Answers
[tex]\\ \sf\longmapsto a+\dfrac{1}{a}=\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto \left(a+\dfrac{1}{a}\right)^3=\sqrt{3}^3[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}+\dfrac{3a^2}{a}+\dfrac{3a}{a^2}=3\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}+3a+\dfrac{3}{a}=3\sqrt{3}[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=3\sqrt{3}-3a-\dfrac{3}{a}[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=3\left(\sqrt{3}-a-\dfrac{1}{a}\right)[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=3(0)[/tex]
[tex]\\ \sf\longmapsto a^3+\dfrac{1}{a^3}=0[/tex]
ProvedAnswer:
Tn=a+(n−1)d, where a= First term, d= Difference between terms ... (2)
Equating (1) and (2)
6n+5=a+(n−1)d
6n+5=a+nd−d ..... (3)
Equating n terms:6n=nd
d=6 ...... (4)
Substituting (4) in (3)
6n+5=a+6n−6
5=a−6
a=11 ..... (5)
Now
Sn=2n(2a+(n−1)d)
Sn=2n(a+Tn) ....... (6)
Substituting (1) and (5) in (6)
Sn=2n(11+6n+5)
Sn=2n(16+6n)
Sn=n(8+3n)
Tn=a+(n−1)d, where a= First term, d= Difference between terms ... (2)
Equating (1) and (2)
6n+5=a+(n−1)d
6n+5=a+nd−d ..... (3)
Equating n terms:6n=nd
d=6 ...... (4)
Substituting (4) in (3)
6n+5=a+6n−6
5=a−6
a=11 ..... (5)
Now
Sn=2n(2a+(n−1)d)
Sn=2n(a+Tn) ....... (6)
Substituting (1) and (5) in (6)
Sn=2n(11+6n+5)
Sn=2n(16+6n)
Sn=n(8+3n)
Tn=a+(n−1)d, where a= First term, d= Difference between terms ... (2)
Equating (1) and (2)
6n+5=a+(n−1)d
6n+5=a+nd−d ..... (3)
Equating n terms:6n=nd
d=6 ...... (4)
Substituting (4) in (3)
6n+5=a+6n−6
5=a−6
a=11 ..... (5)
Now
Sn=2n(2a+(n−1)d)
Sn=2n(a+Tn) ....... (6)
Substituting (1) and (5) in (6)
Sn=2n(11+6n+5)
Sn=2n(16+6n)
Sn=n(8+3n)
Related Questions
WORTH 50 POINTS HELP ASAP WILL GIVE BRAINLIEST!
The price of a new pair of shoes is $52.00. If you order them directly from the company on the internet, you can save money and the price is only $42.64. What is the percent change?
18% decrease
22% decrease
18% increase
22% increase
Answers
18% decrease
Hope this helped you-have a good day bro cya)
Answer:
The percent change is an 18% decrease.
Step-by-step explanation:
only 23 please. And you can get 50 points
Answers
Step-by-step explanation:
Having built a graph, we can immediately understand that this is a linear functiony=kx+bHaving built a graph, we can immediately understand that this is a linear functiony=kx+bIn order to determine which rule the function follows, it is only enough for us to know the coordinates of only two points, let them be points (-3 ; 8 ) and (-2 ; 3 ) Substitute the values of x and y into an unknown function y=kx+b [tex]\displaystyle \large \boldsymbol {} \left \{ {{-3k+b=8} \atop {-2k+b=3 }} \right.=> -k=5=>k=-5 \ \ ; \ \ b=3+2k=-7[/tex]Then we get the function :
[tex]\large \boldsymbol {} \displaystyle y=-5x-7[/tex] The graph in attached file
[tex]\large \boldsymbol{}[/tex]
what is the standard form of of a line with a slope of -3/2 that passes through the point (4,-1)
Answers
Answer:
y=[tex]-\frac{3}{2}x-5[/tex]
Step-by-step explanation:
Use the point slope formula
[tex]y-y_1=m(x-x_1)[/tex]
y-1=[tex]-\frac{3}{2}[/tex](x-4)
Multiply -3/2 by (x-4) which equals -3/2x-6
Move the 1 by adding to both sides
The gives us y=[tex]-\frac{3}{2}x-5[/tex]
Barty is going to flip a coin three times. What is the probability that he will see at least
two tails? Can you use a Probability Area Model for this situation?
Answers
Answer:
1/2
Step-by-step explanation:
For three coin tosses, the posible outcomes are:
[(HHH), (HHT), ( THH), (HTH), ( THT), (TTH), (HTT), (TTT)
The outcomes where there are at least 2 tails are:
(TTT), (TTH), (THT), (HTT)
So, the probability that the coin will land tails at least 2 times is 4/8 or 1/2
2. On the graph below you will find two different triangles, and three points identified along the line.
(a) Identify the coordinates of Point A, B, & C? Explain.
(b) Does each triangle have the same change in x-values? Explain.
(c) Does each triangle have the same change in y-values? Explain.
(d) Does each triangle have the same ratio of change in y-values over change in x-values? Explain.
Answers
#a
Co-ordinates are
A(0,0)B(3,3)C(9,6)#b
No,Both triangles are congruent not same.
#c
No! Both triangles are not same#d
Yes ratio is same as they are congruent
Answer:
Question A:
A.) (0,0)
B.) (3,3)
C.) (9,6)
Question B:
No, both triangles are congruent, not the same change in x-values.
Question C:
No, both triangles do not have are not the same change in y-values.
Question D:
Yes, their ratios of change are the same.
the sum of the reciprocals of two consecutive integers is -11/30
Answers
1 pint=how many cups
Answers
Answer:
2
Step-by-step explanation:
.
cho khối chóp có diện tích đáy B=3 và chiều cao h=4. Thể tích của khối chóp đã cho bằng
A.6
B.12
C.36
D.4
Answers
Answer:
D. 4
Step-by-step explanation:
[tex]V =\frac{1}{3}Bh=\frac{1}{3}.3.4=4[/tex]
plsss help urgent !
Answers
can someone give me a full explanation on how to do this? thank you have a great day !
Answers
Answer:
Exact area = 1800 - 450pi square cm
Approximate area = 387 square cm
I used 3.14 for pi to get the approximate value.
============================================================
Explanation:
Check out the diagram below.
As the diagram shows, the largest radius possible is half of the shortest dimension of this rectangle. So the radius of each identical circle is 30/2 = 15 cm. The radius cannot exceed this value, or else the circle will spill outside the rectangle.
The area of one circle would be
A = pi*r^2
A = pi*15^2
A = pi*225
A = 225pi
Two identical circles like this combine to a total area of 2A = 2*225pi = 450pi square cm.
The area of the brown shaded region in the figure, aka the amount of cardboard leftover, is exactly 1800 - 450pi. The 1800 is from the computation of 60*30 = 1800, which is the area of the original rectangle before we made any cuts.
If we wanted to find the approximate area, then we could use pi = 3.14 to get
1800 - 450pi = 1800 - 450*3.14 = 387
The approximate area remaining is 387 square cm. This value is approximate because pi = 3.14 is approximate. If you were to use more decimal digits of pi, then you'd get some other approximate area.
solve the equation: -2(n+3)=13
Answers
Answer:
n is -9.5 ....hyuibgtyujhff
Answer for number 1?
Answers
Answer:
you need to draw a triangle on the grid
Step-by-step explanation:
find point -3 then 7
then find points -2 and 1
then -5 and 2
then join the points together
hope that helps
pls mark brainliest
drake is making capes he used 1/3 yard of fabric for each cape he makes what is the total amount of fabric drake needs to make 96 capes FOR 100
Answers
Someone plz help URGENTLY will mark brainliest plz no links or will be reported
Answers
Step-by-step explanation:
Given the function, f(x) = -3x + 4, you basically need to choose any input (x-value) and substitute those values into the function.
f(0) = -3x + 4, where the input is x = 0.f(0) = -3(0) + 4
f(0) = 0 + 4
f(0) = 4 [this is the value of your final column, in the f(x)].
2. f( 1 ) = -3( 1 ) + 4, where the input is x = 1.
f( 1 ) = -3( 1 ) + 4
f( 1 ) = -3 + 4
f( 1 ) = 1 [this is the value of your final column, in the f(x)].
3. f(2) = -3(2) + 4, where the input is x = 2.
f(2) = -6 + 4
f(2) = -2 [this is the value of your final column, in the f(x)].
All you need to do is plot the following points on your graph:
{(0, 4), (1, 1), (2, -2)}
Use the graph of the quadratic function, g(x), to answer each question.
Answers
Answer:
it is -3 8 and 2
Step-by-step explanation:
Answer:
i think its -3 8 and 2 (maybe)
Step-by-step explanation:
i asked my friend
Classify the following triangle. Check all that apply
Answers
Answer:
A. Acute and B. Equilateral
Step-by-step explanation:
help please and thank youu
Answers
Answer:
5
Step-by-step explanation:
f(x) just means y
find the spot on the line that hits y at 7.
then look directly down to the x line to see that the intersection is (5,7)
Tom is deciding whether or not he should become a member gym to use their basketball courts. The membership cost is $135. Members pay $2 to rent out the basketball courts. Non-members can rent the court also, but they have to pay $11 each time. how many times would Tom need to rent the court in order for it be cheaper to be a member than a non member?
Answers
Answer:
16 times
Step-by-step explanation:
Membership cost:
C = 135 + 2x
Non-members:
C = 11x
____
135 + 2x = 11x
135 = 9x
x = 15
The cost would be the same after renting 15 times, so after 16 times the cost would be cheaper for a member.
WILL NAME brainliest
Answers
Answer:
[tex]x=13[/tex]
Step-by-step explanation:
By the definition of an angle bisector, we have that [tex]8x-23=5x+16[/tex].
We can add [tex]23[/tex] to both sides to get [tex]8x=5x+39[/tex].
We can then subtract [tex]5x[/tex] from both sides to get [tex]3x=39[/tex].
We can finally divide both sides by [tex]3[/tex] to get [tex]\boxed{x=13}[/tex]
A class contributed $19.00 in quarters and dimes to a local homeless shelter. In
all there were 100 coins. How many were there of each kind.
Answers
Answer: 60 quarters and 40 dimes
Step-by-step explanation:
Step 1: Setup Coin Value and Coin Total Equation:
Coin Value Equation → 0.1d + 0.25q = $19.00 where d = dimes and q = quarters
Coin Total Equation → d + q = 100
Step 2: Rearrange Coin Total Equation in terms of dimes (d)
d = 100 - q ← Revised Coin Total Equation
Step 3: Plug in our Revised Coin Total Equation for d into our Coin Value Equation:
0.1(100 - q) + 0.25q = $19.00
0.1(100) - 0.1(q) + 0.25q = $19.00
10 - 0.1q + 0.25q = $19.00
10 + (0.25 - 0.1)q = $19.00
10 + 0.15q = $19.00
Step 4: Subtract 10 from each side of the equation to isolate q
10 - 10 + 0.15q = $19.00 - 10
0.15q = 9
Step 5: Divide each side of the equation by 0.15 to isolate q
0.15q/0.15 = 9/0.15
q = 60
Step 6: Using our value for q, Solve for d using our Coin Total Equation:
d + 60 = 100
Subtracting 60 from both sides, we get d + 60 - 60 = 100 - 60
d = 40
Summarizing our word problem, we see that 60 quarters and 40 dimes add up to $19.00
Algebra 2 Piece-wise functions!!
Answers
It's A.
1. The closed circle connects to the x≥1 function, so that rules out B and C.
2. The x≥1 piece has a positive slope on the graph, so that rules out D.
PLEASE HELP THIS IS FOR A TEST I AM TAKING RN AND MY TEACHER DOESN'T TEACH US AT ALL!!!
You are a graphic artist. You are given an image that is 1.2 inches tall and 2.1 inches wide. Your customer wants the image enlarged to create a banner 7 feet wide. Calculate how tall your banner should be to create a proportional image. Remember to include correct units in your answer!
Answers
Height / Width = 1.2in / 2.1in
Height / Width x / 84in (7feet)
Solve for X using cross multiplation
2.1x = 1.2 * 84
2.1x = 100.8
x (height) = 48 inches or 4 feet.
J=b-q/g solve for b.
Answers
Answer:
[tex]j = b - \frac{q}{g} \\ j + \frac{q}{g } = b \\ b = \frac{gj + q}{g} \\ thank \: you[/tex]
could someone name some games that are unblocked that I can play on a school computer?
lol 50 pts to answer
Answers
Answer:
Agar.io
Buildroyale.io
Gats.io
Krunker.io
Narwhale.io
1v1.lol
1v1.fail
Or look up your favorite computer games but put (Gooogle Sites) at the end
Step-by-step explanation:
what is (4x+1)(2x-1)
Answers
–112.84 – 54.14 – (–29.18)
Answers
Answer:
-137.8
Step-by-step explanation:
Helppppp plzzzzzzzzzzz
Answers
Look at the end number of computers, which is 40 right?
So with the total number of 40, you will simply subtract 10 and 5, to get the missing number.
Which is 40-10-5= 25
Then for printers you would do, 8-2= 6
Then by filling in the first blank you can move into the second blank by adding up all the three numbers you now have,
8+2+6= 16
how much 14 do u need to make 100
Answers
Answer:
You cant
Step-by-step explanation:
To make 100, you cant have a solid number of 14's to make 100. The closest to 100 is 14 * 7.
Atul, Bryony and Charlotte share an amount of money in the ratio 4:11:10
What fraction of the money does Bryony get?
Answers
4 + 11 + 10 = 25.
Assuming Bryony is the middle number, she gets 11/25 fraction of the money.
simplify -1 1/2 divided by 1 2/3
Answers
Answer:
-5/2
Step-by-step explanation:
Or -2.5
If you divide a negative by a positive it becomes a negative.
Hope this helps any!