Geometric summations and their variations often occur because of the nature of recursion. The sum of the series i=0 to n-1 (2^i) is 2^n - 1.
The sum of the geometric series i=0 to n-1 (2^i) can be expressed as:
2^n - 1
Therefore, the simple expression for the sum i=0 to n-1 (2^i) is 2^n - 1.
To derive this expression, we can use the formula for the sum of a geometric series:
S = a(1 - r^n) / (1 - r)
In this case, a = 2^0 = 1 (the first term in the series), r = 2 (the common ratio), and n = number of terms in the series (which is n in this case). Substituting these values into the formula, we get:
S = 2^0 * (1 - 2^n) / (1 - 2)
Simplifying, we get:
S = (1 - 2^n) / (-1)
S = 2^n - 1
Therefore, the sum of the series i=0 to n-1 (2^i) is 2^n - 1.
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Choose SSS, SAS, or AA to prove
the triangles are similar.
A. SSS
B. SAS
C. AA
Choose SSS, SAS, or AA to prove the triangles are similar.
A. SSS
B. SAS
C. AA
Answer :As, all sides are given so we can use SSS to prove the triangles are similar.
So, correct option is A.
Explanation :Given : Sides of 1st triangle = 24, 32 and 40Sides of 2nd triangle = 27, 36 and 45To Prove :Triangles are similarProof :As, all three sides are given so let's check ratio of all three sides.
1. [tex] \tt \cancel{\dfrac{24}{27}} = \dfrac{8}{9}[/tex]
2. [tex] \tt \cancel{\dfrac{32}{36}} = \dfrac{8}{9}[/tex]
3. [tex] \tt \cancel{\dfrac{40}{45}} = \dfrac{8}{9}[/tex]
As, all sides are in equal ratio.
So, by SSS
∆1 ~ ∆2
Simplify.
6⁴
౼
6²
simplify that
Answer:
6⁴/4²
Since, a^m/a^n = a^m-n
→ 6^4-2
→ 6^2
→ 6*6 = 36 Ans.
The question is in the picture
Answer:
(8, - 7)
Step-by-step explanation:
Since, (8, 7) is reflecting over x-axis, so after reflection, x- coordinate will remain same and y-coordinate changes from 7 to -7.
Therefore,
[tex] J(8,\: 7) \rightarrow J'(8,\: - 7)[/tex]
Answer:
-8,7 is the ans of the question
558 cups of water fill 412 identical water bottles. How many cups fill each bottle ?
Answer:
5/4 cups fill each bottle
Step-by-step explanation:
5 5/8=45/8
4 1/2=9/2
Step by Step:
------------------
(45/8)/(9/2)
(45/8)(2/9)
(45/4)(1/9)
45/36
5/4
Número de departamento vendidos en un edificio cualitativa o cuantitativa.
Answer:The nucleus / large central vacuole contains
genetic material of a eukaryotic cell.
Step-by-step explanation:The nucleus / large central vacuole contains
Find the midpoint of the line segment from (4,5) to (-4,4)
9514 1404 393
Answer:
(0, 4.5)
Step-by-step explanation:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
((4, 5) +(-4, 4))/2 = (4-4, 5+4)/2 = (0, 9)/2 = (0, 4.5)\
The midpoint is (0, 4.5).
Cool down tickets, a school is holding a carnival and hopes to raise $500. Child tickets cost $3 and adult tickets cost $5. If the school sells x child tickets and y adults, then the equation 3x + 5y=500 expresses the fact that school raised exactly $500 from ticket sales. Solve thevequation for x. 2. Explain whenot might be helpful to resrite the equation this way.
Answer:
x = 1/3(500 + 5y)
Step-by-step explanation:
Given that:
x child tickets for $3
y adult tickets for $5
3x + 5y = 500
To solve for x
3x = 500 + 5y
Divide through by 3
3x /3 = 500/3 + 5y/3
x = 1/3(500) + 1/3(5y)
x = 1/3(500 + 5y)
2.)
If the total number of tickets sold was made available, then a more direct solution would have been obtainable as we can have two different equations;
One for the total number of ticket sales and the other of the total revenue from ticket sales.
Write the equation of the line that passes through the points (1,4) and (1,-3).
y = -7x+11
X=1
y = 7x - 3
Select the correct answer.
Identify the vertex of the function graphed below.
A.
(0,-2)
B.
(3,1)
C.
(1,1)
D.
(2,2)
Answer:
I think the answer is B
Step-by-step explanation:
Answer:
think it d
Step-by-step explanation:
because when i pick (3,1) it was wrong so that why it think it D
Find the equation of the line which passes through (0,8) and (1,12)
Answer:y =4x + 8
Step-by-step explanation:
X-0/0-1 = y-8/8-12
Or,-4x = -y +8
So, y-4x = 8
Zoltan read 15 pages of his book in 6 minutes. At this rate, how many pages can he read in 10 minutes?
Answer:
25 pages in 10 minutes.
help????????????????????
Answer:
x=11
Step-by-step explanation:
12x+2 and 2x+112 are opposite exterior angles so they are congruent
Answer:
x=11
Step-by-step explanation:
12x + 2 and 2x + 112 are vertical angles meaning that they are equal to each other so we set up an equation that says 12x + 2 = 2x + 112 and solve for x
12x+2=2x+112
step one subtract 2 from each side
12x=2x+112
step 2 subtract 2x From each side
10x=110
step three divide each side by 10
x=11
Here is an inequality: -x > 18. List some values for x that would make this inequality true.
Answer:
some examples x could equal:
x = -19
x = -20
x = -50
x = -100
so on
Step-by-step explanation:
remember negative x negative = positive
so any negative value beneath -18 will satisfy this because it will turn positive when multiplied by that outer minus sign.
hope this helped
Solve each inequality for the variable. Show your work. 3x-7>4x+2
Step-by-step explanation:
3x-4x>2+7
-x>9
x>-9
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Help please I have to submit it pretty soon.
help
3 − 4 + 16 − 10 + 2=
Step-by-step explanation:
3 - 4 + 16 - 10 + 2
= 7
hope it helps :)
Step-by-step explanation:
3 − 4 + 16 − 10 + 2 [B.O.D.M.A.S rule] (First addition)
= 3 + 16 + 2 - 4 -10
= 21 - 14. (Then subtraction)
= 7 (Ans)
In an inverse variation, x = -6 when y = -1/2. What is the value of y when x = 4?
Answer:
[tex]9 \frac{1}{2} [/tex]
Step-by-step explanation:
just add 5.5 to each number and make it in fraction
hop it helps you
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Giselle's as a wallet containing four $5 bills, five $10 bills and three $20 bills. She pulls out two bills, one at a time without the first bill being returned to the wallet. Find the probability that both bills that she pulls out will be $5 bills.
Answer:
the answer is 4/12
Step-by-step explanation:
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Answer:
[tex]\frac{81}{m^7}[/tex]
Step-by-step explanation:
We have a certain expression and are asked to find its equivalent with the answers provided :
[tex](3m^{-4} )^3(3m^5)[/tex]
Remove the parenthesis around 3m^5 :
[tex](3m^{-4} )^3*3m^5[/tex]
Do the exponent rule for outside and inside exponent parenthesis :
[tex](3m^{-4*3} )[/tex]
[tex]3^3m^{-12} *3m^5[/tex]
Apply addition exponent rule :
[tex]m^{-12} *3^{3+1} m^5[/tex]
Add :
[tex]m^{-12} *3^4m^5[/tex]
Apply the addition rule for -12 + 5 :
[tex]3^{4} m^{-7}[/tex]
Apply negative exponent rule for m^-7 :
[tex]3^4*\frac{1}{m^7}[/tex]
Multiply the fractions :
[tex]\frac{1*3^4}{m^7}[/tex]
[tex]\frac{81}{m^7}[/tex]
Every time Kristina bakes a batch of brownies, she uses 1/8
a cup of chocolate. If she has 3/4
cup(s) of chocolate remaining, how many batches of brownies can Kristina make?
Answer:
6 batches
Step-by-step explanation:
3/4 divided by 1/8 = 6/8 divided by 1/8 = 6 batches
-2(6) + 3(5 – 4· 2)
Answer:
-21
Step-by-step explanation:
Write the expanded form of the expression.
y(0.25 +5)
y(0.25 + 5) =
The expanded form of the expression y(0.25 +5) is 0.25y + 5y.
What are GCF and distributive property?The GCF of two or more than two numbers is the highest number that divides the given two numbers completely.
We also know that distributive property states a(b + c) = ab + ac.
Expanded form or Distributive properties are the same in mathematics.
Given, An expression y(0.25 + 5).
So, applying distributive property a(b + c) = ab + ac to y(0.25 + 5) we have
0.25y + 5y.
= 5.25y.
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Can someone help me on this is for today pls!!!
Answer:
C
Step-by-step explanation:
The answer must be in square inches, not inches, so a and b are automatically wrong.
Couple of ways of doing it - the large triangles are congruent, so the area of each is the same. Since the area of a triangle is 1/2 base times height, the area of the 2 large triangles is just base times height, which is 18 * 11 or 198
Same principle for the smaller triangles at the top, area is 8 times 11, or 88. Add them up, you get 286 sq inches.
Help me PLEASE! I will give Brainliest to the first correct answer.
Jada’s dog was 5 and 1/2 inches tall when it was a puppy. Now her dog is 14 and 1/2 inches taller than that. How tall is Jada’s dog now?
Answer:
20 inches tall
Step-by-step explanation:
First, I did 1/2+1/2=1. Then, I did 5+14=19. So, 19+1=20.
At a certain store a half gallon jug of milk cost 2.95 and a gallon jug of milk costs 5.95. Which milk has cheaper price?
Answer:
The first milk
Step-by-step explanation:
2.95 × 2 = 5.90
The first milk has cheaper price.
Mrs. Corbett signed 1/2 of all the holiday cards and Mr. Corbett signed 3/8 of all of them. Mrs. Smith will sign the rest of them. If there were 32 cards in all, how many are left to be signed by Mrs. Smith?
Answer:
4 cards
Step-by-step explanation:
1. Approach
First, find how much ([tex]\frac{1}{2}[/tex]) of all the holiday cards is. Then find out how much [tex]\frac{3}{8}[/tex] of all the cards is. After doing so, subtract both amounts from the total number of holiday cards.
2. Find out how many were signed
To find out how much a fraction of a certain value is, multiply the fraction by the value.
[tex]32*\frac{1}{2}=16\\\\32*\frac{3}{8}=12[/tex]
3. Find out how many were left
Now subtract the number of signed cards from the total number of cards.
[tex]32 -( 16 + 12)\\\\= 32 - 16 - 12\\\\= 16 - 12\\\\= 4[/tex]
pls help me plssssss
Answer:
1
Step-by-step explanation:
It's the correct spelling.
WILL GIVE BRAINLIEST!!!!!!!
2(x+1)^2=12
Answer:
Step-by-step explanation:
Find the value of x in the following figure.
Answer:
x = 8
Step-by-step explanation:
180-(89+57)= 180-146 = 34
(5x -6) = 34
5x = 34 + 6
5x = 40
x = 40 ÷ 5
x = 8
Whos HAPPYYYYY today
Answer:
meeeeeeeeeeee super happy