Answer:
[tex]\sum\limits_{i=1}^{n} c \cdot a_i \ is \ equal \ to \ c = \ c \cdot \sum\limits_{i=1}^{n} a_i[/tex]
[tex]\sum\limits_{i=1}^{n} i \ is \ equal \ to \ b = \dfrac{n \cdot (n + 1)}{2}[/tex]
[tex]\sum\limits_{i=1}^{n} c \ is \ equal \ to \ d = c \cdot n[/tex]
[tex]\sum\limits_{i=1}^{n} i^3 \ is \ equal \ to \ e = \left [ \dfrac{n \cdot (n + 1)}{2} \right]^2[/tex]
[tex]\sum\limits_{i=1}^{n} i^2 \ is \ equal \ to \ a = \dfrac{n \cdot (n + 1) \cdot (2 \cdot n + 1)}{6}[/tex]
Step-by-step explanation:
1) The sum of a series of the cubes of numbers 'i' is given as follows;
Sₙ = n/2 × (1st term + Last term)
∴ Sₙ = n/2 × (1 + n) = n·(n + 1)/2
It can be shown that the sum of a series of the cubes of numbers 'i²' is given as follows;
Sₙ = (n·(n + 1)·(2·n + 1))/6
It can be also be shown that the sum of a series of the cubes of numbers 'i³' is given as follows;
Sₙ = (n·(n + 1)/2)²
Therefore, we have;
[tex]\sum\limits_{i=1}^{n} c \cdot a_i= c \cdot \sum\limits_{i=1}^{n} a_i = c[/tex]
[tex]\sum\limits_{i=1}^{n} i = \dfrac{n \cdot (n + 1)}{2} = b[/tex]
[tex]\sum\limits_{i=1}^{n} c = c \cdot n = d[/tex]
[tex]\sum\limits_{i=1}^{n} i^3 = \left [ \dfrac{n \cdot (n + 1)}{2} \right]^2 = e[/tex]
[tex]\sum\limits_{i=1}^{n} i^2 = \dfrac{n \cdot (n + 1) \cdot (2 \cdot n + 1)}{6} = a[/tex].
Answer:
c, b, d, e, a
Step-by-step explanation:
Multiply polynomials #3
Multiplying the two together, you get an equation such as
-6x^4 - 12x^3 +33x^2 +12x -27.
Answer:
-6x^4-12x^3+33x^2+12x-27
Step-by-step explanation:
For which of the following is x = -5 a solution? Select all that apply.
Answer:
Options 2, 3, 4, 5 are the solutions.
Step-by-step explanation:
Option 1).
x + 10 = -5
x = -10 - 5
x = -15
Therefore, x = -5 is not the solution.
Option 2).
-x² + 50 = 25
-x² = 25 - 50
-x² = -25
x² = 25
x = ±5
Therefore, x = -5 is a solution
Option (3)
|2x| = 10
2x = ± 10
x = ± 5
Therefore, x = -5 is a solution.
Option (4)
x < 0
Since, -5 < 0
Therefore, x = -5 is a solution.
Option (5)
2x < 10
x < 5
Since, -5 < 5
Therefore, x = -5 is a solution.
Options 2, 3, 4, 5 are the solutions.
determine the equation that is represented by the table below. x 3 4 5 6 y -3 0 3 6 can some one answer please
Layla calculates the mean of the ages of 10 students on her bus, and she discovers the average(mean) age is 12.8. What will happen to the mean if she includes her bus driver's age of 56 in her data set? *
A.The mean will stay the same.
B.The mean will decrease.
C.The mean will increase.
D.There isn't enough information.
Answer:
The mean will increase
Step-by-step explanation:
I need help!! asap angles
Answer:
i do not know
Step-by-step explanation:
ummmmmmmmm x = well you see you have to solve for x mmmmmm hhhhhhmmmmm yup
I hope the answer is helpful
Heya!
[tex] \underline{ \underline{ \bf{Question}}}: [/tex] In the given figure , ABC is a triangle in which AB = AC. Also a circle passing through B and C intersects the sides AB and AC at the points D and E respectively. Prove that AD = AE.
~Thanks in advance! :)
Answer:
See Below.
Step-by-step explanation:
We are given that ABC is a triangle in which AB = AC.
A circle passing through B and C also intersects the sides AB and AC at points D and E respectively.
And we want to prove that AD = AE.
By the secant-secant theorem (shown below), we know that:
[tex]AD(AB)=AE(AC)[/tex]
We are given that AB = AC. So, by substitution:
[tex]AD(AB)=AE(AB)[/tex]
And by dividing both sides by AB (AB ≠ 0), we acquire:
[tex]AD=AE[/tex]
Q.E.D.
Jason is installing new carpet In a room. The dimensions of the room are shown in the diagram.
12 ft
20 ft
30 ft
20 ft
10 ft
32 ft
What is the area of the floor?
Answer:
46080000
I think you didnt give the dimensions right so I had to get them
∠C and \angle{D}∠D are vertical angles. If the m\angle{C} m∠C=66o, then what is the m\angle{D} m∠D ?
Answer:
The measure of angle D is of 66º.
Step-by-step explanation:
Vertical Angles:
If two angles are vertical, they have the same measure.
In this question:
Angles C and D are vertical.
Angle C measures 66º.
So the measure of angle D is of 66º.
What is the missing value in the proportion 5/8 = k/16?
5/8 = 10/16
The missing value is: 10
Please help answer these, thank you
Completing the square Acellus please help! x^2 + 10x -y + 15 = 0
Thank you!!
Step-by-step explanation:
y-15=x^2+10x
y-15+25=x^2+10x+25
y+10=(x+5)^2
Kelly bought three watermelons for the class picnic. The watermelons weighed 124 pounds, 13 pounds, and 15 pounds.
What is the total weight of the watermelons?
Answer:
40/10
Step-by-step explanation:
Lol help now files just type it
Answer:
2 = 4/2
Step-by-step explanation:
Well the one for the 2 wholes, Since 2 wholes equal 4/2
because 4/2 simplified is 2 whole it I believe would be 4/2
Answer:4/2,5/2
Step-by-step explanation:
I believe that 4,2 because it's going in order and 4/2= 2 which is shown below. And 5,2 because 5/2=2.5 which is half of 2 and 3.
I need emergency help if you help I’ll be soo happy :) plsss
Answer:
900 square feet :)
Step-by-step explanation:
plz give brainliest
Please help I really need help
Answer:
-23
Step-by-step explanation:
16 x 1/4^2 - 4 x 6 = -23
My brain refuses to work because I can only think of Diagon Alley
Answer:
30 cm
Step-by-step explanation:
1. Given the length, width and tallness discover the volume, surface region and inclining of a rectangular crystal
h, l and w are known; discover V, S and d
V = lwh
S = 2(lw + lh + wh)
d = √(l2 + w2 + h2)
2. Given the surface region, length and width discover the tallness, volume and askew of a rectangular crystal
S, l and w are known; discover h, V and d
h = (S - 2lw)/(2l + 2w)
V = lwh
d = √(l2 + w2 + h2)
3. Given the volume, length and width discover the stature, surface territory, and slanting of a rectangular crystal
V, l and w are known; discover h, S and d
h = V/lw
S = 2(lw + lh + wh)
d = √(l2 + w2 + h2)
4. Given the inclining, length and width discover the tallness, volume and surface space of a rectangular crystal
d, l and w are known; discover h, V and S
h = √(d2 - l2 - w2)
V = lwh
S = 2(lw + lh + wh)
please help meeeeee! pleaseeeee
Answer:
905in²
Step-by-step explanation:
How many 2-liter bottles of soda will you need to fill ten 500 milliliter containers?
Answer:
2.5 bottles
Step-by-step explanation:
10 * 500 ml = 5000 ml
5000 ml = 5 l
5/2 = 2.5
2-liter bottles of soda will need 2.5 bottles to fill ten 500 milliliter containers.
How many milliliters in 1 liter?A liter is a cubic meter unit of volume which is equal to 1000 cubic centimeters.
1 liter = 1000 milliliters
Ten 500 milliliter containers
10 × 500 ml = 5000 ml
5000 ml = 5 l
2-liter bottles of soda will you need
5/2 = 2.5bottles
Therefore, 2-liter bottles of soda will need 2.5 bottles to fill ten 500 milliliter containers.
Learn more about liter;
https://brainly.com/question/2882095
(-4)^6 (-4)^5 into a single power
[tex] \huge { - 4}^{11} [/tex]
Simplify the expression by combining like terms: 4x - 2 - 8x + 1
Answer:
-4x-1
Step-by-step explanation:
combine 4x and -8x to make -4x and combine -2 and 1 to make -1
What is the vertex of the parabola f(x) = x^2 – 2x – 8 that has an axis of symmetry at 2 = 12
A (2,-8)
B (1,-9)
C (3,-5)
D (4,0)
Answer: i am pretty sure it is c
OR A
NOT SURE THOUGH trust ur gut
Step-by-step explanation:
Find the volume of the figure please.
Answer:
volume=90 sq m
Step-by-step explanation:
v=Ab×h
v=1/2(10)(3.6)×5
v=90 sq
hope it helps
3/4x8/9 as simpiest form
Answer:
2/3
Step-by-step explanation:
3/4 x 8/9 = 24/36 or 2/3 simplified
Please help with Volume
Given:
Length of the cuboid tank = 4 m
Breadth = 2.5 m
Height = 2.4 m
One third of the tank is filled with water.
1 cubic meter = 1000 liters.
To find:
The quantity of the water in the tank.
Solution:
Volume of a cuboid is:
[tex]V=l\times b\times h[/tex]
Where, l is length, b is breadth and h is the height.
The volume of the tank is :
[tex]V=4\times 2.5\times 2.4[/tex]
[tex]V=24[/tex]
Volume of tank is 24 cubic meter.
One third of the tank is filled with water. So, the volume of the water is
[tex]\dfrac{24}{3}=8[/tex]
The volume of water is 8 cubic meters.
We have,
1 cubic meter = 1000 liters.
8 cubic meter = 8000 liters.
Therefore, the quantity of the water in the tank is 8000 liters.
What is the one shape of cross-section we could create by slicing the cone parallel to its base?
Answer:
Circle
Step-by-step explanation:
A cross section of a cone sliced parallel to iits bases is a circle and a rectangle when sliced perpendicular to its bases.
Answer:
its a circle
Step-by-step explanation:
got this from Khan and micaelaamisial :)
Please help me complete this. And please do not guess
Answer the following questions:
1. Find the scale factor of ABCDE to VWXYZ.
2. Find the scale factor of VWXYZ to ABCDE.
3. Find the value of r.
4. Find the value of s.
5. Find the value of t.
6. Find the value of u.
7. Find the perimeter of ABCDE.
8. Find the perimeter of VWXYZ.
9. Find the ratio of the perimeter ABCDE to the perimeter of VWXYZ.
Answer:
1. 1/3
2. 3
3. 9
4. 13.5
5. 7
6. 5
7. 23.5
8. 70.5
9. 1:3
Evaluate -2(|2|-(-3)(-4))
The cost of 6 CDs are $12, $13, $20, $20, $12.50 and $18.50. What is the median?
Sarah is finding the surface area of a cube. Find the surface area of the cube with dimensions of 8 cm each
Answer:
384 cm^2
Step-by-step explanation:
A = 6a^2 (a = side length)
A = 6(8^2)
A = 6(64)
A = 384 cm^2
More explain stuff:
a^2 is what is used to find the area of a 2 dimensional square. You can also use a · a. Remember, a = side length. Since there are 6 sides/faces in a cube, you multiply the area of each face by 6. :D
Please helpp ASAP
Extra 100 point and brainleist
Answer:
Ive done those before the first one is 7 and the second one is 4
Step-by-step explanation: