specific formula to describe the variation:x varies indirectly with the cube root of y;x=3when y= 125
Answer:
x=15(1/3√y)
Step-by-step explanation:
X varies indirectly with the cube root of y
x=k/3√y
x=3 when y=125
3=k/3√125
3=k/5
3=k(1/5)
k=3÷1/5
k=3×5/1
k=15
x=15(1/3√y)
can someone help me please
Answer:
I THINK its D and E because C can simplify to 2/3 and 1/2 making C wrong.
Step-by-step explanation:
Answer:
B C
Step-by-step explanation:
Find the common denominators
For example: 1/3 [tex]\leq[/tex]4/12
It is 12
3 goes into 12 4 times
so now its
?/12[tex]\leq[/tex]4/12
4*1 is 4 so its
4/12[tex]\leq[/tex]4/12
solve for 5/8= x-1/9
Answer:
[tex] \dfrac{53}{8} [/tex]
Step-by-step explanation:
[tex] \dfrac{5}{8} = \dfrac{x - 1}{9} [/tex]
Cross multiply.
[tex]8(x - 1) = 9 \times 5[/tex]
[tex] 8x - 8 = 45 [/tex]
[tex] 8x = 53 [/tex]
[tex] x = \dfrac{53}{8} [/tex]
Answer: x = 53/8
Step-by-step explanation:
5/8 = x-1 / 9
45 = 8(x-1)
45 = 8x - 8
-8x = -8 - 45
x = 53/8
find points of discontinuity y=x-8/x^2+6x-7
Answer:
Step-by-step explanation:
You'll need to use parentheses here to remove ambiguity regarding what's in your denominators:
x - 8 x - 8
y = ------------------ = -----------------
x^2 + 6x - 7 (x + 7)(x - 1)
This last result becomes undefined at x = -7 and x = 1, and thus its graph is discontinuous at those x- values.
The points of discontinuity is x = -7, x = 1
Use parentheses to remove ambiguity considering the denominators
[tex]y=x-8/x^{2} +6x-7[/tex]
= x-8 ÷ (x+7)(x-1)
The result becomes undefined at x = -7
and x = 1,
thus its graph is discontinuous at those x values.
Therefore the points of discontinuity is x =-7 and x = 1.
Learn more about discontinuity points, refer:
https://brainly.com/question/9553665#SPJ2
2 Points
Which of the following appear in the diagram below?
Check all that apply.
Y
x
O A. _XYZ
OB. ZX
OC. YX
OD. _ZXY
SUBMI
Answer:
D and B
Step-by-step explanation:
hope this is correct!
The following appears in the diagram below are:
XZ and XY and ∠ZXY.
Options B, C, and D are the correct answer.
What is an angle?In mathematics and geometry, an angle is a measure of the amount of rotation or turn between two lines or line segments that meet at a common endpoint, called the vertex of the angle.
Angles are typically measured in degrees (°) or radians (rad).
A full rotation around a point is 360 degrees or 2π radians.
We have,
An angle is a measure of the amount of rotation or turn between two lines or line segments that meet at a common endpoint, called the vertex of the angle.
Arc length is the distance along the curve of a circle or any other curved shape. It is defined as the length of the portion of the circumference of a circle or a portion of a curve between two endpoints, measured along the arc of the curve.
From the diagram,
XZ and XY are arc lengths.
∠ZXY is an angle.
Thus,
The following appears in the diagram below are:
XZ and XY and ∠ZXY.
Learn more about angles here:
https://brainly.com/question/15277238
#SPJ7
1. A school has 400 students. They all come to school by bus, and each bus carries the same number of students. How many students might there be on each bus? PS the number of buses is 100
Answer:
4, I believe
Step-by-step explanation:
400 students
100 buses
400/100=4
Answer:
4
Step-by-step explanation:
There are 400 students, and 100 buses, so number of student in each bus= 400/100
= 4
